Arity is a concept that refers to the number of arguments or operands that a function or operation takes. It's commonly used in mathematics and programming to describe how many inputs a function requires to produce an output. For example: - A function with an arity of 0 takes no arguments (often referred to as a constant function). - A function with an arity of 1 takes one argument (e.g., a unary function).
OK, there's a billion questions:
- SQL Server
- stackoverflow.com/questions/485409/generating-a-histogram-from-column-values-in-a-database OP did not know the difference between count and histogram :-) But it's the number one Google result.
- stackoverflow.com/questions/19103991/create-range-bins-from-sql-server-table-for-histograms has a minor extra group by twist, but otherwise fine
- stackoverflow.com/questions/16268441/generate-histogram-in-sql-server
- SQLite
- stackoverflow.com/questions/67514208/how-to-optimise-creating-histogram-bins-in-sqlite perf only, benchmarking would be needed. SQLite.
- stackoverflow.com/questions/32155449/create-a-histogram-with-a-dynamic-number-of-partitions-in-sqlite variable bin size, same number of entries per bin
- stackoverflow.com/questions/60348109/histogram-for-time-periods-using-sqlite-regular-buckets-1h-wide time
- MySQL: stackoverflow.com/questions/1764881/getting-data-for-histogram-plot MySQL appears to extend
ROUNDto also round by integers:ROUND(numeric_value, -2), but this is not widely portable which is a shame - stackoverflow.com/questions/72367652/populating-empty-bins-in-a-histogram-generated-using-sql specifically asks about empty bins, which is amazing. Amazon Redshift dialect unfortunately, but answer provided works widely, and Redshift was forked from PostgreSQL, so there's hope. Those newb open source server focused projects that don't use AGPL!
Let's try it on SQLite 3.40.1, Ubuntu 23.04. Data setup:
sqlite3 tmp.sqlite 'create table t(x integer)'
sqlite3 tmp.sqlite <<EOF
insert into t values (
0,
2,
2,
3,
5,
6,
6,
8,
9,
17,
)
EOF
sqlite3 tmp.sqlite 'create index tx on t(x)'For a bin size of 5 ignoring empty ranges we can:which produces the desired:
sqlite3 tmp.sqlite <<EOF
select floor(x/5)*5 as x,
count(*) as cnt
from t
group by 1
order by 1
EOF0|4
5|5
15|1And to consider empty ranges we can use SQL which outputs the desired:
genenerate_series + as per stackoverflow.com/questions/72367652/populating-empty-bins-in-a-histogram-generated-using-sql:sqlite3 tmp.sqlite <<EOF
select x, sum(cnt) from (
select floor(x/5)*5 as x,
count(*) as cnt
from t
group by 1
union
select *, 0 as cnt from generate_series(0, 15, 5)
)
group by x
EOF0|4
5|5
10|0
15|1Physical phenomena refer to observable events or occurrences in the natural world that are governed by the laws of physics. These phenomena can be categorized into various types based on their characteristics and the physical principles that describe them. Examples of physical phenomena include: 1. **Motion**: The movement of objects, including concepts like velocity, acceleration, and momentum. 2. **Forces**: Interactions that cause changes in motion, such as gravitational, electromagnetic, and nuclear forces.
Classical probability density refers to a function that describes the likelihood of a continuous random variable taking on a specific value within a given range. It is a key concept in the field of probability and statistics, particularly in the context of continuous probability distributions. Here are some key points about classical probability density: 1. **Probability Density Function (PDF)**: The probability density function is the mathematical function that defines the probability density.
The term "covariance group" can refer to different contexts in mathematics and physics, often related to how certain structures behave under transformations. However, it is not a widely used or standardized term like "group theory" or "covariance" in statistics or relativity. In general, covariance is a measure of how two variables change together.
A physical object is anything that has a tangible presence and occupies space. This means that it has specific dimensions (length, width, height), mass, and is made of matter, which can be solid, liquid, or gas. Physical objects can be perceived through our senses, particularly sight and touch.
Quantum non-equilibrium refers to the state of a quantum system that is not in thermodynamic equilibrium. In thermodynamics, systems at equilibrium exhibit well-defined macroscopic properties, such as temperature and pressure, and statistical distributions of their internal states (like the Boltzmann distribution). In contrast, non-equilibrium systems display time-dependent behavior and can have spatial gradients in quantities such as temperature, chemical potential, and density.
Analytic philosophy is a tradition in Western philosophy that emphasizes clarity of expression, logical reasoning, and the use of formal logic to analyze philosophical problems. This approach emerged in the early 20th century, primarily in the English-speaking world, and is often contrasted with continental philosophy, which may focus more on historical context, existential themes, and subjective experience.
The Analytical Society was a group formed in the early 19th century, primarily in Britain, that aimed to promote the use and understanding of analytical methods in mathematics, particularly calculus. Founded in 1813, it was a response to the predominance of the traditional calculus taught in British universities, which was often based on the work of Newton rather than the more rigorous methods developed by mathematicians like Joseph-Louis Lagrange and Augustin-Louis Cauchy.
A tensor is a mathematical object that generalizes scalars, vectors, and matrices to higher dimensions. Tensors are used in various fields such as physics, engineering, and machine learning to represent data and relationships in a structured manner. ### Basic Definitions: 1. **Scalar**: A tensor of rank 0, which is a single number (e.g., temperature, mass).
Geometry is a branch of mathematics that deals with the properties, measurements, and relationships of points, lines, shapes, and spaces. It encompasses various aspects, including: 1. **Shapes and Figures**: Geometry examines both two-dimensional shapes (like triangles, circles, and rectangles) and three-dimensional objects (like spheres, cubes, and cylinders). 2. **Properties**: It studies properties of these shapes, such as area, perimeter, volume, angles, and symmetry.
Graph theory is a branch of mathematics and computer science that studies the properties and applications of graphs. A graph is a collection of nodes (or vertices) connected by edges (or arcs). Graph theory provides a framework for modeling and analyzing relationships and interactions in various systems. Key concepts in graph theory include: 1. **Vertices and Edges**: The basic building blocks of a graph. Vertices represent entities, while edges represent the connections or relationships between them.
Mathematical analysis is a branch of mathematics that deals with the properties and behaviors of real and complex numbers, functions, sequences, and series. It provides the rigorous foundation for calculus and focuses on concepts such as limits, continuity, differentiation, integration, and sequences and series convergence. Key topics within mathematical analysis include: 1. **Limits**: Exploring how functions behave as they approach a specific point or infinity.
**Probability and Statistics** are two related but distinct branches of mathematics that deal with uncertainty and data analysis. ### Probability Probability is the branch of mathematics that deals with the likelihood or chance of different outcomes occurring. It provides a framework for quantifying uncertainty and making predictions based on known information. Some key concepts in probability include: - **Experiment**: A procedure that yields one of a possible set of outcomes (e.g., rolling a die).
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact