Particle Physics

Particle physics (also high energy physics) is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word particle can refer to various types of very small objects (e.g. protons, gas particles, or even household dust), particle physics usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity.^[1][2]

 

Null Hypothesis

In inferential statistics, the term "null hypothesis" usually refers to a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.^[1] Rejecting or disproving the null hypothesis—and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science, and gives a precise criterion for rejecting a hypothesis.
The null hypothesis is generally assumed to be true until evidence indicates otherwise. In statistics, it is often denoted H₀ (read “H-nought”, "H-null", or "H-zero").

https://en.wikipedia.org/wiki/Null_hypothesis 

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MIT Mathlets

Here you will find a suite of dynamic Javascript "Mathlets" for use in learning about differential equations and other mathematical subjects, along with examples of how to use them in homework, group work, or lecture demonstration, and some of the underlying theory. There are also voice-over animated demos. 

http://mathlets.org/ 

Laplace Transform

In mathematics the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace (/ləˈplɑːs/). It takes a function of a positive real variable t (often time) to a function of a complex variable s (frequency).
The Laplace transform is very similar to the Fourier transform. While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are usually restricted to functions of t with t > 0. A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable s. Unlike the Fourier transform, the Laplace transform of a distribution is generally a well-behaved function. Also techniques of complex variables can be used directly to study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory.

https://en.wikipedia.org/wiki/Laplace_transform 

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Slope Field

In mathematics, a slope field (or direction field) is a graphical representation of the solutions of a first-order differential equation. It is useful because it can be created without solving the differential equation analytically. The representation may be used to qualitatively visualize solutions, or to numerically approximate them.

https://en.wikipedia.org/wiki/Slope_field 

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Word2vec

Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a high-dimensional space (typically of several hundred dimensions), with each unique word in the corpus being assigned a corresponding vector in the space. Word vectors are positioned in the vector space such that words that share common contexts in the corpus are located in close proximity to one another in the space.^[1]
Word2vec was created by a team of researchers led by Tomas Mikolov at Google. The algorithm has been subsequently analysed and explained by other researchers^[2][3] and a Bayesian version of the algorithm is proposed as well.^[4] Embedding vectors created using the Word2vec algorithm have many advantages compared to earlier algorithms like Latent Semantic Analysis.

https://en.wikipedia.org/wiki/Word2vec 

https://code.google.com/archive/p/word2vec/ 

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https://github.com/dav/word2vec
https://code.google.com/archive/p/word2vec/

Logistic Growth Model

The function was named in 1844–1845 by Pierre François Verhulst, who studied it in relation to population growth. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.

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