The Pythagorean trigonometric identities are fundamental relationships between the sine and cosine functions that stem from the Pythagorean theorem. They are derived from the fact that for a right triangle with an angle \( \theta \), the following equation holds: \[ \sin^2(\theta) + \cos^2(\theta) = 1 \] This is the most basic Pythagorean identity.
The HOMFLY polynomial is a knot invariant, which means it is a mathematical object that can be used to distinguish different knots and links in three-dimensional space. It extends the concepts of the Alexander polynomial and the Jones polynomial, making it a more powerful tool in the study of knot theory. The HOMFLY polynomial was introduced by HOMFLY, which is an acronym for the initials of the authors: H. G. H. Kauffman, M. W. W. L.
Gi Group Spa is an Italian multinational company that operates in the field of personnel services and human resources management. Founded in 1998, the company provides a range of services including recruitment, staffing, training, and consulting for businesses across various sectors. Gi Group is recognized for its focus on flexible workforce solutions and has expanded its presence internationally, serving clients and candidates in numerous countries. The company typically aims to connect employers with suitable candidates, while also offering career development and training opportunities for individuals.
A K-trivial set is a specific type of computably enumerable (c.e.) set that is closely related to algorithmic randomness and Kolmogorov complexity. More formally, a set \( A \) is defined to be K-trivial if the prefix-free Kolmogorov complexity \( K(A \cap \{0, \ldots, n\}) \) is bounded by a constant for all \( n \).
"Linear partial information" is not a standard term widely used in information theory, statistics, or related fields, which may lead to some ambiguity in its meaning. However, it could refer to concepts related to how information is represented or processed in a linear fashion when only a part of the entire dataset or information set is available. Here are some interpretations based on the key components of the term: 1. **Linear Information**: This could refer to situations where information is represented or analyzed using linear models.
Fletcher's checksum is a type of error-detecting checksum algorithm that is designed to detect errors in data transmission or storage. It was developed by John G. Fletcher in 1982 and is commonly used in applications where performance and error detection capabilities are necessary. Fletcher's checksum is particularly known for its simplicity and efficiency.
Heap's algorithm is a classic method for generating all possible permutations of a set of objects. It was developed by B. R. Heap in 1963. The algorithm is particularly efficient because it generates permutations by making only a small number of swaps, which minimizes the amount of work done compared to other permutation algorithms. ### Overview of Heap's Algorithm Heap's algorithm works by recursively generating permutations and is structured to handle the generation of permutations in a way that involves swapping elements.
Quarter-pixel motion refers to a technique used in video compression and processing, particularly in the context of motion estimation within video codecs. In video encoding, to reduce the amount of data needed to represent a video sequence, motion compensation is employed. This technique involves estimating and predicting motion between consecutive frames. Motion estimation determines how blocks or pixels in one frame move or shift to match blocks in another frame.
Repetitive control is a control strategy used primarily in control systems and automation that focuses on improving the performance of systems when subjected to repetitive tasks or periodic disturbances. This approach is particularly useful in scenarios where the same input or set of conditions is encountered repeatedly, allowing for the system to learn from past experiences and adjust its responses accordingly. ### Key Features of Repetitive Control: 1. **Periodicity**: Repetitive control is highly effective for systems that experience periodic inputs or disturbances.
The separation principle is a concept that can be applied in various fields, including control theory, economics, and decision-making processes. Here are some prominent interpretations of the separation principle based on different contexts: 1. **Control Theory**: In control theory, the separation principle refers to the idea that the control design process can be separated from the state estimation process.
Subspace identification methods are a set of techniques used in system identification, particularly for modeling dynamic systems based on measured input-output data. These methods are notable for their ability to handle large datasets and provide efficient and reliable estimates of the system's state-space representation.
Surprisal analysis is a concept rooted in information theory, primarily developed by Claude Shannon. It measures the amount of information or "surprise" associated with the occurrence of a particular event, which is based on the probability of that event. The basic idea is that events that have low probability are more surprising when they occur than events that are highly probable.
The Uncertainty Coefficient, also known as the Uncertainty Measure or the Uncertainty Coefficient of a variable, is a statistical measure used to quantify the uncertainty associated with a random variable or the amount of information that one variable provides about another. It is especially relevant in information theory and statistics. ### Key Points: 1. **Definition**: The Uncertainty Coefficient measures how much knowing the value of one variable reduces the uncertainty about another variable.
Ciro Santilli feels that all really important and productive activities come spontaneously, without being internally forced upon people.
You may say that this is because Ciro is lazy and irresponsible, but Bill thinks this isn't necessarily always bad:This is yet another manifestation of YAGNI.
I will always choose a lazy person to do a difficult job because a lazy person will find an easy way to do it.
As another way to put it, Ciro has very little "self-discipline", and acts very heavily based on small passions that take hold of him. Related: high flying bird vs gophers.
You may also say that Ciro is an idealist, because what to do when the food will run out and you have to hunt? To which Jesus replies at Matthew 6:25-34 "Do Not Worry" (archive):Also closely related: man shall not live by bread alone.
Therefore I tell you, do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more than food, and the body more than clothes? Look at the birds of the air; they do not sow or reap or store away in barns, and yet your heavenly Father feeds them. Are you not much more valuable than they? Can any one of you by worrying add a single hour to your life?And why do you worry about clothes? See how the flowers of the field grow. They do not labor or spin. Yet I tell you that not even Solomon in all his splendor was dressed like one of these. If that is how God clothes the grass of the field, which is here today and tomorrow is thrown into the fire, will he not much more clothe you - you of little faith? So do not worry, saying, "What shall we eat?" or "What shall we drink?" or "What shall we wear?" For the pagans run after all these things, and your heavenly Father knows that you need them. But seek first his kingdom and his righteousness, and all these things will be given to you as well. Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.
Ciro is also fond of the description of the work method of Yukio Mishima presented in Mishima: A Life in Four Chapters (TODO based on Mishima's self descriptions?). Ciro Santilli's father highlighted this to him, and Ciro had already watched that movie and thought it was amazing:
This is perfectly complemented by him making tea, as if suggesting:
Don't rush the work. Just let it happen. Every day at midnight, I would boil a teapot of tea. I would watch the steam rise, and with it feel my consciousness deepen. Everything was pure silence. When the hand was ready, it would, by itself, pick up the brush, and writing would start.
Ciro generally feels that many major developments in his life happened "by miracle", beyond his control. So when he saw the quote by Carl Jung:Ciro tends to do major decisions in his life due to uncontrollable passion rather than logic.
Until you make the unconscious conscious, it will direct your life and you will call it fate.
Ciro believes that this is linked to his self perceived creative personality, Because Ciro gives in to such uncontrollable passions, this leads him to do things which are more unusual/creative, because other more logical people would write such options off as weird.
Another type of laziness Ciro is to blame for is passionately seeking instrumental goals rather than hard end goals, in order to reach the hard goals more effectively. This is well put in the quote apocryphallyref attribute to Abraham Lincoln:For example, whenever joining a new company, Ciro would first try to improve any exceedingly shitty systems, like the build system or test system, rather than doing whatever random task the manager felt like doing that week. He was somewhat fired for that actually. But in the end, if your infrastructure sucks, your project will fail, so better be fired early and go work on something that might succeed than later when the enterprise goes bankrupt.
Related:
Alan Watts' wuwei talk
. Source. During this talk, Alan quotes Jesus: Matthew 18:3 "Truly I tell you, unless you change and become like little children, you will never enter the kingdom of heaven.".Alan Watts' "How to turn work into play" talk
. Source. We work too hard. We try too hard. Don’t try. Don’t work. It’s there. It’s been looking right at us, aching to kick out of the closed womb. There’s been too much direction. It’s all free, we needn’t be told. Classes? Classes are for asses. Writing a poem is as easy as beating your meat or drinking a bottle of beer.
Charles Bukowski Scandanavian TV interviews
. Source. Accelerator neutrinos are neutrinos that are produced as a result of high-energy particle collisions in particle accelerators. In these facilities, protons or other particles are accelerated to near-light speeds and then smashed into a target, which produces a range of particles, including pions (π mesons). These pions subsequently decay into neutrinos. Neutrinos are extremely light and neutral particles that interact very weakly with matter, making them challenging to detect.
Structural bioinformatics is a specialized branch of bioinformatics that focuses on the analysis and prediction of the three-dimensional structures of biological macromolecules, primarily proteins and nucleic acids (like DNA and RNA). It combines concepts from biology, chemistry, computer science, and information technology to understand the structure-function relationships of biological molecules.
"Contact order" can refer to different concepts depending on the context, but it is often associated with legal or social settings, particularly in the context of family law or child custody arrangements. Here are the primary meanings: 1. **Family Law Context**: In custody disputes, a contact order is a legal decision made by a court that outlines the terms under which a non-custodial parent can have contact with their child.
In silico PCR refers to a computational method used to simulate the polymerase chain reaction (PCR) process using software tools. Instead of performing the physical PCR in a laboratory, in silico PCR allows researchers to predict the outcome of a PCR experiment by modeling the amplification of specific DNA sequences based on known parameters such as DNA templates, primers, and reaction conditions.
Template modeling score is a specific metric used in the context of protein structure prediction and modeling. It typically indicates the quality or accuracy of a model generated using a template, which is often based on known structures from databases like the Protein Data Bank (PDB). When creating a model using template modeling, researchers align a target sequence (the sequence of the protein being studied) with a known structure (the template) and predict the 3D structure of the target based on this alignment.
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