OpenLLM-France/wikimedia huggingface dataset:
# Proteomics/Proteolytic processing/Proteolytic processing- role in therapeutics
## Proteolytic processing- role in therapeutics

The fact that certain proteins can modify others by binding to specific site and alter its activity is used as a principle in the development of certain modern therapeutics. Here is an example of how the process of proteolytic processing has been used to find possible cure for diseases. Human coronavirus is the causative agent of the common respiratory disease in adults and children. There are no current cure for CoV as a result proteolytic processing is being exploited to find new drug targets. Biochemical analysis of HCoV –NL63 virus showed 2 viral papain like protease PLP1 and PLP2 which process viral replicase polyprotein. In this case they generated polyclonal antisera against 2 of replicase non structural proteins nsp3 and nsp4. It was found that PLP1 processes clevage site to release 1 to release nsp1 whereas PLP2 released nsp2 and nsp3. Also by using hexa ubiquitin substrate and ubiquitin vinylsulphonate inhibitor specific to deubiquitinization enzyme further show that CoV has deubiquititination activity. Understanding the concept of proteolytic processing and deubiquitinating of PLP’s can pave a way to the development of novel antisera regents directed against HCoV.
Next section: Proteomics/Proteolytic processing/Autoprocessing
# Quantum Graphs/Introduction

Studying operators of Schrödinger type on metric graphs is a growing subfield of mathematical physics which is motivated both by direct applications of the graph models to physical phenomena and by use of graphs as a simpler setting in which to study complex phenomena of quantum mechanics, such as Anderson localization, universality of spectral statistics, nodal statistics, scattering and resonances, to name but a few.
The name "quantum graphs" is most likely a shortening of the title of the article "Quantum Chaos on Graphs" by Kottos and Smilansky \cite{KotSmi_prl97}. The model itself has been studied well before the name appeared, for example in \cite{Pau_jcp36,RueSch_jcp53,Rot_crasp83,Bel_laa85,Nic_incol85}.
Several reviews and monographs cover various directions within the quantum graphs research \cite{GnuSmi_ap06,Post_book12,Mugnolo_book}. However, when starting a research project with students, both (post-) graduate and undergraduate, the author felt that a more elementary introduction would be helpful. The present manuscript grew out of the same preparatory lecture repeated, at different points of time, to several students. It is basically a collection of minimal examples of quantum graphs which already exhibit behavior typical to larger graphs. We supply the examples with pointers to the more general facts and theorems. Only in the last sections we explore a research topic (the nodal statistics on graphs) in some depth.
For obvious reasons the pointers often lead to the monograph \cite{BerKuc_graphs}.

### Sources

* Kottos, Tsampikos; Smilansky, Uzy (December 1997). "Quantum Chaos on Graphs". Phys. Rev. Lett. 79: 4794--4797. doi:10.1103/PhysRevLett.79.4794.
* Pauling, Linus (October 1936). "The Diamagnetic Anisotropy of Aromatic Molecules". J. Chem. Phys. 4 (10): 673–677. doi:https://doi.org/10.1063/1.1749766. {{cite journal}}: Check |doi= value (help); External link in |doi= (help)
# Quantum Mechanics/Complex Waves

In quantum mechanics we are interested in solutions to the Schrödinger equation that are renormalizable. One class of functions that does this is the complex exponentials, and we can write a solution to the Schrödinger equation as the sum of two complex exponentials
$\Psi (x)=Ae^{ikx}+Be^{-ikx}$
which is the superposition of waves, one traveling from the left, the other from the right. k is the wave number which is in units of 1/m and is usually given by $2*\pi /L$ where L is determined by boundary conditions.
Let us consider a situation in which there is a wave traveling from the left to the right. On the interval (-$\infty$,0) V(x)<E(x)and from [0, $\infty$) V(x)>E(x) and the solutions of the Schrödinger Equation are of the form
$\Psi (x)=Ae^{i{\sqrt {{\frac {2m}{\hbar ^{2}}}(E(x)-V(x))}}x}+Be^{-i{\sqrt {{\frac {2m}{\hbar ^{2}}}(E(x)-V(x))}}x}$
on the first interval and
$\Psi (x)=Ce^{{\sqrt {{\frac {2m}{\hbar ^{2}}}(E(x)-V(x))}}x}+De^{-{\sqrt {{\frac {2m}{\hbar ^{2}}}(E(x)-V(x))}}x}$
on the second interval
Even though at first glance our wave equation looks like a superposition of normal exponentials, it is still a complex wave though because the term inside of the square root is negative and this allows us to always have renormalizable solutions.
# Quantum Mechanics

This book is part of a series on Modern Physics:
Waves General Mechanics Special Relativity Quantum Mechanics Electrodynamics Nuclear Physics

## Matter Waves

* Introduction to QM
* Waves and Modes
* Blackbody Radiation
* Bragg's Law
* X-Ray Diffraction Techniques
* Operators and Commutators
* Heisenberg Uncertainty Principle
* Meaning of Quantum Wave Function
* Time Independent Schrödinger
* Mass, Momentum and Energy
* Perturbation Theory
* Quantum Scattering
    Problems

## Symmetry and Bound States

* Complex Waves
* Symmetry and Quantum Mechanics
* Confined Matter Waves
    Problems

## Measuring the Very Small

* Continuous Matter or Atoms?
* The Ring Around the Moon
* The Geiger-Marsden Experiment
* Cosmic Rays and Accelerator Experiments
* Commentary
    Problems

## Atoms

* Fermions and Boson
* The Hydrogen Atom
* The Periodic Table of the Elements
* Atomic Spectra
    Problems

## The Standard Model

* Quarks and Leptons
* Quantum Chromodynamics
* The Electroweak Theory
* Grand Unification?
    Problems

## Further Reading and Resources

* This Quantum World - a complete introductory text.
* Quantum theory of observation
* Quantum Field Theory
* Quantum Chemistry
# Quantum Mechanics/Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle states that the product of uncertainties in related physical quantities (e.g. position and momentum, energy and time, etc.) has a finite lower bound. This arises from the fact that the momentum and position operators do not commute. A common misunderstanding is that in simple terms this means that a measurement for position disturbs the momentum of a particle, and a measurement for the momentum of a particle disturbs its position. All of this information is false.
In other words, if you know the position of a particle and you measure the momentum, it disturbs the position - thus you are less certain of its position. This is incorrect.
In actuality, the uncertainty arises from fundamental underlying physical laws governing physical systems which can be measured. Particles have a fundamental dual nature and may be considered either a point source or a probability distribution of position depending upon what one is trying to accomplish by interacting with the particle.
Repeated measurements of particles in known/delivered states will give a distribution range governed by a probability function for either of the two conjugate properties, position (x) or momentum (p). The Uncertainty Principle gives a mathematically provable lower bound of the product of the uncertainty (error or deviation from a precise center of the probability wave law) in the measured conjugate properties.
$\Delta x\Delta p\geq {\frac {\hbar }{2}}={\frac {\frac {h}{2\pi }}{2}}\,$ where $\pi \approx 3.14$ and h is Planck's constant with $\hbar$ being Planck's reduced constant.
Thus the precision with which one can know one property is related mathematically to what is known of the conjugate property. If position is known with great precision for a specific particle or wave then the conjugate momentum is not known with a precision greater than that allowed by the lower bound provided by the Uncertainty Principle equation shown above.
Here is the derivation for the general uncertainty principle for two operators, A and B, that do not commute.
Let iC be the commutator of A and B:
[A,B] = iC
Furthermore, A and B are Hermitian operators. Recall the definition of the uncertainties:
$\left(\Delta A\right)^{2}=\langle \left(A-\langle A\rangle \right)^{2}\rangle$
$\left(\Delta B\right)^{2}=\langle \left(B-\langle B\rangle \right)^{2}\rangle$
To do:
Find a mathematically simple derivation of uncertainty principle and provide it here.
Find an intuitive example and provide here.
Provide a variety of equivalent derivations using different techniques to allow understanding by widest possible audience.
External links: Wikipedia:Uncertainty Principle
# Quantum Graphs

This is a book devoted to the spectral theory of Schrödinger operator on metric graphs (also known as "quantum graphs"). Every theoretical concept is to be illustrated by studying in detail several examples. The exposition is to be kept as elementary and accessible as possible.

## Table of Contents

* Introduction
* Schrödinger equation on a metric graph
* Vertex (Matching) Conditions
* Secular Determinant
* Dirichlet-to-Neumann Map

### Sources

* Berkolaiko, Gregory. "An elementary introduction to quantum graphs". In "Geometric and Computational Spectral Theory" (eds: A. Girouard, D. Jakobson, M. Levitin, N. Nigam, I. Polterovich and F. Rochon), Contemp. Math. 700, AMS, 2017. Amer. Math. Soc. doi:10.1090/conm/700. Preprint available: arXiv:1603.07356.
# Quantum Mechanics/Blackbody Radiation

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and non-reflective body). It has a specific spectrum and intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.
Considering a cavity at temperature $T$ in radiation equilibrium, the volume of the cavity is $V=L^{3}$, the energy density (energy per unit volume and frequency) $u(\omega )$. Here $u(\omega )\mathrm {d} \omega$expresses the energy per unit volume in the interval$[\omega ,\omega +\mathrm {d} \omega ]$. Classically, the situation is described by the Rayleigh–Jeans law $u(\omega )={\frac {k_{B}T}{\pi ^{2}c^{3}}}\omega ^{2}$.One can easily make this plausible by considering standing plane waves in a cavity with reflecting metal walls.
Where L is defined as ____ and
Where u($\omega$) is defined as ____ and
Where k is defined as ____ and
Where B is defined as ____ and
Where c is defined as ____ and
Where $\omega$ is defined as ____
# Saylor.org's Ancient Civilizations of the World/The Warring States Period and the Classical Age in China

The breakdown of the Zhou Empire, in the third century B.C.E., permitted the establishment of many small kingdoms ruled by former vassals and incursions of nomadic peoples who lived on the Chinese border. This period of internal warfare—called the “Warring States Period”—stimulated intellectual ferment and the formulation of new conceptions of political and social organization. The creation of the brief Qin Empire in 221 B.C.E. seemed to promise a return to political order. Qin tyranny, however, produced resistance and the collapse of the dynasty in 207 B.C.E. The Han dynasty (which replaced the Qin dynasty) ruled for nearly four centuries, and political unity was achieved through the creation of a large civil bureaucracy.
In this unit, we will examine how political and social disorder later resulted in consolidation and the emergence of a distinct Chinese state—a far different polity than the fragmentation and chronic instability that characterized the Zhou.
# Saylor.org's C++ Programming/Advanced Concepts

Upon successful completion of this unit, students will be able to:
* Write class and function templates.
* Code with a class that manipulates the files.
* Use namespaces and exceptions in C++ code.
* Write preprocessor instructions.
# R Programming/Probability Functions/Bernoulli
### The Bernoulli Distribution

A Bernoulli trial is a chance event that can have one of two outcomes, usually called "success" or "failure."
This distribution has one parameter, the unobserved probability of success, p. The probability of failure, often designated q, is the complement of p: 1-p
Some Bernoulli trials:
* Tossing a coin (Heads = success = 1, Tails = failure = 0)
* A single oocyst is detected with probability R and not detected with probability 1-R, R = recovery
* A marksman using a certain weapon aims at a target of a certain size that is a certain distance away. Each time he fires, he can either hit or miss the target.
* Walking Betty, we encounter a jogger. Betty either lunges, barking viciously, or totally ignores the jogger. (In this case, a lunge would be considered a "failure.")
* Your PARS evaluation results either in "fully successful" or something else. Do you think of fully successful a "success" or "failure?"
* Mike has written a number on a piece of paper. Your computer will generate one realization of a standard uniform random variable. It "succeeds" if the random number is less than Mike's. It is best to establish your prior before obtaining any data. Consider:
** How likely is it that Mike would pick a number less than zero, making the success probability 0?
** How likely is it that Mike would pick a number greater than one, making the success probability 1?
** Between 0 and 1, are there special values? Is 1/2 special? 1? 0? Others?
** A good prior might be Pr{0} = 1/3, Pr{1} = 1/3, with remaining 1/3 weight evenly spread across the range [0,1]

#### Probability Mass Function
##### f(x) = dbinom(x,1,P)

    = P if x = 1

##### = 0 otherwise
#### Distribution Function
##### F(x) = pbinom(x,1,P)

    = 0 for x<0
    = 1-P for 0 <= x < 1
    = 1 for 1 <= x

#### Common Statistics

* Mean = E(X) = P
* Var = P*(1-P) or P*Q

#### Generating Random Variables

1s and 0s:
* rbinom(M,1,P)
* rbinom(10,1,0.3) --> 0 0 1 1 0 0 0 0 1 0
* sample(c("success", "failure"),10, replace=T, prob=c(0.9, 0.1)) -->

##### [8] "success" "success" "success"
#### Parameter Estimation

* Maximum Likelihood
** P = X
* Bayesian
** If prior is Beta(alpha,beta), then posterior is Beta(alpha+X, beta+1-X)
** Coin tossing
* Classical
** (Correction) What hit rate (p) is so small that data as extreme as what was observed would occur with at most probability 0.05? Answer: If datum is "success," a hit rate of 0.05 or less would produce "success" with at most probability 0.05 (duh). If datum is "failure," then a hit rate of 0.95 or greater would produce "failur" with at most probability 0.05.

#### Related Distributions

Binomial is sum of repeated Bernoulli trials.

#### External Links

* Wikipedia: http://en.wikipedia.org/wiki/bernoulli_distribution
# R Programming/Probability Functions/Binomial
### The Binomial Distribution

* The sum of N Bernoulli trials (all with common success probability)
* The number of heads in N tosses of possibly-unfair coin.
* Of N oocysts truly present in a sample of water, the number actually counted, given each has same recovery probability.
* This distribution has 2 parameters (N and P), though we usually know the number of trials (N), so only one parameter is unknown (P).

#### Probability Mass Function

* dbinom(K,N,P), where K is the number of success, N is the number of trials, and P is the probability of success.
* dbinom(5,10,0.5) = 0.2460938
    ${\begin{array}{l}\operatorname {dbinom} (K,N,P)=\operatorname {combin} (N,K)\cdot p^{K}\cdot (1-p)^{N-K}\\\operatorname {combin} (N,K)={\frac {\displaystyle N!}{\displaystyle K!\cdot (N-K)!}}\end{array}}$

#### Distribution Function

* pbinom(K,N,P)
* pbinom(5,10,0.5) = 0.6230469

#### Generating Random Variables

* rbinom(M,N,P)
* rbinom(12,10,0.5) -> 5 5 7 5 5 6 7 6 6 6 4 7
* hist(rbinom(1000,10,0.5)) --> histogram
* hist(rbinom(1000,10,0.5), breaks = seq(from=-0.5, to=12.5)) will put integer values at bar centers (rather than at bar-right.

#### Parameter Estimation

Most of the time, we get to count the number of trials, so that parameter (N) is known. We observe the number of positives (K) and use this information to estimate the unobserved "success" probability (P).
* Sum of M binomials is same as sum of M*N Bernoulli Trials = binom(M*N,P)
* Maximum Likelihood
** lambda = sum(successes)/sum(trials) = sum(K)/sum(N)
* Bayesian
** With uniform prior, posterior is Beta(alpha=1+sum(K), beta=1+sum(N)-sum(K))
** With prior probability mass on 0 and 1 and the remaining mass given to Beta(1,1), see coin tossing example.
* Classical
** Normal Approximation
** Exact Confidence Interval
BUT, what if the number of trials is not known for M binomial trials? Can we used the data K[1] through K[M] to estimate both N and P?
Estimating both parameters from repeated i.i.d. binomial trials

#### External Links

* Wikipedia: http://en.wikipedia.org/wiki/binomial_distribution
* NIST/SEMATECH: http://www.itl.nist.gov/div898/handbook/eda/section3/eda366i.htm
# R Programming/Profiling R code

R Programming
* R Basics
** Introduction
** Sample Session
** Manage your workspace
** Settings and Installation
** Documentation
** Control Structures
** Working with functions
** Debugging
** Using C or Fortran
** Utilities
** Estimation utilities
** Packages
* Data Management
** Data types
** Working with data frames
** Importing and exporting data
** Text Processing
** Times and Dates
* Graphics
** Grammar of graphics
* Publication quality output
* Descriptive Statistics
* Mathematics
** Optimization
** Probability Distributions
** Random Number Generation
* Statistical Core Methods
** Maximum Likelihood
** Method of Moments
** Bayesian Methods
** Bootstrap
** Multiple Imputation
** Nonparametric Methods
* Regression Models
** Linear Models
** Quantile Regression
** Binomial Models
** Multinomial Models
** Tobit And Selection Models
** Count Data Models
** Duration Analysis
* Time Series
* Factor Analysis
* Classification
** Ordination
** Clustering
* Network Analysis
* High Performance Computing
** Profiling R code
** Parallel computing with R
* Appendix
** Sources
** Index
Before starting with parallel or high performance computing it is important to analyze and optimize R code. R provides some useful tools to analyze and profile R code. A good and short introduction is provided in the R extension documentation.
Soon we are going to provide some example code:
# R Programming/Parallel computing with R

R Programming
* R Basics
** Introduction
** Sample Session
** Manage your workspace
** Settings and Installation
** Documentation
** Control Structures
** Working with functions
** Debugging
** Using C or Fortran
** Utilities
** Estimation utilities
** Packages
* Data Management
** Data types
** Working with data frames
** Importing and exporting data
** Text Processing
** Times and Dates
* Graphics
** Grammar of graphics
* Publication quality output
* Descriptive Statistics
* Mathematics
** Optimization
** Probability Distributions
** Random Number Generation
* Statistical Core Methods
** Maximum Likelihood
** Method of Moments
** Bayesian Methods
** Bootstrap
** Multiple Imputation
** Nonparametric Methods
* Regression Models
** Linear Models
** Quantile Regression
** Binomial Models
** Multinomial Models
** Tobit And Selection Models
** Count Data Models
** Duration Analysis
* Time Series
* Factor Analysis
* Classification
** Ordination
** Clustering
* Network Analysis
* High Performance Computing
** Profiling R code
** Parallel computing with R
* Appendix
** Sources
** Index
There are many packages and tools available for parallel computing with R. A good overview is provided by the CRAN Task View: High-Performance and Parallel Computing with R and several publications:
Soon we are going to provide some code examples:
# R Programming/Ordination

R Programming
* R Basics
** Introduction
** Sample Session
** Manage your workspace
** Settings and Installation
** Documentation
** Control Structures
** Working with functions
** Debugging
** Using C or Fortran
** Utilities
** Estimation utilities
** Packages
* Data Management
** Data types
** Working with data frames
** Importing and exporting data
** Text Processing
** Times and Dates
* Graphics
** Grammar of graphics
* Publication quality output
* Descriptive Statistics
* Mathematics
** Optimization
** Probability Distributions
** Random Number Generation
* Statistical Core Methods
** Maximum Likelihood
** Method of Moments
** Bayesian Methods
** Bootstrap
** Multiple Imputation
** Nonparametric Methods
* Regression Models
** Linear Models
** Quantile Regression
** Binomial Models
** Multinomial Models
** Tobit And Selection Models
** Count Data Models
** Duration Analysis
* Time Series
* Factor Analysis
* Classification
** Ordination
** Clustering
* Network Analysis
* High Performance Computing
** Profiling R code
** Parallel computing with R
* Appendix
** Sources
** Index

## Overview

This page provides basic code for creating a distance matrix and running and plotting a Non-metric Multidimensional Scaling (NMDS) ordination.
Read more about Ordination on Wikipedia.
This code relies on package vegan in R by Jari Oksanen.

## Data

First, import data and load required libraries:

## Distance matrix
# Unconstrained Ordination
## Displaying dissimilarity using NMDS

NMDS analysis and plotting:
In the metaMDS function, k is user-defined and relates to how easily the projection fits the dataframe when constrained to k dimensions. Conventional wisdom seems to suggest that stress should not exceed 10-12%. Stress is reduced by increasing the number of dimensions. However, increasing dimensionality might decrease the "realism" of a 2-dimensional plot of the first two NMDS axes.
We can also run a nMDS with 3 dimensions, fit environmental vectors and create a dynamic graph:
# R Programming/Quantile Regression

R Programming
* R Basics
** Introduction
** Sample Session
** Manage your workspace
** Settings and Installation
** Documentation
** Control Structures
** Working with functions
** Debugging
** Using C or Fortran
** Utilities
** Estimation utilities
** Packages
* Data Management
** Data types
** Working with data frames
** Importing and exporting data
** Text Processing
** Times and Dates
* Graphics
** Grammar of graphics
* Publication quality output
* Descriptive Statistics
* Mathematics
** Optimization
** Probability Distributions
** Random Number Generation
* Statistical Core Methods
** Maximum Likelihood
** Method of Moments
** Bayesian Methods
** Bootstrap
** Multiple Imputation
** Nonparametric Methods
* Regression Models
** Linear Models
** Quantile Regression
** Binomial Models
** Multinomial Models
** Tobit And Selection Models
** Count Data Models
** Duration Analysis
* Time Series
* Factor Analysis
* Classification
** Ordination
** Clustering
* Network Analysis
* High Performance Computing
** Profiling R code
** Parallel computing with R
* Appendix
** Sources
** Index
Quantile regression is a very old method which has become popular only in the last years thanks to computing progress. One of the main researcher in this area is also a R practitioner and has developed a specific package for quantile regressions (quantreg) ·.
In theory, Quantile regression are also linear and thus could have been included in the Linear regression page. However, this is a very specific topic and we think that it is worth writing a specific page for this topic.

## Simple quantile model

We simulate from a simple quantile model. We first generate a uniform error term u and a covariate x.
We estimate the quantile model for some values of tau (the quantile) and plot the coefficients :
We then plot the scatterplot, the predicted values using a standard linear model and the predicted values using a quantile linear model :
We can also estimate the model for all quantiles at the same time :

### Computing time

For large data sets it is better to use the "fn" or "pfn" method.

## Resources

* Koenker, Roger (2005) Quantile Regression, Cambridge University Press. ISBN 0-521-60827-9

## References

* ↑ Roger Koenker (2010). quantreg: Quantile Regression. R package version 4.50. http://CRAN.R-project.org/package=quantreg
* ↑ Roger Koenker's personal webpage