OpenLLM-France/wikimedia huggingface dataset:
# Quantum Mechanics/Time Independent Schrödinger

Consider a particle confined to a one-dimensional box with impenetrable walls. When you solve the Schrödinger equation for the wavefunctions you get two sets of solutions: those of positive parity, and those of negative parity:
$\Psi _{P=1}=A\cos \left[{\frac {(2n+1)\pi x}{a}}\right]$
$\Psi _{P=-1}=A\cos \left({\frac {2n\pi x}{a}}\right),$
where n is any positive integer and A is a normalisation constant. Now, we can have all of these infinite states and if you've ever studied Fourier Analysis you may have noticed, with these states you can form any function you wish---that is, the wavefunctions are complete. So what have we learned? Well, a lot actually: we have discovered the eigenstates of the Hamiltonian which can be used to determine the particle's time dependance.

## Derivation of the Time-Independent Schrödinger Equation

We start with the general Schrödinger Equation, and use separation of variables. We have
$H\Psi ={\hat {\epsilon }}\Psi$
We separate $\Psi$ into two functions:
$\Psi (x,t)=T(t)X(x)$
So now the Schrödinger Equation is
$HTX={\hat {\epsilon }}TX$
We know from earlier that the "interesting" part of the energy operator ${\hat {\epsilon }}$ is a partial derivative with respect to time, and the "interesting" part of the Hamiltonian $H$ is a partial derivative with respect to position. As $T$ does not depend on position, it is not affected by $H$. Similarly, $X$ is not affected by ${\hat {\epsilon }}$.
So we have:
$THX=X{\hat {\epsilon }}T$
We can multiply on the left by $T^{-1}X^{-1}$ to obtain
$X^{-1}HX=T^{-1}{\hat {\epsilon }}T$
Note that the left side only depends on x, on the right side only depends on t. We have two functions which are totally indenpendent, but are somehow equal to each other. This is only possible if both functions are equal to a constant, which we call E.
i.e.
$X^{-1}HX=E$
$T^{-1}{\hat {\epsilon }}T=E$
Naturally this implies
$HX=EX$
and
${\hat {\epsilon }}T=ET$
We can then expand $H$ and ${\hat {\epsilon }}$ and solve this equation.
# SAS/Graphics

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis

## Gplot

* The symbol statement defines the color, the value and the interpolation between the points on the plot.
** interpol can be "none" (scatterplot), "needle", "regression" (regression line), "line", "spline".
* You can put two plots on the same graph with the 'overlay' option in the plot statement

## Export to other format

You can export to png, jpeg, pdf … Here is an example with a png file.
# SAS/Linear Models

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis

## The linear model

* proc reg
* One can also use the proc glm
* The least square estimator can be programmed using the IML procedure. See Least Square in IML section.
The model instruction gives the model. The outcome is on the lefthandside of the = sign. All explanatory variables are on the right handside. The constant is included by default.
* Note that the proc reg is an interactive command. Therefore you have to add quit; after the command.
* The clb option in the model statement gives the 95% confidence interval.
* The test statement adds tests for linear hypothesis.
* the output statement creates a table with the residuals.
You can also store parameters in a new database :
* Output the main calculation steps :

## Robust Regressions
### See Also

* The Robustreg Procedure

## Instrumental Variables

You can perform 2 stage least square estimation with a 'proc syslin' and the '2sls' option. You specify the endogenous predictors in the endogenous statement, the instrument in the instruments statement and your model in the model statement.

## Panel data

* PROC TSCSREG provides options for fixed and random effects models.
# SAS/Data Management

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis

## Library

Data are stored in a directory. You can give a name to that directory using the 'libname' statement.

## Read/Describe/list data

* Proc dataset
* Proc content
* Proc print
The Proc datasets allow to list the content of all the datasets in a library

## Generate Random Variables

The following program draws 5 observations from a normal distribution with expectancy 1.75 and standard deviation 0.1. The rannor function draws from a standard normal distribution. The argument specifies the seed. This allows reproducibility.
If you know the quantile function (inverse CDF), you can draw in the distribution using the inverse CDF method. You simple have to draw in a uniform distribution and transform the draw using the inverse CDF function. Here is an example with a Gumbel distribution :

## Sorting

The default is ascending sort. If you want to put the highest values first, you can use by descending.

## Merge

It is better to sort the data before merging them.

## Import from other format

You can import from a CSV:
You can also specify the delimiter.
You can import from an xls file.

## Export to other format

First one can export to Excel :

## Creating aggregate tables

One can create aggregate table using the output delivery system (ODS). The following program creates a table of the cross tabulation and store it in a new dataset.
# SAS/Math Functions

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis

## Probabilistic Functions

SAS includes a set of probabilistic functions. Instead of reading quantile tables, one can print the quantiles of a variable in the SAS log.
Note that we use a data step but we do not create any table. We also use the 'put' instruction to print the result in the log. Alternatively one can also use the PROC IML and print the results in the output window :
For a Student distribution, the first number is the quantile and the second the number of degrees of freedom.
For a $\chi ^{2}$ distribution :
For a Fisher distribution :
| Distribution | CDF | Quantile | PDF | Random Deviates |
| Beta | probbeta(p,$\alpha$,$\beta$) | betainv(q,$\alpha$,$\beta$) | _ | |
| $\chi ^{2}$ | probchi(p,n) | cinv(q,n) | _ | |
| Fisher | probf(p,d1,d2) | finv(q,d1,d2) | | |
| Gaussian | probnorm(p) | probit(q) | | rannor(0) |
| Student | probt(p,n) | tinv(q,n) | | |
| Uniform | | | | ranuni(0) |

## Statistical Functions

* mean
* N
* Nmiss

## Maths Functions

* log
# SAS/Maximum Likelihood

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis
* parms gives initial values to the parameters
* xb is an intermediate step which gives the list of covariates
* then we define the likelihood and we specify the model
# SAS/Descriptive Statistics

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis

## List and describe your data

Describe your data :
The proc contents returns the list and the type of all variables in the datasets.
List your data in the output :
The proc print prints the data in the output window. The firstobs option gives the first line to be printed and the obs option the number of lines to print.

## Discrete Variables

* weight specify weights

### Contingency Tables
## Continuous Variables

proc means presents descriptive statistics for each variable listed in the var statement or for each numeric variable in the data set if there is no var statement. Here are some of the keywords that can be used to tell SAS which statistics you wish to see.
* n : count of non missing variables
* sum : summation of the variable
* range : largest value minus smallest value
* mean : average
* var : variance
* stddev : standard deviation
The class statement makes statistics for each group of the categorical variable in the class statement. The weights statement weights the observations.
The proc univariate gives more options. It also returns the quantiles. There is also an histogram statement which can be useful.

### Kernel and Histograms

If you want to do a kernel or an histogram, you can use proc univariate with the histogram statement or the proc capability.
Proc capability :

### T Test

The following code test the assumption that the expected value of variable x in the dataset taille is 1.75.
# SAS/Documentation

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis
* SAS online documentation
** List and help of all SAS procedures
** The Graph Gallery
* UCLA Stat computing SAS
* Google Code Search
* A Brief Introduction to SAS (10 pages)
* StackOverflow
* (fr) Olivier Godechot's macros (mainly for textmining)
* SAS Community wiki
# SAS/IML

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis
IML is an Interactive Matrix Programming Language for SAS. This is similar to R, Matlab and Stata/Mata language. You deal with matrix and you can perform any operation on those matrix.

## Optimization

IML includes lots of optimization routines.

## Resources

* SAS Help for IML
* Introduction to SAS IML (1000 pages, pdf)
* Introduction to SAS IML by Michael Friendly
# SAS/Introduction

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis
SAS is a database. As opposed to Relational Databases, SAS is used primarily for batch processing of massive amounts of data. It can be found here. SAS is the largest privately held software company in the world.
SAS is made up of a number of modules with specialized procedures for analysis relating to various disciplines. The foundation of the software is the Base/SAS product. If one is interested in producing graphical output, it would be necessary to purchase a license to SAS/Graph. Statistical tools are in SAS/Stat and Economic/time-series procedures are in SAS/ETS. There are other modules for Executive Information Systems (SAS/EIS), Operational Research (SAS/OR) and many more that could be mentioned.
SAS is fundamentally the premier data analysis software on the market today. It utilizes a specialized data set table proprietary to SAS, however the SAS System has modules to be able to read and write to many other data base products like Oracle and ODBC compliant products like MS-SQL Server or PROGRESS.
SAS is generally utilized by government organizations and large businesses. It is also found being used by many colleges and universities. The greatest use for research is hard to identify, but there has been a great focus of users in the pharmacological research field. It is also used for analysis and reporting of data in social science fields and engineering companies like electric utilities.
SAS licenses tend to be expensive and complicated, based on the number of users and the number of processors in the host computer. It runs on server environments and is licenceable for workstation users on PCs or other common machines. It does not run on Macintosh machines, but a special product called JMP, and marketed by SAS Institute is available. It analyses market data or survey data and notable for its ability to visualize 'data cloud' arrays.
Dr. Jim Goodnight and a few other individuals were the founders of the product and Mr. Goodnight is CEO of SAS Institute. The SAS Institute is located in Cary, North Carolina.
Television (60 minutes or 20/20) featured SAS in one of their programs.
# SAS/Basics

SAS
* SAS Basics
** Introduction
** Basics
** Settings
** Documentation
** Math Functions
** String Functions
** Data Management
** Graphics
** Programming
** IML
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Method of Moments
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Duration Analysis
** Factor Analysis

## Why use SAS ?

* SAS works directly on the data sets without loading them into memory. This allows you to manipulate large database such as census data sets.

## Why not use SAS ?

* SAS is not available for mac users
* SAS is proprietary and expensive. You may prefer R which is open-source and cross-platforms.
* There is no systematic syntax. The syntax is specific to each PROC.

## Alternative to SAS

* R : an open source statistical package
* Stata : includes the very latest econometric methods
* SPSS : an easy to use statistical software

## SAS Environment
### EDITOR (F5)

    This is a text editor with syntax highlighting where you write your program. You can save your program with the .sas extension.

### LOG (F6)

    includes all information about the computing process such as errors, warnings, computing time (cpu). You can save it with the .log extension.

### OUTPUT (F7)

    This includes all the results. You can save it with the .lst extension.

### EXPLORER (CTRL +D)

    browse all your SAS libraries and open datasets in the SAS data editor.

### HELP (F1)

    Help system.

## SAS Programming Style

* SAS includes procedures and data step. data steps generally create a new dataset and procedure step compute some quantity of interest using existing data.
* Each step is ended with the run ; statement.
* Semicolons ; are end of statement delimiter.
* SAS works directly on a database without loading it into memory. This facilitates manipulation of large databases.
* F3 executes the current program or the selected lines of the program.
* After executing a program, you first look at your log and then you can have a look at your results.
* Comments begin with a star and terminated by a semicolon or are contained within a slash-star and a star-slash c-style block comment:
* SAS is not case sensitive ("a" and "A" are similar to SAS)

## Preamble

The following lines are often useful at the beginning of a SAS program :
* Libname : It is often useful to defines libname. A libname is nothing more than an alias for a directory.
* Options : the following line in head of a program makes it easier to read the log.
* Clean log and output windows : At the beginning of a program it is often convenient to clean the log and the output:
dm stands for "Display Manager"
# Radiation Oncology/Tumor markers

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials

## Gastrointestinal cancers

* 2006 ASCO Guidelines - PMID 17060676 — "ASCO 2006 Update of Recommendations for the Use of Tumor Markers in Gastrointestinal Cancer." Locker GY et al. JCO 2006 Nov 20;24(33):5313-27.
* 2000 ASCO Guidelines - PMID 11251019 — "2000 update of recommendations for the use of tumor markers in breast and colorectal cancer: clinical practice guidelines of the American Society of Clinical Oncology." Bast RC Jr et al. J Clin Oncol. 2001 Mar 15;19(6):1865-78.
* 1997 ASCO Guidelines - PMID 9469371 — "1997 update of recommendations for the use of tumor markers in breast and colorectal cancer." [No authors listed] J Clin Oncol. 1998 Feb;16(2):793-5.

## Breast cancer

* 2007 ASCO Guidelines - PMID 17954709 — "American Society of Clinical Oncology 2007 update of recommendations for the use of tumor markers in breast cancer." Harris L et al. J Clin Oncol. 2007 Nov 20;25(33):5287-312.
* 2000 ASCO Guidelines - PMID 11251019 — "2000 update of recommendations for the use of tumor markers in breast and colorectal cancer: clinical practice guidelines of the American Society of Clinical Oncology." Bast RC Jr et al. J Clin Oncol. 2001 Mar 15;19(6):1865-78.
* 1997 ASCO Guidelines - PMID 9469371 — "1997 update of recommendations for the use of tumor markers in breast and colorectal cancer." [No authors listed] J Clin Oncol. 1998 Feb;16(2):793-5.
# Radiation Oncology/Tumors of the Great Vessels

* Tumors of the great vessels (GVs) are extremely rare
* About as common as primary malignant pericardial mesothelioma
* Armed Forces Institute of Pathology report
** Sarcomas, including intimal (undifferentiated) sarcoma, angiosarcoma, leiomyosarcoma, and synovial sarcoma
# Radiation Oncology/Uterine Sarcoma

Uterine Sarcomas
* Staging
* Overview
* Uterine leiomyosarcoma
# Radiation Oncology/Uterine Sarcoma/Overview

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Uterine Sarcoma Overview
* Comprise <1% of GYN malignancies and 2-5% of uterine malignancies
* Three distinct tissues of origin:
** Carcinosarcoma (mixed mullerian tumor): endometrium, accounts for 40-50%. High frequency of TP53 mutations.
*** Subtypes:
**** Heterologous type:
***** Sarcomatous components derived from skeletal muscle, cartilage, or bone; frequently rhabdomyosarcomas or chondrosarcomas
***** More aggressive, poorer prognosis, higher risk of recurrence
**** Homologous type: Sarcomatous component derived from endometrium, usually resemble high-grade undifferentiated sarcoma or fibrosarcoma
*** GOG 150: Whole Abdominal Irradiation (WAI) vs Cisplatin-Ifosfamide and Mesna (CIM) as post-surgical therapy
*** 206 patients with uterine carcinosarcoma
**** Stages I-IV eligible as long as no demonstrable parenchymal hepatic involvement or extra-abdominal distant disease
**** All patients underwent TAH, BSO, and maximal resection of all gross intra-abdominal/pelvic disease, including macroscopically involved pelvic and para-aortic nodes, leaving no residual disease any larger than 1 cm
**** WAI: 1 cm margins on the diaphragm superiorly, the inguinal ligament inferiorly, and the lateral aspect of the peritoneal margin laterally; AP/PA; total dose 30 Gy. 20 Gy 4-field boost to true pelvis.
**** CIM: cisplatin (20 mg/m2/day IV × 4 days) that was to be followed by a one hour IV administration of Ifosfamide (1.5 g/m2/day IV × 4 days) with mesna (120 mg/m2 IV bolus over 15 minutes on day one, followed by 1.5 g/m2/day IV continuous infusion × 4 days beginning with day one) every three weeks for three cycles.
**** Primary endpoints: Death and recurrence rates
***** No statistically significant difference in time to recurrence (at 5 years, 58% WAI vs 52% CIM)
***** No statistically significant difference in survival time (at 5 years, 35% WAI vs 45% CIM)
***** Slightly more vaginal recurrences in CIM group and more abdominal recurrences in WAI group, but not statistically significant
**** AEs: Higher grade 3 or 4 acute anemia and neuropathy in CIM group, higher grade 2-4 gastrointestinal events in WAI group. Two WAI patients died of radiation hepatitis. One CIM patient died of acute port infection complicated by neutropenia.
** Leiomyosarcoma: myometrial muscle, accounts for ~30%
** Endometrial stromal sarcoma: endometrial stroma, accounts for ~15%
* Please see more detail at cancer.gov PDQ
* Shueng et al. (2013) Unusual Oligometastases of Distant Nodes as the Initial Relapse Site of Uterine Sarcoma: A Case Report, Therapeut Radiol Oncol 2013; 20(4): 315-321.
# Radiation Oncology/Unsealed sources

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
    See also: Isotopes used in Radiation Oncology

## For bone metastases

These have usefulness in treating blastic bone lesions (basically anything that lights up a bone scan). The dose limiting toxicity is bone marrow. Observe platelet counts.
* Please see the bone metastases page
* Phosphorus 32 - beta emitter
    Gets taken up in bone
    Not commonly used
* Strontium 89 (Metastron) - beta emitter
    Calcium analog, gets taken up in bone
    Long half life (50.5 days physical half-life)
    Usual dose 4 mCi (supplied as a 4 mCi vial)
    May also be dosed at 0.040-0.060 mCi/kg
* Samarium 153 (Quadramet) - beta and gamma emitter
    Bound to a tetraphosphonate, which gets taken up in area of active
    Usual dose 1 mCi/kg (may use 0.5 mCi/kg)
    Short half life (about 3 days)
    Can repeat dose after about 6-8 weeks
    Lowest effective range (compared to Sr and P) and thus lower bone marrow toxicity
    Can be used for imaging also due to its photon component

## P-32

* ovarian cancer
* endometrial cancer
* uterine papillary serous carcinoma
* pancreatic cancer
* Pure Beta emitter
** Energy: 1.71 MeV and 0.69 MeV electrons
** Average tissue penetration: 1.4-3mm
** T ½ : 14.3 days
** Benefit: no photon contamination
* Typical dose: 10-15 mCi
** 10 mCi gives equivalent of 30Gy to the peritoneum
* Distribution
** Test intraperitoneal distribution with T-99mc prior to treatment
** Inhomogeneous dose distribution.
** Mainly absorbed in the peritoneal surface
** Some enters systemic circulation via lymphatics and is removed by the liver
** LNs receive low, subtheraputic doses
** Little hemopoietic toxicity
** Peripheral blood dose: 1.2 cGy
** Bone marrow dose: 6 cGy

## Research

* Experimental antibody based methods - alpha emitters
    At the ITU (Institute for Transuranium Research; website) work is being done on Alpha-Immunotherapy, an experimental method using antibodies bound to alpha isotopes. Bismuth-213 is one of the isotopes which has been used. This is made by the alpha decay of Ac-225. The generation of one shortlived isotope from longer lived isotope is a useful method of providing a portable supply of a shortlived isotope. This is similar to the generation of technetium-99m by a technetium cow. The actinium-225 is made by the irradation of radium-226 with a cyclotron.

## Guidelines

* see also: Guidelines at Bone metastases

## Reviews

Samarium-153:
* 2004 PMID 16985930 -- Full text "Overview of Samarium Sm 153 Lexidronam in the Treatment of Painful Metastatic Bone Disease" (Sartor O, Rev Urol. 2004;6 Suppl 10:S3-S12.)