content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
September 2017 - e-LUMINESCIENCES: the blog of Jean-Pierre Luminet
This post is an adaptation of a chapter of my book “The Wraparound Universe” with many more illustrations.
Thus we may perhaps, one day, create new Figures
that will allow us to put our trust in the Word,
in order to traverse curved Space, non-Euclidean Space.
Francis Ponge[1]
The oldest known fragment of Euclid’s Elements as part of the Oxyrhynchus papyri, dated from the Ptolemaic period and belonging to the famous Alexandrian Library
In book I of the Elements,[2] Euclid poses the five “requests” that, according to him, define planar geometry. These postulates would become the keystone for all of geometry, a system of absolute
truths whose validity seemed irrefutable. One of the reasons for this faith is that these postulates seem obvious: the first of them stipulates that a straight line passes between two points, the
second that any line segment can be indefinitely prolonged in both directions, the third that, given a point and an interval, it is always possible to trace out a circle having the point for its
center and the interval as its radius, the fourth that all right angles are equal to each other. The fifth postulate is however less obvious:
As the sum of the interior angles α and β is less than 180°, according to the fifth postulate the two straight lines extended indefinitely, meet on that side.
“If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side
on which the angles sum to less than two right angles.”
Although the statement does not refer explicitly to parallel lines, the the fifth postulate is currently called “Parallel postulate”. This can be better understood given the more popular version of
the fifth postulate due to the Scottish mathematician John Playfair (1748-1819), who demonstrated that it was equivalent to the one given by Euclid : “Given a straight line and a point not belonging
to this line, there exists a unique straight line passing through the point which is parallel to the first“.
A picturesque English edition of Euclid’s Elements by Oliver Byrne, 1847.
[3] In the other geometry, called hyperbolic geometry, through any given point there passes an infinite number of lines parallel to another straight line. Continue reading | {"url":"https://blogs.futura-sciences.com/e-luminet/2017/09/","timestamp":"2024-11-09T09:33:07Z","content_type":"text/html","content_length":"55455","record_id":"<urn:uuid:21fccf38-5925-4206-8eda-c8b525162e26>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00438.warc.gz"} |
What does watts and amps mean?
What does watts and amps mean?
A watt describes the rate of power flow. When one amp flows through an electrical difference of one volt, its result is expressed in terms of watts. “W” is the symbol for watt or watts. Watts are
derived from the formula V x A = W.
What is amp in simple terms?
An “amp”, short for ampere, is a unit of electrical current which SI defines in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric
How many watts are in an amp?
120 watts
How many watts make an amp? At 120V, 120 watts make 1 amp. That means that 1 amp = 120 watts.
What is the difference between watts volts and amps?
Watts refer to “real power,” while volt-amperes refer to “apparent power.” Both are simply the product of voltage (V) multiplied by amperage (A). Thus, a device drawing 3 amps at 120 volts would be
rated at 360 watts or 360 volt-amperes.
Is higher or lower amps better?
A higher voltage system is more efficient than a lower voltage since it experiences less energy loss from resistance given the same amount of power draw.
What is the difference between A watt and an amp?
Amps is the unit of current flow, while Watts is the unit for power. Amps, when multiplied by voltage, equates to Watts. Measuring amps is much easier compared to measuring watts. Amps is applicable
only to electricity while watts is can be used for other forms of energy.
Does higher Watts mean more power?
What does a Watt mean? The Wattage of the light is the amount of energy it takes to produce a certain amount of light. The higher the wattage, the brighter the light, but also the more power it uses.
What happens if Amps are too low?
Amperage Provided versus Amperage Required Device may fail, may run or charge slowly, power supply may overheat, may damage the device being charged — all depending on the magnitude of the
difference. The amperage provided by your charger must match or exceed what the device being charged requires.
Do you want more volts or Amps?
Volts and Amps As long as you can draw enough current (amps) from the battery, you can get the same amount of power out of many voltages. So theoretically, the higher voltage doesn’t mean more power
in and of itself. Voltage numbers like 40V, 80V, and 120V often represent peak (max) volts.
How do you determine amps from Watts?
Calculate Watts from Volts and Amps. If you want to convert watts to amps on your own, you can use this equation: Watts = Amps x Volts or W = A x V. As long as you know two of the electrical ratings,
you can calculate the missing info with simple math. Wattage is equal to amps multiplied by volts.
What’s the difference between amps, volts and Watts?
Amps represent the volume of water present.
Voltage represents the water pressure
Watts are the energy created by the closed system that powers the mill.
Ohms represent the amount of resistance created by the size of the pipe.
What is the formula for converting watts to amps?
Converting watts to amps can be done using the Watt’s Law formula, which states that I = P ÷ E, where P is power measured in watts, I is current measured in amps, and E is voltage measured in volts.
How do Watts compare to amps?
Amps is the unit of current flow, while Watts is the unit for power. Amps, when multiplied by voltage, equates to Watts. Measuring amps is much easier compared to measuring watts. Amps is applicable
only to electricity while watts is can be used for other forms of energy. | {"url":"https://morethingsjapanese.com/what-does-watts-and-amps-mean/","timestamp":"2024-11-14T23:27:14Z","content_type":"text/html","content_length":"130234","record_id":"<urn:uuid:81dd9145-0485-46b5-b320-cf3a09bc092e>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00810.warc.gz"} |
Descriptive Data Analysis
Universitat Internacional de Catalunya
Descriptive Data Analysis
Second semester
Mètodes Quantitatius per a empresaris
Main language of instruction: Catalan
Other languages of instruction: English, Spanish
If the student is enrolled for the English track then classes for that subject will be taught in the same language.
Teaching staff
Lecture days or else by appointment
A course in basic statistics is offered in a wide variety of disciplines, from the social sciences to business to the natural sciences. The same statistical methods are applied across disciplines.
Therefore, it should not be surprising that the tools you will learn to use in this course will benefit you in your future studies and career, regardless of whether your career interest is finance,
accounting, strategy, management or marketing. In this course you will learn basic statistical measures, descriptive statistical methods, sampling methodology and the main probability distributions.
I believe statistics is best taught through a series of clear and carefully worked examples. A theoretical background to descriptive and inferential statistical methods will be provided, however much
of the time will be spent teaching you how to apply the theory to the real world. Statistics is not about memorising formulas: it is about recognising the appropriate statistical test to perform in a
given situation. This requires practice by the student. As we cover the topics, if you do not have a clear understanding of one topic it is wise to seek help immediately. The next topic will build
upon the previous one. Please allow me to assist you as soon as you find that you have any questions.
Pre-course requirements
Before taking this module, it is highly recommended that students have completed Mathematics 1, Mathematics 2 and Information Systems.
To learn the terminology, notation and different methods of quantitative analysis.
To be able to identify and understand the fundamental concepts of quantitative analysis.
To be able to analyse and synthesise information presented in the classroom and complementary material provided by the lecturer.
To be able to select appropriate statistical or mathematical methods for solving a particular economic problem.
Competences/Learning outcomes of the degree programme
• 19 - To analyse quantitative financial variables and take them into account when making decisions.
• 28 - To be able to work in another language and use terminology and structures related to the economic-business world.
• 31 - To develop the ability to identify and interpret numerical data.
• 32 - To acquire problem solving skills based on quantitative and qualitative information.
• 35 - To analyse time series.
• 36 - To interpret quantitative and qualitative data and apply mathematical and statistical tools to business processes.
• 40 - To be able to choose statistical methods appropriate to the object of analysis.
• 41 - To be able to descriptively summarise information.
• 42 - To be able to empirically analyse financial phenomena.
• 43 - To acquire skills for using statistical software.
• 50 - To acquire the ability to relate concepts, analyse and synthesise.
• 51 - To develop decision making skills.
• 52 - To develop interpersonal skills and the ability to work as part of a team.
• 53 - To acquire the skills necessary to learn autonomously.
• 54 - To be able to express one’s ideas and formulate arguments in a logical and coherent way, both verbally and in writing.
• 56 - To be able to create arguments which are conducive to critical and self-critical thinking.
• 64 - To be able to plan and organise one's work.
• 65 - To acquire the ability to put knowledge into practice.
• 66 - To be able to retrieve and manage information.
• 67 - To be able to express oneself in other languages.
Learning outcomes of the subject
To learn the terminology, notation and different methods of quantitative analysis.
To be able to identify and understand the fundamental concepts of quantitative analysis.
To be able to analyze and synthesize information presented in the classroom and complemetary material provided by the teacher.
To be able to select appropriate statistical or mathematical method to solve a particular economic problem.
Lesson 1.Descriptive statistics: concepts, measures, graphs. What is statistics? Descriptive versus inferential statistics. Sample and population. Types of data. Measurements of central tendency.
Measurements of dispersion. Measurements of shape. Measurements of concentration. Bar charts and pie charts. Frequency distribution. Other type of graphs. Misleading graphs.
Lesson 2. Bivariate analysis: frequencies, tables, scatter plots, conditional and marginal distribution, measures, etc. Covariance and correlation.
Lesson 3.Probability and distribution functions. Introduction to probability. Classical probability. Tree diagrams. Bayes' theorem. Moments about the origin. Central moments. Discrete versus
continuous probability distribution.
Teaching and learning activities
In person
Theoretical explanations will be presented in the classroom on PowerPoint slides, accompanied by additional explanations on the board.
The theory will be combined with problem-solving.
Problems will be solved jointly between the lecturer and students as a way of improving the learning process.
Evaluation systems and criteria
In person
Two evaluation methods will be used:
1. Class activities and participation (20%)
2. Final examination (80%)
If a midterm is carried out during the term then percentages will be 30/70. The grade of the final exam must be above 4/10.
If any student does not pass the course at the first attempt and is required to retake in July, the final grade will be that of the second-sitting examination.
Bibliography and resources
Students’ proficiency in Statistics 1 will be achieved by means of active practice. This means working on problems and understanding and explaining the results. The various textbooks recommended have
hundreds of problems students can use to gain additional practice. Answers to most of the problems can be found at the back of the textbooks.
Keller, G. Statistics for Management and Economics. South Western Cengage Learning.
Lind, D.A., Marchal, W.G. & S.A. Wathen. Statistical Techniques in Business and Economics. McGraw-Hill International Edition.
Schiller, John J. & Srinivasan, R. Alu. Schaum's Outline of Probability and Statistics. Ringgold, Inc.
Wonnacott T. & Wonnacott R.J. Introductory Statistics. John Wiley & Sons.
Notice that additional material may be handed over in class or shared through the virtual classroom. | {"url":"http://www.uic.es/en/subject/printable-version/14582/2024","timestamp":"2024-11-09T16:04:50Z","content_type":"text/html","content_length":"21789","record_id":"<urn:uuid:d1606e8c-2ea4-43d1-97bb-ee5dd550f681>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00719.warc.gz"} |
Improved explicit data structures in the bitprobe model
Buhrman et al. [SICOMP 2002] studied the membership problem in the bitprobe model, presenting both randomized and deterministic schemes for storing a set of size n from a universe of size m such that
membership queries on the set can be answered using t bit probes. Since then, there have been several papers focusing on deterministic schemes, especially for the first non-trivial case when n=2. The
most recent, due to Radhakrishnan, Shah, and Shannigrahi [ESA 2010], describes non-explicit schemes (existential results) for t≥3 using probabilistic arguments. We describe a fully explicit scheme
for n=2 that matches their space bound of Θ(m ^2/5) bits for t=3 and, furthermore, improves upon it for t>3, answering their open problem. Our structure (consisting of query and storage algorithms)
manipulates blocks of bits of the query element in a novel way that may be of independent interest. We also describe recursive schemes for n≥3 that improve upon all previous fully explicit schemes
for a wide range of parameters.
Publication series
Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume 8737 LNCS
ISSN (Print) 0302-9743
ISSN (Electronic) 1611-3349
Conference 22nd Annual European Symposium on Algorithms, ESA 2014
Country/Territory Poland
City Wroclaw
Period 8/09/14 → 10/09/14
Bibliographical note
Funding Information:
This work was supported in part by NSERC, the Canada Research Chairs program, a David Cheriton Scholarship, and a Derick Wood Graduate Scholarship.
This work was supported in part by NSERC, the Canada Research Chairs program, a David Cheriton Scholarship, and a Derick Wood Graduate Scholarship.
Funders Funder number
Natural Sciences and Engineering Research Council of Canada
Natural Sciences and Engineering Research Council of Canada
Canada Research Chairs
Dive into the research topics of 'Improved explicit data structures in the bitprobe model'. Together they form a unique fingerprint. | {"url":"https://cris.biu.ac.il/en/publications/improved-explicit-data-structures-in-the-bitprobe-model-2","timestamp":"2024-11-05T12:15:27Z","content_type":"text/html","content_length":"59559","record_id":"<urn:uuid:6c5e7da4-3a0c-4f59-a5dd-29a38b68a576>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00267.warc.gz"} |
Shanks' Conjecture -- from Wolfram MathWorld
Let prime which follows a prime gap of primes. Shanks' conjecture holds that
Wolf conjectures a slightly different form
which agrees better with numerical evidence.
See also
Prime Difference Function
Prime Gaps
Explore with Wolfram|Alpha
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 21, 1994.Rivera, C. "Problems & Puzzles: Conjecture 009.-Shanks' Conjecture." http://www.primepuzzles.net/
conjectures/conj_009.htm.Shanks, D. "On Maximal Gaps Between Successive Primes." Math. Comput. 18, 646-651, 1964.Wolf, M. "First Occurrence of a Given Gap Between Consecutive Primes." http://
Referenced on Wolfram|Alpha
Shanks' Conjecture
Cite this as:
Weisstein, Eric W. "Shanks' Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ShanksConjecture.html
Subject classifications | {"url":"https://mathworld.wolfram.com/ShanksConjecture.html","timestamp":"2024-11-05T22:41:32Z","content_type":"text/html","content_length":"52830","record_id":"<urn:uuid:da8b3528-114f-4c3a-bfe8-65f6968a19e8>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00429.warc.gz"} |
Divine Proportion in Web Design
Effective web design doesn't have to be pretty and colorful – it has to be clear and intuitive; in fact, we have analyzed the principles of effective design in our previous posts. However, how can
you achieve a clear and intuitive design solution? Well, there are a number of options – for instance, you can use grids, you can prefer the simplest solutions or you can focus on usability. However,
in each of these cases you need to make sure your visitors have some natural sense of order, harmony, balance and comfort. And this is exactly where the so- called Divine proportion becomes
This article explains what is the Divine proportion and what is the Rule of Thirds and describes how you can apply both of them effectively to your designs. Of course, there are many possibilities.
Hopefully, this post will help you to find your way to more effective and beautiful web designs or at least provide some good starting points you can build upon or develop further.
Divine Proportion
Since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio – especially in the form of the golden rectangle, in which the ratio of the longer
side to the shorter is the golden ratio. The rationale behind it is the belief that this proportion is organic, universal, harmonic and aesthetically pleasing. Indeed, being evident everywhere in the
universe (in fact, many things around us can be expressed in this ratio), divine proportion (which is also called Golden ratio, divine section, golden cut and mean of Phidias) is probably the most
known law of proportion which can dramatically improve the communication of your design.
As Mark Boulton states in his article Design and the Divine Proportion, "one of the key components in the vehicle of communication is composition, and in design schooling it is something that is
taught as something you should feel rather than create logically." Hence, to comfort your visitors with a pleasing and intuitive composition it is often worth considering the Golden ratio. So what
exactly is Golden ratio? Basically, it is a proportion 1.618033988749895 ≈ 1.618 which holds between objects placed within some context.
Consider the example above. You would like to create a fixed width layout. The width of your layout is 960px. You would to have a large block for your content (#content) and a smaller block for your
sidebar (#sidebar). How would you calculate the widths of your columns?
1. First, calculate the width of your #content-block. You need to make sure that the ratio between this block and the overall layout width is 1.62. Hence you divide 960px by 1.62 which results in
approximately 593px.
2. Subtract 593px from the overall layout width (which is 960px) and get 960px – 593px = 367px.
3. Now if you calculate the ratio between the #content-block and the #sidebar-block (593px : 367px ≈ 1.615) and the ratio between the container-width and the width of the content-block (960px :
593px ≈ 1.618) you have achieved almost the same ratio.
This is the whole idea behind the "Golden" proportion. The same holds for fluid and elastic layouts, too.
Of course, a web design doesn't need to be organized according to the Divine proportion. However, in some cases it can improve not only the communication of your design, but also improve further
details of your layouts. As an example consider The 404 Blog. The design itself is visually appealing, provides calm and supporting color scheme and has a nice composition.
However, the design does not correspond to the Divine proportion as you can see from the image below. Actually, users don't necessarily feel it, because they intuitively split the layout in two
separate blocks of the width 583px (630px – 31px – 31px) and 299px (330px - 31px). The reason behind it is that white space of the main area is passive (three columns, each 31px wide), it clearly
supports the content next to it rather than being the content itself.
The ratio between the layout blocks is 630 : 330 px ≈ 1.91 ≠ 1.62, and the ratio between the content blocks is 583 : 299px ≈ 1.92 ≠ 1.62. The reason why the layout looks almost perfect although it
doesn't stick to the Divine proportion is the simple fact that it is balanced – both the layout blocks and the content blocks have the same proportion. Hence the design provides some sense of closure
and structural harmony.
The interesting thing is, however, that due to a suboptimal layout length visitors are offered a suboptimal text length of over 90 symbols per line. However, an optimal number for comfortable reading
lies between 60 and 80 symbols per line. The improvement of the layout would therefore lead to the improved readability of the content, too. That's a useful side- effect of getting things done
according to the laws of nature.
For some quick'n'dirty drafts you may use the ratio 5 : 3 which is not exactly the Divine proportion, but can turn out to be a useful rule of thumb in case you don't have a calculator near you.
Divine proportion usually provides bulletproof values one can perfectly incorporate in almost every design. When working on your next project you may want to consider using the following tools to
calculate the widths "on the fly":
• Phiculator
Phiculator is a simple tool which, given any number, will calculate the corresponding number according to the golden ratio. The free tool is available for both Win and Mac.
• Golden Section Ratio Design Tool
Atrise Golden Section is a program, which allows avoiding the routine operations, calculator compilations, planning of grouping and forms. You can see and change the harmonious forms and sizes,
while being directly in the process of working on your project.
The Rule of Thirds
Basically, the Rule of Thirds is a simplified version of the Golden ratio and as such poses a compositional rule of thumb. Dividing a composition into thirds is an easy way to apply divine proportion
without getting out your calculator.
It states that every composition can be divided into nine equal parts by two equally-spaced horizontal lines and two equally-spaced vertical lines. The four points formed by the intersections of
these lines can be used to place the most important elements – the elements you'd like to give a prominent or dominant position in your designs. Aligning a composition according to Rule of thirds
creates more tension, energy and interest in the composition than simply centering the feature would.
In most cases it is neither possible nor useful to use all four points to highlight the most important functions or navigation options in a design. However, you can definitely use some of them
(usually one or two) to properly place the most important message or functionality of the site. The left upper corner is usually the strongest one, since users scan websites according to the
So how do you split a layout into 9 equal parts? Jason Beiard states the following method for applying the Rule of Thirds to your layouts:
1. To start the pencil-and-paper version of your layout, draw a rectangle. The vertical and horizontal dimensions don't really matter, but try to keep straight lines and 90- degree angles.
2. Divide your rectangle horizontally and vertically by thirds.
3. Divide the top third of your layout into thirds again.
4. Divide each of your columns in half to create a little more of a grid.
5. You should have a square on your paper that looks similar to the rule of thirds grid.
Let's consider the following situation. Assume you have a layout of fixed width 960px. Consider the area above the fold which is likely to have the height between 750 and 950px.
1. Divide the width of your layout by 3. In an example you get 960px / 3 = 320px.
2. Divide the height of your layout by 3. In an example you get ( (750 + 950 px) / 2 ) / 3 ≈ 285px.
3. Each rectangle should have the size of 320px × 285px.
4. Construct the grid of the rectangles described in step 4 by drawing lines going through the ends of rectangles.
5. Place the most significant elements of your designs in the meeting points of horizontal and vertical lines.
Consider the design of the website presented below (formerly Demandware.com, now owned by Salesforce). Although the design uses a number of vibrant colors, it is not noisy and seems to be both simple
and clear. The navigation options are clearly visible and the structure of the site seems to be easy to scan.
However, if you consider the effectiveness of this design, you might find a perfect balance the design actually has. Indeed, it almost perfectly uses the Rule of Thirds as two out of four
intersections of the lines (pink blocks in the picture below) contain exactly the information which the company wants its users to see – namely what the site is all about and an example of their
work. Note also how perfectly the main sections are placed on the second horizontal axis. That is effective.
In some cases, applying the Divine proportion and the Rule of Thirds may significantly improve the communication of your design to your visitors. Offering your users an almost natural balance in
proportion 1 : 1.62 you literally impose the natural order on it and force your design layout to become more scannable and well-structured.
Using the Rule of Thirds you can also effectively highlight important functions of your site providing your visitors with a design they can easily work with and effectively delivering the message you
want to deliver in the first place.
Source Notes
This article was first published in Smashing Magazine, © 29 May 2008; reprinted with permission.
Author: Vitaly Friedman
Vitaly Friedman loves beautiful content and doesn’t like to give in easily. Vitaly is writer, speaker, author and editor-in-chief of Smashing Magazine. He runs responsive Web design workshops, online
workshops and loves solving complex UX, front-end and performance problems in large companies. He may be contacted through Smashing Magazine. | {"url":"https://uraniatrust.org/articles/sacred/divine-proportion-and-web-design","timestamp":"2024-11-14T01:28:43Z","content_type":"text/html","content_length":"48599","record_id":"<urn:uuid:7144e3b1-4ef5-4e19-9aef-fa3dc361e786>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00770.warc.gz"} |
Lookup & Display First Non Empty Cell In A Range of cells within a column
I am attempting to write a formula in a header cell that returns the first Non-Blank row in a series within the related column. Excel permits this by using the Index and Match formulas but requires
that "CONTROL, SHIFT & ENTER" be pressed for the formula to work.
When attempting this in SmartSheet, I receive an "#INCORRECT ARGUMENT" error message. Sigh!
Any help here is appreciated.
Thank you.
• You could use an INDEX/COUNTIFS. It looks as if you are using hierarchies, so I will leverage the CHILDREN function. If that's not correct, just change the ranges to whatever you need.
=INDEX(CHILDREN(), COUNTIFS(CHILDREN(), ISBLANK(@cell)))
Does this work?
• I tried the following without success in the Phase 2 Cell:
=INDEX(CHILDREN(Phase3:Phase8), COUNTIFS(Children(Phase3:Phase8), ISBLANK(@cell)))
Which "cell" are you referencing at the end of the formula?
The column is formatted to Text/Number
Thanks for your help. This is above my pay grade.
• Try removing the ranges from the CHILDREN function. Leave those as CHILDREN(). When you don't specify a range in a CHILDREN function, it automatically looks at the children rows in the column
that the formula is in.
The @cell reference just tells a function to look at each cell within the range on an individual basis.
• @Paul Newcome Can this type of formula be used to find the first non-blank cell in a column? I am not getting the syntax right, but I am trying to find the contents of the first non-blank cell in
a column.
• Nevermind, I think I figured it out with this formula: =IFERROR(INDEX(COLLECT([Range]:[Range], [Range]:[Range], <>""), 1), "")
Help Article Resources | {"url":"https://community.smartsheet.com/discussion/50311/lookup-display-first-non-empty-cell-in-a-range-of-cells-within-a-column","timestamp":"2024-11-05T01:05:38Z","content_type":"text/html","content_length":"431367","record_id":"<urn:uuid:adff3aba-05a4-41be-8334-4d4da0f113c0>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00405.warc.gz"} |
Lecture 5 - Turing Machine
Lecture 5 - Turing Machine¶
Turing Machine¶
A Turing machine is a mathematical model of computation that defines an abstract machine. It was invented by Alan Turing in 1936. A Turing machine can simulate the logic of any computer algorithm,
and is therefore the theoretical foundation of all modern computers.
A Turing machine is a 5-tuple \((K, \Sigma, \delta, s, H)\), where:
• \(K\) is a finite set of states.
• \(\Sigma\) is a finite set of symbols.
• s \(\in\) \(K\) is the start state.
• \(H\) \(\in\) \(K\) is the halt state.
• \(\delta\) is the transition function, which maps \((K - H)(\text{current state}) \times \Sigma\) to \(K (\text{next state})\times (\Sigma(\text{write})\cup\{L,R\}(\text{moving}))\).
The transition function \(\delta\) satisfies the following properties:
• \(\forall q \in K - H, \delta(q,\triangleright) = (p,L)\) for some \(p \in K\).
• \(\forall q \in K - H, \forall a \in \Sigma, if\ \delta(q,a) = (p,b,D)\), then \(b \neq \triangleright\).
leftend \(\triangleright\) is a special symbol that is used to indicate the left end of the tape.
blank symbol \(\cup\) is a special symbol that is used to indicate the blank symbol.
A configuration of a Turing machine is a member of
\[(K \times \triangle(\Sigma-\{\triangleright\})^*) \times ((\Sigma-\{\triangleright\})^* (\Sigma - \{\triangleright,\cup\})\cup \{e\}).\]
• \(\Sigma - \{\triangleright,\cup\}\) is the last symbol that is not \(\cup\)
• {e} represents the following all symbols are \(\cup\).
We say \((q,\triangleright w_1au_1) \vdash_M (q_2,\triangleright w_2a_2u_2)\) if
• writing : \(\delta(q_1,a_1) = (q_2,a_2) and a_2 \in \Sigma - \{\triangleright\}\) and \(w_2 = w_1\) and \(u_2 = u_1\).
• moving left : \(\delta(q_1,u_1) = (q_2,L)\) and \(w_1=w_2a_2\) and \(u_2 = a_1u_1\).
M halts if it reaches a halting configuration
Acceptance and Rejection¶
A Turing machine M accepts a string w if \((s,\triangleright\cup w) \vdash^* (yes,\triangleright\cup aw)\)
A Turing machine M rejects a string w if \((s,\triangleright\cup w) \vdash^* (no,\triangleright\cup aw)\)
Given a Turing machine M, we can define the language accepted by M as \(L(M) = \{w \in \Sigma^* | M \text{ accepts w}\}\).
• M seme-decides L
• But M does not decide L
• Adding a condition: If M halts on all inputs, then M decides L.
M decides a language \(L\) if M accepts all strings in L and rejects all strings not in L.
M semi-decides a language \(L\) if M accepts all strings in L and may loop (or reject) on strings not in L.
Reccursive Language¶
A language \(L\) is recursive if there exists a Turing machine that decides \(L\).
Every recursive language is recursively enumerable.
• Explanation: A language \(L\) is recursively enumerable if there exists a Turing machine that semi-decides \(L\).
Multi-tape Turing Machine¶
A multi-tape Turing machine is a Turing machine with multiple tapes. Each tape has its own head and can move independently.
\[\delta: (K - H) \times \Sigma^k \rightarrow K \times ((\Sigma -\triangleright)\cup \{L,R\})^k.\]
Two-way Infinite Tape¶
Multi-head Turing Machine¶
A multi-head Turing machine is a Turing machine with multiple heads on a single tape.
2D-Tape Turing Machine¶
• Simulate a 2D-Tape Turing machine with a 1D-Tape Turing machine.
Random Access Turing Machine¶
• A Turing machine which can move to any position on the tape in a single step.
• \(L = \{a^nb^nc^n|n\geq 0\}\) can be decided by a Turing machine.
Non-deterministic Turing Machine (NTM)¶
• Deterministic TM: At each step, there is one possible next state, symbols to be written and direction to move the head, or the TM may halt.
• Nondeterministic TM: At each step, there are finitely many possibilities.
• So formally, \(M = (Q,\Sigma,\Gamma,\delta,q_0,q_{acc},q_{rej})\), where
• \(Q,\Sigma,\Gamma,q_0,q_{acc},q_{rej}\) are as before for 1-tape machine
• \(\delta : (Q- \{q_{acc},q_{rej}\}) \times \Gamma \rightarrow P(Q \times \Gamma \times \{L,R\})\)
• If there is a computation path that leads to \(q_{acc}\), then \(M\) accepts \(w\).
• If every computation path leads to \(q_{rej}\), then \(M\) rejects \(w\).
M decides a language \(L\) if
• Fir all \(w \in L\), there is a integer \(N\), depending on \(w\) and \(M\) such that every branch halts in at most N steps.
• If \(w \in L\), then there exists a branch that halts in an accepting state.
• If \(w \notin L\), then every branch halts in a rejecting state.
M semi-decides a language \(L\) if for any \(w \in L\):
• If \(w \in L\), then there exists a branch that halts in an accepting state.
• If \(w \notin L\), then no branch halts in a accepting state. -- No branch accepts \(w\).
Let \(C = {100,110,1000,...}\) C is composed of all binary numbers that are not prime. -- Construct a NTM that semi-decides C.
Theorem 1¶
Every NTM can be simulated by a DTM.
A NTM semi-decides a language \(L\) if and only if there exists a DTM that semi-decides \(L\).
• A NTM semi-decides a language \(L\) \(\Rightarrow\) There exists a DTM that semi-decides \(L\).
• Use a three-tape DTM to simulate a NTM.
Church-Turing Thesis¶
• Every algorithm can be simulated by a Turing machine.
• Intuition of Algorithm is equivalent to Turing machine.
Description of a Turing Machine¶
A Turing machine can be described by high-level pseudocode.
• Any Finite Set can be encoded.
• Any Finite Tuple whose elemnets are finite stes can be encoded.
• \(G = (V,E)\) is a graph. \(V\) is a finite set of vertices and \(E\) is a finite set of edges.
• \(L = \{G|G \text{ is connected}\}\)
M on input \(G\):
0. If the input is illegal (not a graph), reject.
1. select a node of G and mark it.
2. repeat the following until no new nodes are marked: * For each marked node, mark all its neighbors.
3. If all nodes are marked, accept; otherwise, reject.
Input: \(\langle B,w \rangle\), where \(B\) is a DFA and \(w\) is a string.
Output: Accept if \(B\) accepts \(w\); reject otherwise.
Solution:Construct a Turing machine that simulates the DFA \(B\) on input \(w\).
\(M_{R_1}\) = on input \(\langle B,w \rangle\):
1. run D on input \(w\).
2. If D accepts \(w\), accept; otherwise, reject.
Input: \(\langle B,w \rangle\), where \(B\) is a NFA and \(w\) is a string.
Output: Accept if \(B\) accepts \(w\); reject otherwise.
Solution: Construct a Turing machine that simulates the NFA \(B\) on input \(w\).
\(M_{R_2}\) = on input \(\langle B,w \rangle\):
1. Convert NFA \(B\) to a DFA \(B'\).
2. run \(M_{R_1}\) on input \(\langle B',w \rangle\).
3. If \(M_{R_1}\) accepts, accept; otherwise, reject.
This involves the process of reduction.
Input: \(\langle R,w \rangle\), where \(R\) is a regular expression and \(w\) is a string.
Output: Accept if \(R\) accepts \(w\); reject otherwise.
Solution: Construct a Turing machine that simulates the NFA \(B\) on input \(w\).
• A REX can be converted to a NFA.
• Use \(M_{R_2}\) to simulate the NFA.
\(M_{R_3}\) = on input \(\langle R,w \rangle\):
1. Convert REX \(R\) to a NFA \(B\).
2. run \(M_{R_2}\) on input \(\langle B,w \rangle\).
3. If \(M_{R_2}\) accepts, accept; otherwise, reject.
Input: \(\langle B \rangle\), where \(B\) is a DFA.
Output: Accept if \(L(B) = \emptyset\); reject otherwise.
Solution: Construct a Turing machine that simulates the DFA \(B\) on input \(w\).
\(M_{R_4}\) = on input \(\langle B \rangle\):
1. Run DFS on the state diagram of \(B\).
2. If there is a path from the start state to an accepting state, reject; otherwise, accept.
Input: \(\langle B_1,B_2 \rangle\), where \(B_1\) and \(B_2\) are DFAs.
Output: Accept if \(L(B_1) = L(B_2)\); reject otherwise.
Solution: Construct a Turing machine that simulates the DFA \(B\) on input \(w\).
• Symmetric difference -- \((L(B_1) \cup L(B_2) )- (L(B_1) \cap L(B_2))\)
• Convert the problem to whether the symmetric difference is empty.
\(M_{R_5}\) = on input \(\langle B_1,B_2 \rangle\):
1. Construct a DFA \(B\) that recognizes the symmetric difference of \(L(B_1)\) and \(L(B_2)\). \((L(B) = (L(B_1) \cup L(B_2)) - (L(B_1) \cap L(B_2))\)
2. Run \(M_{R_4}\) on input \(\langle B \rangle\).
Input: \(\langle G,w \rangle\), where \(G\) is a CFG and \(w\) is a string.
Output: Accept if \(G\) generates \(w\); reject otherwise.
\(A_{CFG} = \{ \langle G,w \rangle | G \text{ is a CFG and G generates w}\}\)
Chonsky Normal Form¶
A CFG \(G\) is in Chonsky Normal Form if every rule is of the form:
• \(S \rightarrow e\)
• \(A \rightarrow BC\) B and C are non-terminal symbols. BC \(\in V-\Sigma-{S}\)
• \(A \rightarrow a\).
So if final \(w\) has length \(n\), the number of steps of subtitution is \(2n-1\).
\(M_{C1}\) = on input \(\langle G,w \rangle\): 1. Convert CFG \(G\) to Chonsky Normal Form \(G'\). 2. Enumerate all derivations of length at most \(|R'|^{2n-1}\). 3. Acscept if any derivation
generates \(w\); otherwise, reject.
Input: \(\langle P,w \rangle\), where \(P\) is a PDA and \(w\) is a string.
Output: Accept if \(P\) accepts \(w\); reject otherwise.
\(A_{PDA} = \{ \langle P,w \rangle | P \text{ is a PDA and P accepts w}\}\)
\(M_{C_2}\) = on input \(\langle P,w \rangle\): 1. Convert PDA \(P\) to a CFG \(G\). 2. Run \(M_{C_1}\) on input \(\langle G,w \rangle\). 3. If \(M_{C_1}\) accepts, accept; otherwise, reject.
Input: \(\langle G \rangle\), where \(G\) is a CFG.
Output: Accept if \(L(G) = \emptyset\); reject otherwise.
\(E_{CFG} = \{ \langle G \rangle | L(G) = \emptyset\}\)
\(M_{C_3}\) = on input \(\langle G \rangle\): 1. Mark all terminals and \(e\). 2. Look through all rules and if there is a rule that all symbols on the right side are marked , mark the left side. 3.
Repeat step 2 until no new symbols are marked. 4. If \(S\) is marked, reject; otherwise, accept.
Input: \(\langle P \rangle\), where \(P\) is a PDA.
Output: Accept if \(L(P) = \emptyset\); reject otherwise.
\(E_{PDA} = \{ \langle P \rangle | L(P) = \emptyset\}\)
\(M_{C_4}\) = on input \(\langle P \rangle\): 1. Convert PDA \(P\) to a CFG \(G\). 2. Run \(M_{C_3}\) on input \(\langle G \rangle\). 3. If \(M_{C_3}\) accepts, accept; otherwise, reject.
\(A_{DFA}\) is recursive \(\rightarrow\) \(L(D)\) is recursive.
最后更新: 2024年10月28日 20:54:30
创建日期: 2024年10月16日 00:17:47 | {"url":"https://note.lilyarnold.cc/%E8%AE%A1%E7%AE%97%E7%90%86%E8%AE%BA/lec5/Lecture5/","timestamp":"2024-11-04T23:49:51Z","content_type":"text/html","content_length":"116770","record_id":"<urn:uuid:155ac4f6-b1f9-4d6a-be02-2f8c7dc8b5cf>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00640.warc.gz"} |
In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported.
Holonomy is a general geometrical consequence of the curvature of the connection. For flat connections, the associated holonomy is a type of monodromy and is an inherently global notion. For curved
connections, holonomy has nontrivial local and global features.
Parallel transport on a sphere along a piecewise smooth path. The initial vector is labelled as ${\displaystyle V}$, parallel transported along the curve, and the resulting vector is labelled as ${\
displaystyle {\mathcal {P}}_{\gamma }(V)}$. The outcome of parallel transport will be different if the path is varied.
Any kind of connection on a manifold gives rise, through its parallel transport maps, to some notion of holonomy. The most common forms of holonomy are for connections possessing some kind of
symmetry. Important examples include: holonomy of the Levi-Civita connection in Riemannian geometry (called Riemannian holonomy), holonomy of connections in vector bundles, holonomy of Cartan
connections, and holonomy of connections in principal bundles. In each of these cases, the holonomy of the connection can be identified with a Lie group, the holonomy group. The holonomy of a
connection is closely related to the curvature of the connection, via the Ambrose–Singer theorem.
The study of Riemannian holonomy has led to a number of important developments. Holonomy was introduced by Élie Cartan (1926) in order to study and classify symmetric spaces. It was not until much
later that holonomy groups would be used to study Riemannian geometry in a more general setting. In 1952 Georges de Rham proved the de Rham decomposition theorem, a principle for splitting a
Riemannian manifold into a Cartesian product of Riemannian manifolds by splitting the tangent bundle into irreducible spaces under the action of the local holonomy groups. Later, in 1953, Marcel
Berger classified the possible irreducible holonomies. The decomposition and classification of Riemannian holonomy has applications to physics and to string theory.
Holonomy of a connection in a vector bundle
Let E be a rank-k vector bundle over a smooth manifold M, and let ∇ be a connection on E. Given a piecewise smooth loop γ : [0,1] → M based at x in M, the connection defines a parallel transport map
P[γ] : E[x] → E[x] on the fiber of E at x. This map is both linear and invertible, and so defines an element of the general linear group GL(E[x]). The holonomy group of ∇ based at x is defined as
${\displaystyle \operatorname {Hol} _{x}(abla )=\{P_{\gamma }\in \mathrm {GL} (E_{x})\mid \gamma {\text{ is a loop based at }}x\}.}$
The restricted holonomy group based at x is the subgroup ${\displaystyle \operatorname {Hol} _{x}^{0}(abla )}$ coming from contractible loops γ.
If M is connected, then the holonomy group depends on the basepoint x only up to conjugation in GL(k, R). Explicitly, if γ is a path from x to y in M, then
${\displaystyle \operatorname {Hol} _{y}(abla )=P_{\gamma }\operatorname {Hol} _{x}(abla )P_{\gamma }^{-1}.}$
Choosing different identifications of E[x] with R^k also gives conjugate subgroups. Sometimes, particularly in general or informal discussions (such as below), one may drop reference to the
basepoint, with the understanding that the definition is good up to conjugation.
Some important properties of the holonomy group include:
Holonomy of a connection in a principal bundle
The definition for holonomy of connections on principal bundles proceeds in parallel fashion. Let G be a Lie group and P a principal G-bundle over a smooth manifold M which is paracompact. Let ω be a
connection on P. Given a piecewise smooth loop γ : [0,1] → M based at x in M and a point p in the fiber over x, the connection defines a unique horizontal lift ${\displaystyle {\tilde {\gamma }}:
[0,1]\to P}$ such that ${\displaystyle {\tilde {\gamma }}(0)=p.}$ The end point of the horizontal lift, ${\displaystyle {\tilde {\gamma }}(1)}$ , will not generally be p but rather some other point p
·g in the fiber over x. Define an equivalence relation ~ on P by saying that p ~ q if they can be joined by a piecewise smooth horizontal path in P.
The holonomy group of ω based at p is then defined as
${\displaystyle \operatorname {Hol} _{p}(\omega )=\{g\in G\mid p\sim p\cdot g\}.}$
The restricted holonomy group based at p is the subgroup ${\displaystyle \operatorname {Hol} _{p}^{0}(\omega )}$ coming from horizontal lifts of contractible loops γ.
If M and P are connected then the holonomy group depends on the basepoint p only up to conjugation in G. Explicitly, if q is any other chosen basepoint for the holonomy, then there exists a unique g
∈ G such that q ~ p·g. With this value of g,
${\displaystyle \operatorname {Hol} _{q}(\omega )=g^{-1}\operatorname {Hol} _{p}(\omega )g.}$
In particular,
${\displaystyle \operatorname {Hol} _{p\cdot g}(\omega )=g^{-1}\operatorname {Hol} _{p}(\omega )g,}$
Moreover, if p ~ q then ${\displaystyle \operatorname {Hol} _{p}(\omega )=\operatorname {Hol} _{q}(\omega ).}$ As above, sometimes one drops reference to the basepoint of the holonomy group, with the
understanding that the definition is good up to conjugation.
Some important properties of the holonomy and restricted holonomy groups include:
• ${\displaystyle \operatorname {Hol} _{p}^{0}(\omega )}$ is a connected Lie subgroup of G.
• ${\displaystyle \operatorname {Hol} _{p}^{0}(\omega )}$ is the identity component of ${\displaystyle \operatorname {Hol} _{p}(\omega ).}$
• There is a natural, surjective group homomorphism ${\displaystyle \pi _{1}\to \operatorname {Hol} _{p}(\omega )/\operatorname {Hol} _{p}^{0}(\omega ).}$
• If M is simply connected then ${\displaystyle \operatorname {Hol} _{p}(\omega )=\operatorname {Hol} _{p}^{0}(\omega ).}$
• ω is flat (i.e. has vanishing curvature) if and only if ${\displaystyle \operatorname {Hol} _{p}^{0}(\omega )}$ is trivial.
Holonomy bundles
Let M be a connected paracompact smooth manifold and P a principal G-bundle with connection ω, as above. Let p ∈ P be an arbitrary point of the principal bundle. Let H(p) be the set of points in P
which can be joined to p by a horizontal curve. Then it can be shown that H(p), with the evident projection map, is a principal bundle over M with structure group ${\displaystyle \operatorname {Hol}
_{p}(\omega ).}$ This principal bundle is called the holonomy bundle (through p) of the connection. The connection ω restricts to a connection on H(p), since its parallel transport maps preserve H(p
). Thus H(p) is a reduced bundle for the connection. Furthermore, since no subbundle of H(p) is preserved by parallel transport, it is the minimal such reduction.^[1]
As with the holonomy groups, the holonomy bundle also transforms equivariantly within the ambient principal bundle P. In detail, if q ∈ P is another chosen basepoint for the holonomy, then there
exists a unique g ∈ G such that q ~ p g (since, by assumption, M is path-connected). Hence H(q) = H(p) g. As a consequence, the induced connections on holonomy bundles corresponding to different
choices of basepoint are compatible with one another: their parallel transport maps will differ by precisely the same element g.
The holonomy bundle H(p) is a principal bundle for ${\displaystyle \operatorname {Hol} _{p}(\omega ),}$ and so also admits an action of the restricted holonomy group ${\displaystyle \operatorname
{Hol} _{p}^{0}(\omega )}$ (which is a normal subgroup of the full holonomy group). The discrete group ${\displaystyle \operatorname {Hol} _{p}(\omega )/\operatorname {Hol} _{p}^{0}(\omega )}$ is
called the monodromy group of the connection; it acts on the quotient bundle ${\displaystyle H(p)/\operatorname {Hol} _{p}^{0}(\omega ).}$ There is a surjective homomorphism ${\displaystyle \varphi :
\pi _{1}\to \operatorname {Hol} _{p}(\omega )/\operatorname {Hol} _{p}^{0}(\omega ),}$ so that ${\displaystyle \varphi \left(\pi _{1}(M)\right)}$ acts on ${\displaystyle H(p)/\operatorname {Hol} _{p}
^{0}(\omega ).}$ This action of the fundamental group is a monodromy representation of the fundamental group.^[2]
Local and infinitesimal holonomy
If π: P → M is a principal bundle, and ω is a connection in P, then the holonomy of ω can be restricted to the fibre over an open subset of M. Indeed, if U is a connected open subset of M, then ω
restricts to give a connection in the bundle π^−1U over U. The holonomy (resp. restricted holonomy) of this bundle will be denoted by ${\displaystyle \operatorname {Hol} _{p}(\omega ,U)}$ (resp. ${\
displaystyle \operatorname {Hol} _{p}^{0}(\omega ,U)}$ ) for each p with π(p) ∈ U.
If U ⊂ V are two open sets containing π(p), then there is an evident inclusion
${\displaystyle \operatorname {Hol} _{p}^{0}(\omega ,U)\subset \operatorname {Hol} _{p}^{0}(\omega ,V).}$
The local holonomy group at a point p is defined by
${\displaystyle \operatorname {Hol} ^{*}(\omega )=\bigcap _{k=1}^{\infty }\operatorname {Hol} ^{0}(\omega ,U_{k})}$
for any family of nested connected open sets U[k] with ${\displaystyle \bigcap _{k}U_{k}=\pi (p)}$ .
The local holonomy group has the following properties:
1. It is a connected Lie subgroup of the restricted holonomy group ${\displaystyle \operatorname {Hol} _{p}^{0}(\omega ).}$
2. Every point p has a neighborhood V such that ${\displaystyle \operatorname {Hol} _{p}^{*}(\omega )=\operatorname {Hol} _{p}^{0}(\omega ,V).}$ In particular, the local holonomy group depends only
on the point p, and not the choice of sequence U[k] used to define it.
3. The local holonomy is equivariant with respect to translation by elements of the structure group G of P; i.e., ${\displaystyle \operatorname {Hol} _{pg}^{*}(\omega )=\operatorname {Ad} \left(g^
{-1}\right)\operatorname {Hol} _{p}^{*}(\omega )}$ for all g ∈ G. (Note that, by property 1, the local holonomy group is a connected Lie subgroup of G, so the adjoint is well-defined.)
The local holonomy group is not well-behaved as a global object. In particular, its dimension may fail to be constant. However, the following theorem holds:
If the dimension of the local holonomy group is constant, then the local and restricted holonomy agree: ${\displaystyle \operatorname {Hol} _{p}^{*}(\omega )=\operatorname {Hol} _{p}^{0}(\omega
Ambrose–Singer theorem
The Ambrose–Singer theorem (due to Warren Ambrose and Isadore M. Singer (1953)) relates the holonomy of a connection in a principal bundle with the curvature form of the connection. To make this
theorem plausible, consider the familiar case of an affine connection (or a connection in the tangent bundle – the Levi-Civita connection, for example). The curvature arises when one travels around
an infinitesimal parallelogram.
In detail, if σ: [0, 1] × [0, 1] → M is a surface in M parametrized by a pair of variables x and y, then a vector V may be transported around the boundary of σ: first along (x, 0), then along (1, y),
followed by (x, 1) going in the negative direction, and then (0, y) back to the point of origin. This is a special case of a holonomy loop: the vector V is acted upon by the holonomy group element
corresponding to the lift of the boundary of σ. The curvature enters explicitly when the parallelogram is shrunk to zero, by traversing the boundary of smaller parallelograms over [0, x] × [0, y].
This corresponds to taking a derivative of the parallel transport maps at x = y = 0:
${\displaystyle {\frac {D}{dx}}{\frac {D}{dy}}V-{\frac {D}{dy}}{\frac {D}{dx}}V=R\left({\frac {\partial \sigma }{\partial x}},{\frac {\partial \sigma }{\partial y}}\right)V}$
where R is the curvature tensor.^[3] So, roughly speaking, the curvature gives the infinitesimal holonomy over a closed loop (the infinitesimal parallelogram). More formally, the curvature is the
differential of the holonomy action at the identity of the holonomy group. In other words, R(X, Y) is an element of the Lie algebra of ${\displaystyle \operatorname {Hol} _{p}(\omega ).}$
In general, consider the holonomy of a connection in a principal bundle P → M over P with structure group G. Let g denote the Lie algebra of G, the curvature form of the connection is a g-valued
2-form Ω on P. The Ambrose–Singer theorem states:^[4]
The Lie algebra of ${\displaystyle \operatorname {Hol} _{p}(\omega )}$ is spanned by all the elements of g of the form ${\displaystyle \Omega _{q}(X,Y)}$ as q ranges over all points which can be
joined to p by a horizontal curve (q ~ p), and X and Y are horizontal tangent vectors at q.
Alternatively, the theorem can be restated in terms of the holonomy bundle:^[5]
The Lie algebra of ${\displaystyle \operatorname {Hol} _{p}(\omega )}$ is the subspace of g spanned by elements of the form ${\displaystyle \Omega _{q}(X,Y)}$ where q ∈ H(p) and X and Y are
horizontal vectors at q.
Riemannian holonomy
The holonomy of a Riemannian manifold (M, g) is the holonomy group of the Levi-Civita connection on the tangent bundle to M. A 'generic' n-dimensional Riemannian manifold has an O(n) holonomy, or SO(
n) if it is orientable. Manifolds whose holonomy groups are proper subgroups of O(n) or SO(n) have special properties.
One of the earliest fundamental results on Riemannian holonomy is the theorem of Borel & Lichnerowicz (1952), which asserts that the restricted holonomy group is a closed Lie subgroup of O(n). In
particular, it is compact.
Reducible holonomy and the de Rham decomposition
Let x ∈ M be an arbitrary point. Then the holonomy group Hol(M) acts on the tangent space T[x]M. This action may either be irreducible as a group representation, or reducible in the sense that there
is a splitting of T[x]M into orthogonal subspaces T[x]M = T′[x]M ⊕ T″[x]M, each of which is invariant under the action of Hol(M). In the latter case, M is said to be reducible.
Suppose that M is a reducible manifold. Allowing the point x to vary, the bundles T′M and T″M formed by the reduction of the tangent space at each point are smooth distributions which are integrable
in the sense of Frobenius. The integral manifolds of these distributions are totally geodesic submanifolds. So M is locally a Cartesian product M′ × M″. The (local) de Rham isomorphism follows by
continuing this process until a complete reduction of the tangent space is achieved:^[6]
Let M be a simply connected Riemannian manifold,^[7] and TM = T^(0)M ⊕ T^(1)M ⊕ ⋯ ⊕ T^(k)M be the complete reduction of the tangent bundle under the action of the holonomy group. Suppose that T^
(0)M consists of vectors invariant under the holonomy group (i.e., such that the holonomy representation is trivial). Then locally M is isometric to a product
${\displaystyle V_{0}\times V_{1}\times \cdots \times V_{k},}$
where V[0] is an open set in a Euclidean space, and each V[i] is an integral manifold for T^(i)M. Furthermore, Hol(M) splits as a direct product of the holonomy groups of each M[i], the maximal
integral manifold of T^(i) through a point.
If, moreover, M is assumed to be geodesically complete, then the theorem holds globally, and each M[i] is a geodesically complete manifold.^[8]
The Berger classification
In 1955, M. Berger gave a complete classification of possible holonomy groups for simply connected, Riemannian manifolds which are irreducible (not locally a product space) and nonsymmetric (not
locally a Riemannian symmetric space). Berger's list is as follows:
Manifolds with holonomy Sp(n)·Sp(1) were simultaneously studied in 1965 by Edmond Bonan and Vivian Yoh Kraines and they constructed the parallel 4-form.
Manifolds with holonomy G[2] or Spin(7) were firstly introduced by Edmond Bonan in 1966, who constructed all the parallel forms and showed that those manifolds were Ricci-flat.
Berger's original list also included the possibility of Spin(9) as a subgroup of SO(16). Riemannian manifolds with such holonomy were later shown independently by D. Alekseevski and Brown-Gray to be
necessarily locally symmetric, i.e., locally isometric to the Cayley plane F[4]/Spin(9) or locally flat. See below.) It is now known that all of these possibilities occur as holonomy groups of
Riemannian manifolds. The last two exceptional cases were the most difficult to find. See G[2] manifold and Spin(7) manifold.
Note that Sp(n) ⊂ SU(2n) ⊂ U(2n) ⊂ SO(4n), so every hyperkähler manifold is a Calabi–Yau manifold, every Calabi–Yau manifold is a Kähler manifold, and every Kähler manifold is orientable.
The strange list above was explained by Simons's proof of Berger's theorem. A simple and geometric proof of Berger's theorem was given by Carlos E. Olmos in 2005. One first shows that if a Riemannian
manifold is not a locally symmetric space and the reduced holonomy acts irreducibly on the tangent space, then it acts transitively on the unit sphere. The Lie groups acting transitively on spheres
are known: they consist of the list above, together with 2 extra cases: the group Spin(9) acting on R^16, and the group T · Sp(m) acting on R^4m. Finally one checks that the first of these two extra
cases only occurs as a holonomy group for locally symmetric spaces (that are locally isomorphic to the Cayley projective plane), and the second does not occur at all as a holonomy group.
Berger's original classification also included non-positive-definite pseudo-Riemannian metric non-locally symmetric holonomy. That list consisted of SO(p,q) of signature (p, q), U(p, q) and SU(p, q)
of signature (2p, 2q), Sp(p, q) and Sp(p, q)·Sp(1) of signature (4p, 4q), SO(n, C) of signature (n, n), SO(n, H) of signature (2n, 2n), split G[2] of signature (4, 3), G[2](C) of signature (7, 7),
Spin(4, 3) of signature (4, 4), Spin(7, C) of signature (7,7), Spin(5,4) of signature (8,8) and, lastly, Spin(9, C) of signature (16,16). The split and complexified Spin(9) are necessarily locally
symmetric as above and should not have been on the list. The complexified holonomies SO(n, C), G[2](C), and Spin(7,C) may be realized from complexifying real analytic Riemannian manifolds. The last
case, manifolds with holonomy contained in SO(n, H), were shown to be locally flat by R. McLean.^[9]
Riemannian symmetric spaces, which are locally isometric to homogeneous spaces G/H have local holonomy isomorphic to H. These too have been completely classified.
Finally, Berger's paper lists possible holonomy groups of manifolds with only a torsion-free affine connection; this is discussed below.
Special holonomy and spinors
Manifolds with special holonomy are characterized by the presence of parallel spinors, meaning spinor fields with vanishing covariant derivative.^[10] In particular, the following facts hold:
• Hol(ω) ⊂ U(n) if and only if M admits a covariantly constant (or parallel) projective pure spinor field.
• If M is a spin manifold, then Hol(ω) ⊂ SU(n) if and only if M admits at least two linearly independent parallel pure spinor fields. In fact, a parallel pure spinor field determines a canonical
reduction of the structure group to SU(n).
• If M is a seven-dimensional spin manifold, then M carries a non-trivial parallel spinor field if and only if the holonomy is contained in G[2].
• If M is an eight-dimensional spin manifold, then M carries a non-trivial parallel spinor field if and only if the holonomy is contained in Spin(7).
The unitary and special unitary holonomies are often studied in connection with twistor theory,^[11] as well as in the study of almost complex structures.^[10]
String Theory
Riemannian manifolds with special holonomy play an important role in string theory compactifications. ^[12] This is because special holonomy manifolds admit covariantly constant (parallel) spinors
and thus preserve some fraction of the original supersymmetry. Most important are compactifications on Calabi–Yau manifolds with SU(2) or SU(3) holonomy. Also important are compactifications on G[2]
Machine Learning
Computing the holonomy of Riemannian manifolds has been suggested as a way to learn the structure of data manifolds in machine learning, in particular in the context of manifold learning. As the
holonomy group contains information about the global structure of the data manifold, it can be used to identify how the data manifold might decompose into a product of submanifolds. The holonomy
cannot be computed exactly due to finite sampling effects, but it is possible to construct a numerical approximation using ideas from spectral graph theory similar to Vector Diffusion Maps. The
resulting algorithm, the Geometric Manifold Component Estimator (GeoManCEr) gives a numerical approximation to the de Rham decomposition that can be applied to real-world data.^[13]
Affine holonomy
Affine holonomy groups are the groups arising as holonomies of torsion-free affine connections; those which are not Riemannian or pseudo-Riemannian holonomy groups are also known as non-metric
holonomy groups. The de Rham decomposition theorem does not apply to affine holonomy groups, so a complete classification is out of reach. However, it is still natural to classify irreducible affine
On the way to his classification of Riemannian holonomy groups, Berger developed two criteria that must be satisfied by the Lie algebra of the holonomy group of a torsion-free affine connection which
is not locally symmetric: one of them, known as Berger's first criterion, is a consequence of the Ambrose–Singer theorem, that the curvature generates the holonomy algebra; the other, known as
Berger's second criterion, comes from the requirement that the connection should not be locally symmetric. Berger presented a list of groups acting irreducibly and satisfying these two criteria; this
can be interpreted as a list of possibilities for irreducible affine holonomies.
Berger's list was later shown to be incomplete: further examples were found by R. Bryant (1991) and by Q. Chi, S. Merkulov, and L. Schwachhöfer (1996). These are sometimes known as exotic holonomies.
The search for examples ultimately led to a complete classification of irreducible affine holonomies by Merkulov and Schwachhöfer (1999), with Bryant (2000) showing that every group on their list
occurs as an affine holonomy group.
The Merkulov–Schwachhöfer classification has been clarified considerably by a connection between the groups on the list and certain symmetric spaces, namely the hermitian symmetric spaces and the
quaternion-Kähler symmetric spaces. The relationship is particularly clear in the case of complex affine holonomies, as demonstrated by Schwachhöfer (2001).
Let V be a finite-dimensional complex vector space, let H ⊂ Aut(V) be an irreducible semisimple complex connected Lie subgroup and let K ⊂ H be a maximal compact subgroup.
1. If there is an irreducible hermitian symmetric space of the form G/(U(1) · K), then both H and C*· H are non-symmetric irreducible affine holonomy groups, where V the tangent representation of K.
2. If there is an irreducible quaternion-Kähler symmetric space of the form G/(Sp(1) · K), then H is a non-symmetric irreducible affine holonomy groups, as is C* · H if dim V = 4. Here the
complexified tangent representation of Sp(1) · K is C^2 ⊗ V, and H preserves a complex symplectic form on V.
These two families yield all non-symmetric irreducible complex affine holonomy groups apart from the following:
{\displaystyle {\begin{aligned}\mathrm {Sp} (2,\mathbf {C} )\cdot \mathrm {Sp} (2n,\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{2}\otimes \mathbf {C} ^{2n}\right)\\G_{2}(\mathbf {C} )&
\subset \mathrm {Aut} \left(\mathbf {C} ^{7}\right)\\\mathrm {Spin} (7,\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{8}\right).\end{aligned}}}
Using the classification of hermitian symmetric spaces, the first family gives the following complex affine holonomy groups:
{\displaystyle {\begin{aligned}Z_{\mathbf {C} }\cdot \mathrm {SL} (m,\mathbf {C} )\cdot \mathrm {SL} (n,\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{m}\otimes \mathbf {C} ^{n}\right)\\
Z_{\mathbf {C} }\cdot \mathrm {SL} (n,\mathbf {C} )&\subset \mathrm {Aut} \left(\Lambda ^{2}\mathbf {C} ^{n}\right)\\Z_{\mathbf {C} }\cdot \mathrm {SL} (n,\mathbf {C} )&\subset \mathrm {Aut} \
left(S^{2}\mathbf {C} ^{n}\right)\\Z_{\mathbf {C} }\cdot \mathrm {SO} (n,\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{n}\right)\\Z_{\mathbf {C} }\cdot \mathrm {Spin} (10,\mathbf {C} )&
\subset \mathrm {Aut} \left(\Delta _{10}^{+}\right)\cong \mathrm {Aut} \left(\mathbf {C} ^{16}\right)\\Z_{\mathbf {C} }\cdot E_{6}(\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{27}\
where Z[C] is either trivial, or the group C*.
Using the classification of quaternion-Kähler symmetric spaces, the second family gives the following complex symplectic holonomy groups:
{\displaystyle {\begin{aligned}\mathrm {Sp} (2,\mathbf {C} )\cdot \mathrm {SO} (n,\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{2}\otimes \mathbf {C} ^{n}\right)\\(Z_{\mathbf {C} }\,\
cdot )\,\mathrm {Sp} (2n,\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{2n}\right)\\Z_{\mathbf {C} }\cdot \mathrm {SL} (2,\mathbf {C} )&\subset \mathrm {Aut} \left(S^{3}\mathbf {C} ^{2}\
right)\\\mathrm {Sp} (6,\mathbf {C} )&\subset \mathrm {Aut} \left(\Lambda _{0}^{3}\mathbf {C} ^{6}\right)\cong \mathrm {Aut} \left(\mathbf {C} ^{14}\right)\\\mathrm {SL} (6,\mathbf {C} )&\subset
\mathrm {Aut} \left(\Lambda ^{3}\mathbf {C} ^{6}\right)\\\mathrm {Spin} (12,\mathbf {C} )&\subset \mathrm {Aut} \left(\Delta _{12}^{+}\right)\cong \mathrm {Aut} \left(\mathbf {C} ^{32}\right)\\E_
{7}(\mathbf {C} )&\subset \mathrm {Aut} \left(\mathbf {C} ^{56}\right)\\\end{aligned}}}
(In the second row, Z[C] must be trivial unless n = 2.)
From these lists, an analogue of Simons's result that Riemannian holonomy groups act transitively on spheres may be observed: the complex holonomy representations are all prehomogeneous vector spaces
. A conceptual proof of this fact is not known.
The classification of irreducible real affine holonomies can be obtained from a careful analysis, using the lists above and the fact that real affine holonomies complexify to complex ones.
There is a similar word, "holomorphic", that was introduced by two of Cauchy's students, Briot (1817–1882) and Bouquet (1819–1895), and derives from the Greek ὅλος (holos) meaning "entire", and μορφή
(morphē) meaning "form" or "appearance".^[14] The etymology of "holonomy" shares the first part with "holomorphic" (holos). About the second part:
"It is remarkably hard to find the etymology of holonomic (or holonomy) on the web. I found the following (thanks to John Conway of Princeton): 'I believe it was first used by Poinsot in his
analysis of the motion of a rigid body. In this theory, a system is called "holonomic" if, in a certain sense, one can recover global information from local information, so the meaning
"entire-law" is quite appropriate. The rolling of a ball on a table is non-holonomic, because one rolling along different paths to the same point can put it into different orientations. However,
it is perhaps a bit too simplistic to say that "holonomy" means "entire-law". The "nom" root has many intertwined meanings in Greek, and perhaps more often refers to "counting". It comes from the
same Indo-European root as our word "number." ' "
See νόμος (nomos) and -nomy.
See also
• Agricola, Ilka (2006), "The Srni lectures on non-integrable geometries with torsion", Arch. Math., 42: 5–84, arXiv:math/0606705, Bibcode:2006math......6705A
• Ambrose, Warren; Singer, Isadore (1953), "A theorem on holonomy", Transactions of the American Mathematical Society, 75 (3): 428–443, doi:10.2307/1990721, JSTOR 1990721
• Baum, H.; Friedrich, Th.; Grunewald, R.; Kath, I. (1991), Twistors and Killing spinors on Riemannian manifolds, Teubner-Texte zur Mathematik, vol. 124, B.G. Teubner, ISBN 9783815420140
• Berger, Marcel (1953), "Sur les groupes d'holonomie homogènes des variétés a connexion affines et des variétés riemanniennes", Bull. Soc. Math. France, 83: 279–330, MR 0079806, archived from the
original on 2007-10-04
• Besse, Arthur L. (1987), Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, ISBN 978-3-540-15279-8
• Bonan, Edmond (1965), "Structure presque quaternale sur une variété différentiable", C. R. Acad. Sci. Paris, 261: 5445–8.
• Bonan, Edmond (1966), "Sur les variétés riemanniennes à groupe d'holonomie G2 ou Spin(7)", C. R. Acad. Sci. Paris, 320: 127–9].
• Borel, Armand; Lichnerowicz, André (1952), "Groupes d'holonomie des variétés riemanniennes", Les Comptes rendus de l'Académie des sciences, 234: 1835–7, MR 0048133
• Bryant, Robert L. (1987), "Metrics with exceptional holonomy", Annals of Mathematics, 126 (3): 525–576, doi:10.2307/1971360, JSTOR 1971360.
• Bryant, Robert L. (1991), "Two exotic holonomies in dimension four, path geometries, and twistor theory", Complex Geometry and Lie Theory, Proceedings of Symposia in Pure Mathematics, vol. 53,
pp. 33–88, doi:10.1090/pspum/053/1141197, ISBN 9780821814925
• Bryant, Robert L. (2000), "Recent Advances in the Theory of Holonomy", Astérisque, Séminaire Bourbaki 1998–1999, 266: 351–374, arXiv:math/9910059
• Cartan, Élie (1926), "Sur une classe remarquable d'espaces de Riemann", Bulletin de la Société Mathématique de France, 54: 214–264, doi:10.24033/bsmf.1105, ISSN 0037-9484, MR 1504900
• Cartan, Élie (1927), "Sur une classe remarquable d'espaces de Riemann", Bulletin de la Société Mathématique de France, 55: 114–134, doi:10.24033/bsmf.1113, ISSN 0037-9484
• Chi, Quo-Shin; Merkulov, Sergey A.; Schwachhöfer, Lorenz J. (1996), "On the Incompleteness of Berger's List of Holonomy Representations", Invent. Math., 126 (2): 391–411, arXiv:dg-da/9508014,
Bibcode:1996InMat.126..391C, doi:10.1007/s002220050104, S2CID 119124942
• Golwala, S. (2007), Lecture Notes on Classical Mechanics for Physics 106ab (PDF)
• Joyce, D. (2000), Compact Manifolds with Special Holonomy, Oxford University Press, ISBN 978-0-19-850601-0
• Kobayashi, S.; Nomizu, K. (1963), Foundations of Differential Geometry, Vol. 1 & 2 (New ed.), Wiley-Interscience (published 1996), ISBN 978-0-471-15733-5
• Kraines, Vivian Yoh (1965), "Topology of quaternionic manifolds", Bull. Amer. Math. Soc., 71, 3, 1 (3): 526–7, doi:10.1090/s0002-9904-1965-11316-7.
• Lawson, H. B.; Michelsohn, M-L. (1989), Spin Geometry, Princeton University Press, ISBN 978-0-691-08542-5
• Lichnerowicz, André (2011) [1976], Global Theory of Connections and Holonomy Groups, Springer, ISBN 9789401015523
• Markushevich, A.I. (2005) [1977], Silverman, Richard A. (ed.), Theory of functions of a Complex Variable (2nd ed.), American Mathematical Society, p. 112, ISBN 978-0-8218-3780-1
• Merkulov, Sergei A.; Schwachhöfer, Lorenz J. (1999), "Classification of irreducible holonomies of torsion-free affine connections", Annals of Mathematics, 150 (1): 77–149, arXiv:math/9907206, doi
:10.2307/121098, JSTOR 121098, S2CID 17314244 ; Merkulov, Sergei; Schwachhöfer, Lorenz (1999), "Addendum", Ann. of Math., 150 (3): 1177–9, arXiv:math/9911266, doi:10.2307/121067, JSTOR 121067,
S2CID 197437925..
• Olmos, C. (2005), "A geometric proof of the Berger Holonomy Theorem", Annals of Mathematics, 161 (1): 579–588, doi:10.4007/annals.2005.161.579
• Sharpe, Richard W. (1997), Differential Geometry: Cartan's Generalization of Klein's Erlangen Program, Springer-Verlag, ISBN 978-0-387-94732-7, MR 1453120
• Schwachhöfer, Lorenz J. (2001), "Connections with irreducible holonomy representations", Advances in Mathematics, 160 (1): 1–80, doi:10.1006/aima.2000.1973
• Simons, James (1962), "On the transitivity of holonomy systems", Annals of Mathematics, 76 (2): 213–234, doi:10.2307/1970273, JSTOR 1970273, MR 0148010
• Spivak, Michael (1999), A comprehensive introduction to differential geometry, vol. II, Houston, Texas: Publish or Perish, ISBN 978-0-914098-71-3
• Sternberg, S. (1964), Lectures on differential geometry, Chelsea, ISBN 978-0-8284-0316-0
Further reading
• Literature about manifolds of special holonomy, a bibliography by Frederik Witt. | {"url":"https://www.knowpia.com/knowpedia/Holonomy","timestamp":"2024-11-12T05:53:05Z","content_type":"text/html","content_length":"284923","record_id":"<urn:uuid:fdbcd5b5-b1d9-403a-97df-253fefeb9c9c>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00880.warc.gz"} |
What Is an Identity in Math Can Be Fun for Everyone
Things You Won’t Like About What Is an Identity in Math and Things You Will
For instance, if you’ve got two terms on the left side and only a single term on the correct side, find the frequent denominator and add both terms on the left side in order that they become one. The
important thing is to select the derivative. For instance, if you’ve got a number which is being multiplied that you have to move to the other side of the equation, then you would divide it from
either side of that equation. A term is a mathematical expression that might form a separable portion of an equation, a series, or a different expression. The preponderance of self-selected
hyphenated names utilised in academia as a way of virtue signaling.
The Secret to What Is an Identity in Math
Engaging http://quzhur.com/6202.html children with an assortment of measurement concepts is a fantastic start. This refers to the lifestyles that individuals embrace in becoming part of a society.
Thus, please take a moment to reassess these few concepts to be sure you understand what they mean. It relates to such a wide variety of concepts. So just bear that in mind for the time being.
The True Meaning of What Is an Identity in Math
In financial decisions this is able to save you a great deal of finances or maybe get you the very best price available. We will need to become in the practice of doing more than accepting the very
first correct answer and moving on. It is not the very first time the project was attacked. Engage in ways to shift thoughts in order to raise calmness and confidence in respect to math.
The War Against What Is an Identity in Math
Multiplication is the procedure of repeated addition. This leads to some other way of solving systems of equations. In the remainder of this section, a technique is developed for locating a
multiplicative inverse for square matrices. Multiplying by the conjugate is a great technique for showing that these 2 forms are equivalent.
Here, we supply completely free math tutoring online. It is possible to get these absolutely free worksheets also by going to the individual book pages at MathMammoth.com. Utilizing picture books is
an excellent way to start conversations about mathematics beyond the standard context of solving equations. That too is going to be the fault of Whiteness. It’s taught to students that are presumed
to haven’t any knowledge of mathematics beyond the fundamental essentials of arithmetic. Give students time to analyze the term from a mathematical perspective in accordance with their level.
Information for degrees and certificates offered for the regions of concentration are observed in the training course catalog. In general, it is a significant crime when it comes to sheer numbers.
Proving trigonometric identities might be big challenge for students, as it’s often very different from anything they’ve previously done. Gender differs from sex in that it doesn’t have any intrinsic
link to anatomy. For each definition, the students are going to have only 60 seconds to recognize the suitable word.
Let’s take a close look. These is achieved by a double-click. We’re simply not smart enough.
In addition to the significant financial damage this could cause, it might also cause incorrect medical history to be added to your medical files. It’s far better make sure you’re utilizing the most
recent version of your preferred web browser. By that moment, there might be quite so much damage done to their credit report that it may take what may look like a lifetime to fix. If you get any
credit reports, immediately place a freeze on the account and work with the 3 credit bureaus to fix your son’s or daughter’s credit. Utilize Expand also wherever there’s no room for extra insertion.
The number line is utilized to symbolize integers. Otherwise, you can imagine a prime number for a number greater than one that isn’t the product of smaller numbers. When you multiply a number with a
different one, you’re repeatedly including a number by the range of times stated by the other number. Don’t use your previous password.
The Chronicles of What Is an Identity in Math
Most people unfamiliar with this sort of dilemma will select the first alternative. Such an identity theft is really straight forward a criminal will employ your identity to find medical therapy or
drugs. If it was as simple as wearing men’s clothes and visiting the football game with the remainder of them, there wouldn’t be a demand for an individual gender identity for dfab people who
identify as male. I don’t know whether you’ve seen all of the news relating to this thing called conversion therapy, but there are lots of smart individuals that are worried about the long-term
effects of attempting to modify your sexuality or gender identity. And there isn’t anything wrong about being outside of the conventional gender binary, except once the world attempts to prevent you
from expressing it. Also, it’s interesting how a single person can belong to numerous groups in forming her or his identity.
Some teachers will allow you to work down both sides until both sides match up. Repeat the process so the kid can observe the range of fruits is the exact same. Spooky and mysterious indeedunless,
obviously, the patterns were produced by humans. There isn’t anything wrong about love, regardless of what direction it flies. All we must do is multiply either side of the equation by the exact
What Is an Identity in Math at a Glance
You’re likely to need to actually define the true world and the non-real world. The issue is some mental models aren’t like others. The strategy may be to concentrate on a decrease price point or
that it is a locally-owned small business. Otherwise it wouldn’t be possible to discover both products. The FreshPet brand highlights its usage of unprocessed ingredients. The genuine difference in
the item and that of the competition may be minuscule or nonexistent.
Cubic quantities of dots can be arranged to create a cube. At some step in the solving of the equation you will receive exactly the same IDENTICAL terms on each side of the equation. The trigonometry
identities There are scores of identities in the discipline of trigonometry. Match trig functions (such as tan) to what’s on the opposite side. For this specific activity, I’ll concentrate on some
trigonometric identities which can be derived utilizing the Pythagorean Theorem. | {"url":"https://eclair-tn.com/en/whatisanidentityinmathcanbefunforeveryone/","timestamp":"2024-11-03T00:37:23Z","content_type":"text/html","content_length":"74188","record_id":"<urn:uuid:0afd9bfd-71be-4b3b-a014-820bb0175c9a>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00106.warc.gz"} |
Martin's blog
In my previous post on hierarchical loss for multi-label classification I gave an implementation of a specific algorithm for calculating the loss between two trees. I then added a quick edit
mentioning that "this algorithm doesn't work too well in practice", and today I want to delve into why.
Imagine you want to predict the cities where someone lived based on some data. The hierarchy of locations is a tree with country at the first level, province or state second, and city at its third
level. This tree has ca. 195 nodes on its first level and a lot more as we go down the tree.
Let's now say that I was supposed to choose Argentina.Misiones.Posadas (which corresponds to a city in Argentina) but I predicted Congo.Bouenza.Loutété; (which is the 10th most popular city in the
Republic of Congo). The loss for this prediction is 0.01, which is surprisingly low - seeing as I wasn't even close to the real answer, I would have expected something near 1.
As we go deeper into the tree, the loss goes down real quick. If I had predicted Argentina.Chubut.Puerto Madryn (a city 1900km away in one of the other 23 possible provinces) the loss would be
0.00043, and if I had predicted Argentina.Misiones.Wanda (one of the other 64 cities in the correct province) my loss would have been 0.000019. If your tree is deeper than this then you will soon
start running into numerical issues.
The problem here is the nature of the problem itself. Because my predictions are multi-label there is no limit to the number of cities where a person may have lived while, simultaneously, there is no
limit to how many cities I may predict. If I predict that a person has lived in every single city in America, from Ward Hunt Island Camp in Canada down to Ushuaia in Argentina and everything in
between, but it turns out that the person has lived in all other cities in the world, my loss would only then be 1. And if it turns out that the person has briefly lived in Argentina.Misiones.Posadas
then my loss goes down to ~0.995 because getting one city right also means that I got the country right.
Now you see why this algorithm is very good in theory but not useful in practice: if you are trying to predict one or two points in a big tree then your losses will always be negligible. No matter
how wrong your prediction is, the loss for a "normal" person will never be high enough to be useful.
On the other hand, if you are expecting your predictions to cover a good chunk of the tree then this algorithm is still right for you. Otherwise a good alternative is to use the Jaccard distance
instead and represent Argentina.Misiones.Posadas as the set {"Argentina", "Argentina.Misiones", "Argentina.Misiones.Posadas"}. This is not as fair a measure as I would like (it punishes small errors
a bit too harshly) but it still works well in practice. You could also look deeper into the paper and see if the non-normalized algorithms work for you.
Here's one of those problems that sounds complicated but, when you take a deep dive into it, turns out to be just as complicated as it sounds.
Suppose you build a classifier that takes a book and returns its classification according to the Dewey Decimal System. This classifier would take a book such as "The return of Sherlock Holmes" and
classify it as, say, "Fiction".
Of course, life is rarely this easy. This book in particular is more often than not classified as 823.8, "Literature > English > Fiction > Victorian period 1837-1900". The stories, however, were
written between 1903 and 1904, meaning that some librarians would rather file it under 823.912, "Literature > English > Fiction > Modern Period > 20th Century > 1901-1945".
Other books are more complicated. Tina Fey's autobiography Bossypants can be classified under any of the following categories:
• Arts and Recreation > Amusements and Recreation > Public Entertainments, TV, Movies > Biography And History > Biography
• Arts and Recreation > Amusements and Recreation > Stage presentations > Biography And History > Biography
• Literature > American And Canadian > Authors, American and American Miscellany > 21st Century
This is known as a hierarchical multi-label classification problem:
• It is hierarchical because the expected classification is part of a hierarchy. We could argue whether Sherlock Holmes should be classified as "Victorian" or "Modern", but we would all agree that
either case is not as bad as classifying it under "Natural Science and Mathematics > Chemistry".
• It is multi-label because there is more than one possible valid class. Tina Fey is both a Public entertainer and an American. There is no need to choose just one.
• It is classification because we need to choose the right bin for this book.
• It is a problem because I had to solve it this week and it wasn't easy.
There seems to be exactly one paper on this topic, Incremental algorithms for hierarchical classification, and is not as easy to read as one would like (and not just because it refers to Section 4
when in reality should be Section 5). Luckily, this survey on multi-label learning presents a simpler version.
I ended up writing a test implementation to ensure I had understood the solution correctly, and decided that it would be a shame to just throw it away. So here it is. This version separates levels in
a tree with '.' characters and is optimized for clarity.
Edit June 17: this algorithm doesn't work too well in practice. I'll write about its shortcomings soon, but until then you should think twice about using it as it is.
Edit June 26: Part II of this article is now up
from collections import defaultdict
def parent(node):
""" Given a node in a tree, returns its parent node.
node : str
Node whose parent I'm interested in.
Parent node of the input node or None if the input Node is already a
root node.
In truth, returning '' for root nodes would be acceptable. However,
None values force us to think really hard about our assumptions at every
parent_str = '.'.join(node.split('.')[:-1])
if parent_str == '':
parent_str = None
return parent_str
def nodes_to_cost(taxonomy):
""" Calculates the costs associated with errors for a specific node in a
taxonomy : set
Set of all subtrees that can be found in a given taxonomy.
A cost for every possible node in the taxonomy.
Implements the weight function from
Cesa-bianchi, N., Zaniboni, L., and Collins, M. "Incremental algorithms for
hierarchical classification". In Journal of Machine Learning Research,
pages 31–54. MIT Press, 2004.
assert taxonomy == all_subtrees(taxonomy), \
"There are missing subnodes in the input taxonomy"
# Set of nodes at every depth
depth_to_nodes = defaultdict(set)
# How many children does a node have
num_children = defaultdict(int)
for node in taxonomy:
depth = len(node.split('.'))-1
parent_node = parent(node)
if parent_node is not None:
num_children[parent_node] += 1
cost = dict()
for curr_depth in range(1+max(depth_to_nodes.keys())):
for node in depth_to_nodes[curr_depth]:
if curr_depth == 0:
# Base case: parent node
cost[node] = 1.0/len(depth_to_nodes[curr_depth])
# General case: node guaranteed to have a parent
parent_node = parent(node)
cost[node] = cost[parent_node]/num_children[parent_node]
return cost
def all_subtrees(leaves):
""" Given a set of leafs, ensures that all possible subtrees are
included in the set too.
leaves : set
A set of selected subtrees from the overall category tree.
A set containing the original subtrees plus all possible subtrees
contained in these leaves.
Example: if leaves = {"01.02", "01.04.05"}, then the returned value is the
set {"01", "01.02", "01.04", "01.04.05"}.
full_set = set()
for leave in leaves:
parts = leave.split('.')
for i in range(len(parts)):
return full_set
def h_loss(labels1, labels2, node_cost):
""" Calculates the Hierarchical loss for the given two sets.
labels1 : set
First set of labels
labels2 : set
Second set of labels
node_cost : dict
A map between tree nodes and the weight associated with them.
If you want a loss between 0 and 1, the `nodes_to_cost` function implements
such a function.
Loss between the two given sets.
The nicer reference of the algorithm is to be found in
Sorower, Mohammad S. "A literature survey on algorithms for multi-label
learning." Oregon State University, Corvallis (2010).
# We calculate the entire set of subtrees, just in case.
all_labels1 = all_subtrees(labels1)
all_labels2 = all_subtrees(labels2)
# Symmetric difference between sets
sym_diff = all_labels1.union(all_labels2) - \
loss = 0
for node in sym_diff:
parent_node = parent(node)
if parent_node not in sym_diff:
loss += node_cost[node]
return loss
if __name__ == '__main__':
# Simple usage example
taxonomy = set(["01", "01.01", "01.02", "01.03", "01.04", "01.05",
"02", "02.01", "02.02", "02.03", "02.03.01"])
weights = nodes_to_cost(taxonomy)
node_2=set(['01.01', '02'])
print(h_loss(node_1, node_2, weights)) | {"url":"https://7c0h.com/blog/tag/classification.html","timestamp":"2024-11-11T20:14:46Z","content_type":"text/html","content_length":"34366","record_id":"<urn:uuid:7d8741b9-1827-4a72-a79e-fa2215bfce0e>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00829.warc.gz"} |
4.4 Geolocation
Positioning a BIM Model using Geolocation
Cartesian coordinates are a way to pinpoint locations on the Earth's surface. They use a grid system that divides the world into zones, like slices of an orange, to make it easier to specify a
location accurately.
Every UTM coordinate is composed of 3 main variables:
• Zone (only for some coordinate systems) - Predefined "slice" of the earth. Each zone has its own set of coordinates, making it simpler to communicate precise locations.
• Easting (E/W) - Distance in meters of how far to the right a point is within its zone
• Northing (N/S) - Distance in meters of how far up it is from the equator.
You can use this system to quickly position your Revit (or other) models in your cmBuilder scenario and here is how:
1. Add your coordinate system to your cmBuilder project
1. Go to your project, and enter Project Settings → Coordinate Settings
2. The appropriate UTM zone is automatically added to all projects. You can delete it if you would like.
3. You can add a new coordinate system by clicking the Add button. You will need to search by part of the coordinate system name. If you need help with this, please reach out to us.
2. Geolocate your model
Once you have uploaded your model in your scenario, you can perform this step.
1. In your model sidesheet, access Move
2. Choose Project Origin
3. Change the Coordinate System to the one you intend to use for geolocation
4. Enter your coordinate values. Note that there are 3 different situations for locating your model:
1. You have the Latitude & Longitude values for your model
2. You have the Easting & Northing values for your model
3. Your model's origin has an Easting & Northing of 0,0.
☆ In Revit, you can identify #2 or #3 by the values of your project origin:
5. If you have situation #2, you will want to also apply your rotation to 0 in your coordinate system.
6. If you have situation #3, you should apply the Transform that is provided (it will adjust the position and rotation).
3. Auto-position additional models
Make sure to use the same IFC export settings for any other models in this project that are using the same coordinates so they will align in cmBuilder.
Once these models are imported, use the "Snap to position using Another Model" function to align models together:
0 comments
Please sign in to leave a comment. | {"url":"https://support.cmbuilder.io/hc/en-us/articles/18089163884443-4-4-Geolocation","timestamp":"2024-11-02T16:05:42Z","content_type":"text/html","content_length":"43110","record_id":"<urn:uuid:3438a5d5-98a3-48be-8f64-e53c4d4ef520>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00436.warc.gz"} |
A student asked “What is a cobordism?” and I checked and realized that the $n$Lab entry cobordism was effectively empty.
So I have now added some basic text in the Idea-section and added a bare minimum of references. Much more should be done of course, but at least now there are pointers.
added graphics (here) illustrating the “pair creation” cobordism for 0-dimensional submanifolds, and its Cohomoitopy charge map
diff, v27, current | {"url":"https://nforum.ncatlab.org/discussion/5712/cobordism/?Focus=45492","timestamp":"2024-11-14T21:14:05Z","content_type":"application/xhtml+xml","content_length":"14448","record_id":"<urn:uuid:2fff1685-e093-4b2d-87de-e03e650ffec9>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00231.warc.gz"} |
I Beam Dimensions Chart
I Beam Dimensions Chart - Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Customary and metric units are both included. Compare the
moment of inertia, elastic. Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Web aisc shapes database v16.0
replaces v15.0.
I Beams or HBeams Structural Steel Metal and Steel Beams, Trusses
Customary and metric units are both included. Web aisc shapes database v16.0 replaces v15.0. Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide
channel i beam as follows: Compare the moment of inertia, elastic. Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam.
I Beam Specifications Chart Design Talk
Compare the moment of inertia, elastic. Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Web aisc shapes database v16.0 replaces v15.0.
Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Customary and metric.
IBeams The Steel Yard
Customary and metric units are both included. Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Compare the moment
of inertia, elastic. Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Web aisc shapes.
I Beam Chart Pdf
Compare the moment of inertia, elastic. Customary and metric units are both included. Web aisc shapes database v16.0 replaces v15.0. Web 69 rows the following chart table gives cross section
engineering data for astm structural steel wide channel i beam as follows: Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam.
I Beam Dimensions Chart
Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Web use this tool to get the beam sizes of regular shapes,
including i beam sizes, h beam sizes and hss sizes. Compare the moment of inertia, elastic. Web aisc shapes database v16.0 replaces v15.0. Customary and metric.
I Beam Sizes And Dimensions Design Talk
Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Web aisc shapes database v16.0 replaces v15.0. Web use this tool
to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Compare the moment of inertia, elastic. Customary and metric.
I Beam Size Chart Metric New Images Beam
Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Web use this tool to get the beam sizes of regular shapes,
including i beam sizes, h beam sizes and hss sizes. Compare the moment of inertia, elastic. Customary and metric units are both included. Web aisc shapes.
I Beam Chart Pdf
Customary and metric units are both included. Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Web use this tool to
get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Web aisc shapes database v16.0 replaces v15.0. Compare the.
I Beam Size Chart Inches
Compare the moment of inertia, elastic. Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Web 69 rows the following chart table gives
cross section engineering data for astm structural steel wide channel i beam as follows: Web aisc shapes database v16.0 replaces v15.0. Customary and metric.
Carnegie steel I beam profile dimensions
Compare the moment of inertia, elastic. Web aisc shapes database v16.0 replaces v15.0. Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes.
Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Customary and metric.
Web 69 rows the following chart table gives cross section engineering data for astm structural steel wide channel i beam as follows: Web aisc shapes database v16.0 replaces v15.0. Web use this tool
to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes. Customary and metric units are both included. Compare the moment of inertia, elastic.
Web 69 Rows The Following Chart Table Gives Cross Section Engineering Data For Astm Structural Steel Wide Channel I Beam As Follows:
Customary and metric units are both included. Compare the moment of inertia, elastic. Web use this tool to get the beam sizes of regular shapes, including i beam sizes, h beam sizes and hss sizes.
Web aisc shapes database v16.0 replaces v15.0.
Related Post: | {"url":"https://untecs.edu.pe/en/I-Beam-Dimensions-Chart.html","timestamp":"2024-11-12T18:31:24Z","content_type":"text/html","content_length":"26256","record_id":"<urn:uuid:449f30d8-6649-43e9-9eac-b61f82b32f5f>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00025.warc.gz"} |
Decision Trees Quiz 1
0004. If my new study method works, I should earn a 98 on the test. If it does not work, I will get a 79. Research suggests that there is a 75% chance it works. What is the expected value of my
A. 87.5 B. 93.25 C. 95.5 D. 79 E. 98
This is an event tree problem, that is, there are no choices to be made. Work out the probabilities of each of the final outcomes.
There is a 72% chance that candidate A will win the presidency over candidate B. There is a 55% chance that candidate A's party will win control of the senate and a 30% chance that his party will
win control of the house.?
0006. I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300 and if one takes it, one is
certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course anyway and then retake the test
(total cost = prep course + twice the exam fee). Should I take the prep course??
0007. Continuation of previous question. I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300
and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course
anyway and then retake the test (total cost = prep course + twice the exam fee).
It turns out that there is pre-test I can take for a fee of $25. It will tell me whether I should take the prep course or not. People who fail the pretest are more likely than the average candidate
to fail the actual test if they do not take the prep course. In fact, the odds drop to only a 20 per cent chance of passing the exam on first try.
Should I pay for the pre-test and what should I do if I pass it? Fail it??
0008. Continuation of previous question. I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300
and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course
anyway and then retake the test (total cost = prep course + twice the exam fee).
It turns out that there is pre-test I can take for a fee of $25. It will tell me whether I should take the prep course or not. People who fail the pretest are more likely than the average candidate
to fail the actual test if they do not take the prep course. In fact, the odds drop to only a 20 per cent chance of passing the exam on first try.
At what pre-test price would I change my decision about taking it??
page revision: 5, last edited: 28 Aug 2013 22:14 | {"url":"http://djjr-courses.wikidot.com/ppol225:decisionquiz01","timestamp":"2024-11-14T18:59:50Z","content_type":"application/xhtml+xml","content_length":"32149","record_id":"<urn:uuid:2567a2eb-a0e8-42b9-997f-7595528e3fd0>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00111.warc.gz"} |
calculate crosswind component e6b
So if you're a half dot off as you approach the runway, you're going to be looking at the runway edge lights. Note that when reading the total wind velocity, follow the shape of the arcs from either
axis instead of tracing vertically or horizontally to the axes. Here is a method an E6B computer might use to calculate crosswind. . The limit for a PA28 is 17kts (only 12kts for a 152 I think).
Calculating the Crosswind components Follow-up to Crosswind Circuits - Lesson 14 from Christine's . To convert 50 degrees into radians, multiply by pi/180, there should be a pi symbol on your calc,
if not, use 3.141. Shop now: https://www.sportys.com/pilotshop/sporty-s-new-electronic-e6b-flight-computer.htmlOver 240,000 pilots have trusted Sportys Electronic E6Bs over the years for fast flight
planning and accurate FAA test calculations. Interested in the math behind this equation? Remember above when we told you to pay attention to the highlighted angles. While this is close enough to fly
with, its right in the middle between 2 of your exam question answers. Lets work through an example now and show how the dot product can be used to calculate the parallel and crosswind components.
The dot product of two vectors A and B is written \(A \cdot B\) (read as A dot B) and is interpreted as the magnitude of vector A multiplied by the magnitude of the component of B in the direction of
A. Check out the table below showing sine for a range of angles. Large aircraft leave trails of turbulent air behind them (especially when landing and taking off). If the magnitude of the crosswind
is too great, the pilot could lose control and the aircraft could potentially drift off the runway. By quickly estimating the crosswind using the above technique, youll be able to focus on the task
at hand. 30-degree wind angle. For most normally-aspirated airplanes, you add about 10% of takeoff roll distance for every 1,000' of density altitude (DA). Often enroute, winds shift, and the little
red/green thing is useless if it hasn't updated in flight. Sine. You will never need another aviation computer.FEATURES:- Backlit screen for night operations in the cockpit- Built-in storage case
protects the screen when not in use- Large keypad for easier operation in turbulence- Rubber feet keep the E6B from moving when in use- Quick reference card - 24 aviation functions- 20 aviation
conversions- Timer and clockShop all pilot supplies: https://www.sportys.com/pilotshop/ Check the table again. | Comments(14) It will ensure that you never exceed landing limits, provided you know
the wind direction and strength. 60 = 6 = 6/6 Considering the above rules, we need to multiply the wind speed by sine to give us a crosswind component strength. Quiz: Can You Answer These 6
Aerodynamics Questions? our airplane has a maximum demonstrated crosswind component of 17 knots, we should evaluate whether the current conditions are beyond our capabilities. Example: Locate the 30
diagonal line on the chart starting at point A, and follow that 30 line towards the center until the line intersects the 40-knot arc at point B. The age difference calculator determines the age gap
between two people. There is actually an official technique utilized when landing in a crosswind. Want a hint? This simple concept is super useful to know when flying. Look on the back of your E6B
for the Wind Correction Chart. The, difference between the runway heading and direction. Using a little simple math and a fair handful of rounding, you can make a really good estimate as to what the
crosswind is. We use the reported wind to decide which runway to use at a non-towered airport, but its extremely rare when a pilot decides not to attempt the landing at all and diverts to another
airport. Some E6Bs even let you calculate the crosswind components prior to landing at runways experiencing strong and/or gusty winds. Angle. Have you ever misunderstood or misread a clearance? The
subscripts refer to the components of the vectors in the x and y direction. Today we demonstrate how to perform a quick crosswind calculation and why it is important to know. How Pitot-Static
Failures Affect Your Indicated Airspeed And Altitude, How To Go Missed From A Circling Approach, High On Final? To get free tips like this each week, subscribe at the bottom of the page. Happy
flying. sin80 = 1.0 (any wind of more than 80 degrees and your cwc is the total wind). Pay particular attention to the highlighted angles and their sine They will be important a little later when we
show you how to perform a really quick crosswind calculation. if angle = 40 deg then crosswind component = 2/3 wind strength As you cross the threshold, 1/2 dot deflection on the localizer = about 1/
2 the runway width. A wind angle of 20 degrees means 20 minutes around the clock face, which is one-third of the way around the clock face. Please refer to our privacy policy for further information.
The most reliable and efficient way to calculate the head/tail wind and crosswind component of the wind relative to the runway heading is to make use of vector notation and the concept of the scalar
dot product. Quiz: These 6 Aerodynamic Designs Are For Quiz: Do You Know These 5 IFR Aircraft Requirements? Handy hints like this make learning to fly so much easier. Mostly it blows at a certain
angle and can be separated into two portions components. First, determine how many degrees off the runway heading the reported wind is. Before a flight, it is important to be familiar with all
current weather information. Skip to the end of the images . ILS: How The Instrument Landing System Works, Restricted Areas: What You Should Know, And How To Operate Around Them, Incorrect Altitude
Readback Leads To Near CFIT Incident. 50 = 5 = 5/6 Tony Harrison-Smith At 15 difference, the crosswind would be approximately 5 knots, At 30 difference, the crosswind would be approximately 10 knots,
At 45 difference, the crosswind would be approximately 15 knots, At 60 or greater difference, the crosswind would be approximately 20 knots. Also remember to convert the degree angles of the runway
and wind vector to radians if you are performing the calculation in a spreadsheet. Make an attempt beyond these limits, and you could find yourself in a sticky situation. Landing In Turbulence: How
To Make Smooth Touchdown, Dihedral: Why Your Wings Have An Upward Angle, How To Make A Perfect Short Field Takeoff. $$ \cos{\theta} = \frac{A \cdot B}{|A||B|} $$. Runway Number : Between 1 and 36.
STEP 3. Flying on an airplane and learning to navigate successfully. Headwind blows in the opposite direction. And if the wind is 60 degrees or more off the runway, the crosswind component is roughly
the same as the total wind. How will you know whether you need to apply it and to what degree unless you can make a valid assessment of the crosswind? What is the crosswind component of this wind? It
is at its highest when an angle reaches 90 and at its lowest when the angle is 0. Relax. D 25 kts. Even with the best weather data in the world, things can change quickly. sin60 = .9 (with a wind
from 60 degrees the cwc is the total wind minus 10%) Ps how u getting on i'm at 50 hours and getting ready for first solo nav Once we have determined this point, we can trace horizontal and vertical
lines to read the value of both the headwind and crosswind components, respectively. The difference between the Runway 01 or 10 degrees and the wind of 60 degrees is 50 degrees. But when you're
approaching an airport, how do you know when to start down? I would switch to degrees mode and try again. Wind affects the motion of vehicles and aircraft. Divide the altitude you need to lose by
300. One item that is frequently misunderstood is how to determine the crosswind component. Coffin Corner And Mach Tuck, Explained: Boldmethod Live, Why Fast Jets Have Swept Wings: Boldmethod Live,
How To Plan Your Arrival At An Unfamiliar Airport, 5 Ways To Prepare For Flying Into Busy Airports, 5 Things You Learn In Your First 50 Hours Of Instructing, How Airline Pilots Manage Maximum Landing
Weight, 8 Tips For Keeping Your Logbooks Clean, Professional, And Interview-Ready, 6 Questions You Should Be Prepared To Answer During Your CFI Interview. Here is a method an E6B computer might use
to calculate crosswind. Restricted airspace is an area typically used by the military where air traffic is restricted or prohibited for safety reasons. Pilots have to consider the effect of wind,
especially while landing or taking off. To calculate the crosswind, you will need three key pieces of information: . Because the directions are on a circle, the closest runway direction to the wind
could be on the opposite side of 360. 45-degree wind angle. xw = tw * sin (wd-heading) xw = crosswind component, tw = total wind, wd = wind direction. This method is the most accurate and, in my
opinion, most straightforward way to calculate a crosswind component in your head. I hadnt seen the one from Peter before. Lucky of all of us, there's an easier way. Note that the headwind + the
crosswind do not equal the wind speed. What makes the dot product so powerful is that it will correctly output the wind components for any combination of runway heading and wind vector, regardless of
whether the angle between them is acute or obtuse. How much crosswind component are you comfortable landing with? Quiz: Do You Know These 6 Uncommon VFR Chart Symbols? Well, watch what happens in our
next example, The wind has now shifted and is only 30 different from our heading. To keep that scan rate going, youll need a few tricks in the bag to estimate crosswind. Your answer of 21.666 looks
like youve used the sixths rule of thumb and calculated 5/6 of 26 knots. The good news is that a crosswind can help push this turbulent air away from the runway. Any exam paper is going to expect you
to round your answers in the safe direction, which in this case it upwards; ie. Keep in mind, you'll want to add a few miles on to your number, so you hit pattern altitude slightly before you get to
the airport. Email me with help as this is really confusing me. It is important to exercise good judgment in such a scenario and err on the side of caution. Using Peters method with Simons question
gives 18kts, when the answer is in fact 23kts. Go for the wingsuit http://www.timesonline.co.uk/tol/life_and_style/men/article4399319.ece by VFR pilots can make good use of the ILS too. Heres a
compact table where the wind speed stays the same and only the direction changes to make life easy. Crosswind component IS a speed. Ive tried various methods including rules of thumb, crosswind
charts and online calculators and the answers are consistently slightly more than 22knots. Wind Direction : Wind Speed : Gust Speed (if any) : Apply gusts at 50%. Quiz: Do You Know What These 5 ATC
Phrases Mean? Looking at the airport diagram in the chart supplement, find the numbers on the end of each runway. Make a note of your heading and calculate the difference between this and the wind
direction. Simon, I think the answer to your question is in fact A 23 knots. Now, add two: 3 + 2 = 5. Follow-up to Crosswind Circuits Lesson 14 from Christine's Flying blog, Cessna 152 has maximun
crosswind component of 12 kts. XWC is 18kts from the left. http://www.paragonair.com/public/aircraft/calc_crosswind.html, Headwind=(wind strength*cos(wind direction-runway direction) positive value
headwind, -ve value is a tailwind, Crosswind=(wind strength*sin(wind direction-runway direction) positive value crosswind is from the right, -ve from left, e.g. Determine, based on the 360 circle,
which runway is closest in direction to the wind direction given. 60 degrees off is 6/6ths - just assume full crosswind at 60 degrees and beyond. These represent the directions on a 360 circle, as
shown above. From that information, the pilot can decide whether it is wise to continue with the landing. Youll find that it works really well to quickly calculate crosswind. Dave I am also doing
circuits at the moment (at Southend) by | Phone: 800.874.5346 | Fax: 352.375.6940. item that is frequently misunderstood is how to determine the crosswind component. The curved lines depict the total
wind velocity. Calculating it with help of the e6b or other ways is often good to do before . C 17 kts The takeaway from the above should be that the greater the angle, the stronger the crosswind!
This Instructable will walk you through how to determine which runway to takeoff and land on, as well as how to find the crosswind and headwind components. This can cause severe upsets to the flight
path of a light aircraft. runway 31 wind 270/10 WA + 20 = %WV 40 + 20 = 60% of 10kts = 6kts, runway 24 wind 270/12 WA + 20 = %WV 30 + 20 = 50% of 12kts = 6kts, runway 18 wind 260/08 WA + 20 = %WV 80
+ 20 = 100% of 8kts = 8kts. E6B, NavLog Calculator, Weather Reports, METAR, TAF, Wind Components, Instrument Simulator, Weight and Balance, Pressure Altitude, Density Altitude, True Air Speed .
Depending on your calculator you have a few options. The crosswind component is one-third of the total wind. . In our scenario, take the wind direction of 210 and subtract the runway heading of 180,
giving us a difference of 30. Estimate the crosswind as 1/6th of the wind speed for each 10 degrees off the runway heading. Performing a quick crosswind calculation is easy once you understand the
basic principles. Thank You!Take our online PILOT GROUND SCHOOLPrivate Pilot:-Everything you need to know start to finish-How to choose an Instructor-How to perform the
maneuvers-Airspace-Landings-Oral and Checkride prep (premium version)-And so much more! Tracing vertically or horizontally leads to the crosswind and headwind components, respectively. Can You Take
Off With Another Plane On The Runway? If the wind is 30 degrees off the runway, your crosswind component is about 50% of the wind speed. Tell us in the comments below. Lucky of all of us, there's an
easier way. It represents a plane's magnetic direction of travel. This is an approximation to Juliexrays answer since the chart isnt really linear but for most purposes it is close enough. You can
either convert the degrees (060-010 = 50 by the way) to radians, or you can switch your calculator into degrees mode and try your calculation again. Here are 4 great rules-of-thumb to use on the hot
days ahead of you. Wind strength = 20kts If the wind is on one side of 360 and the runway is on the other, subtract the higher number from 360, and zero from the lower number. To use a crosswind
component chart follow these few steps: Find the line with the value of an angle between the wind direction and the direction you're facing (it should be between 0 and 90 degrees). Note that when
reading the total wind velocity. Then add the two numbers together to find the difference. At least it would require trigonometry if you didn't use some sort of flight computer, either [] Sure, the
angle is less, but the overall strength of the wind is higher. By making an on the spot appraisal of the crosswind, you can ensure you apply the right control inputs at the right time. As aviators,
we are required to interpret numerous charts for planning purposes. If you are preparing for a knowledge test, you can also use the crosswind chart to work backwards. The calculator side consists of
a stationary portion with a flat circular portion attached. A simpler rule is one of sixths. The diagonal lines represent the angular difference between the runway heading and direction the wind is
coming from. Graphic E6B with Demo Mode! By continuing here you are consenting to their use. Sure, you may know the crosswind component when you take off, but the wind can change direction
completely! If the wind is 30 degrees off the runway, your crosswind component is about 50% of the wind speed. The crosswind calculator will tell you the speeds of all acting wind components. A
relatively mild wind coming from 90 on either side of the aircraft has far less effect than a strong wind coming from the same direction. While pilots may compute the crosswind component for takeoff
and decide whether or not to fly, we almost never compute the crosswind component for landing after hearing ATIS, AWOS or other current wind reports. And the wind strength is 50 knots. This Pilots
Tip of the Week was originally published on 3/21/2018. 60 minutes, which is 100 percent of the way around a clockface. The direction the wind is coming from relative to your aircraft and its
strength. Make a note of the wind speed and general direction. You wear it on your wrist to tell the time (OK, maybe that was a bit obvious). If the wind is on one side of 360 and the runway is on
the other, subtract the higher number from 360, and zero from the lower number. You wont have time to be messing around with a flight computer or crosswind chart. Learn how to determine the crosswind
and headwind components for a flight, using Sporty's Electronic E6B Flight Computer. Any calculation involving weight will be based on the Weight per Volume parameter for the fuel selected. In order
to calculate the crosswind and headwind components, we first need to determine the difference between the runway heading and the direction the wind is coming from. If your skills are getting rusty,
the Gleim Pilot Refresher Course can help you increase your knowledge and abilities to fly safely! Stack Exchange network consists of 181 Q&A communities including Stack Overflow, . You seem to be
confusing it with wind direction. IFR Communication A Pilot-Friendly Manual, VFR Communications A Pilot-Friendly Manual, Airplane Engines A Pilot-Friendly Manual, Pilot Exercise ProgramA
Pilot-Friendly Manual, Flying Companion A Pilot-Friendly Manual, If the wind differs from the runway heading by, If the difference between the wind and runway heading is. Colin is a Boldmethod
co-founder and lifelong pilot. $$ A \cdot B = \left( A_{x} \cdot B_{x} \right) + \left( A_{y} \cdot B_{y} \right) = 0.766044 $$, $$ \cos{\theta} = \frac{A \cdot B}{|A||B|} = \frac{0.766044}{1} =
0.766044 $$. Before you go, learn about the effect of wind on an aircraft flight path in the wind correction angle calculator. For exams, use only approved methods of calculation.. An old, bold pilot
once told us that a weather forecast is simply a horoscope with numbers. The Instrument Landing System (ILS) is a radio navigation system that provides precision guidance to aircraft approaching a
runway. You can also use an E6B Flight Computer to keep a wind component chart and lots of other tools at your fingertips for safe flying! 30 minutes, which is 1/2 around clockface. From this point,
trace the shape of the arc to one of the axes to determine the total wind velocity. Meaning both of the above examples have exactly the same crosswind component. Wind Headwind Crosswind W : Wh : 0.00
Wc : 0.00. The answer is a scalar quantity represented in the image above by |R|. From this point go straight down to find the crosswind component, and straight to the left to find the headwind
component. Lets go through how to perform the calculation. Once we have the angle between the wind and the runway, we can easily resolve this into a parallel component (headwind or tailwind) and a
perpendicular component (crosswind from the left or right) using trigonometry. This website uses cookies to ensure you get the best experience on our website. Why Does Maneuvering Speed Change With
Weight? So we have built in a fully animated graphic E6B with wind slider and calculator wheel. Heres a step-by-step guide to performing a quick crosswind calculation in seconds. Thankfully, there is
an easier way to calculate crosswind. When an aircraft is certified, a pilot tests the crosswind capability with a 90-degree crosswind of at least .2 times V, he vertical axis represents the headwind
component of the wind, he horizontal axis represents the crosswind component. Now that you have mastered an easy technique to quickly calculate crosswind, you may be wondering why it is so important
to know this information. Its pilot-friendly design makes quick work of any navigational, weight and balance, or fuel problem, and it also performs conventional arithmetic calculations.
Loss Of Taste After Tooth Extraction, How Can Civic Responsibility Improve Intercultural Interactions?, Harris Funeral Home Opelika, Al Obituaries, Velo Nicotine Pouches How To Use, Articles C
calculate crosswind component e6b | {"url":"https://www.idehk.com/dlqplg3c/archive.php?page=calculate-crosswind-component-e6b","timestamp":"2024-11-03T02:46:33Z","content_type":"text/html","content_length":"114359","record_id":"<urn:uuid:920900f7-18ee-4a0d-9270-ad25147282b2>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00149.warc.gz"} |
Can a Full Statistical Analysis Prove #Lane8 Had a Faulty Runner?
Recently, there have been claims that the AssaultRunners in Lane 8 for both the European and North America West Semifinals were mis-calibrated. Based on placement for Event 5, it was postulated that
the Assault runner in Lane 8 was significantly slower in Europe and it was significantly faster in North America compared to the other runners. There has been a statistical analysis conducted
combining the men and women in Europe, but no analysis has been conducted for the women and men of Europe separately, or on the athletes in North America West.
The aim of this article is to statistically analyze the placements on Event 5 for all lanes across the male and female fields in Europe and NA West. If you don’t care to read through this analysis,
skip to the final heading of this article (“Final Take Aways”) for the general review and final thoughts. If you are someone who wants to read through the analysis in full, we’ll first look at the
raw data for both the NA West and European fields on Event 5.
Statistical Analysis
To begin, placement in Event 5 was found for each lane. Groups were created based on lane assignment. For most lanes the sample size was 5-6 athletes. The exceptions were lanes 4 and 10 in the
European men’s field where the sample size was 4.
Group size matters because a one-way ANOVA (a statistical test used to assess differences in means of groups) is more accurate with equal samples and has higher power for detecting true differences
between groups. So, even though the samples are small the statistical test still has high power (i.e., the ability to accurately detect a significant effect).
Table 1.
Mean Event 5 Placements
Next, we’ll visualize the data for both the competitions for the women’s field. This is done just to get a gist of what the data looks like and note any potential errors or patterns seen.
Figure 1.
Event 5 Placement Means & Variation of European and NA West Women
Subjectively looking at this data, it appears that for the European women the mean placement in Lane 8 is close to all the other lanes except for maybe lanes 4, 5, and 7. Looking at the women in
North America West, Lane 8 appears to be different from all other lanes. In particular, Lane 8 and Lane 1 seem to have a large difference between means.
Next, we’ll look at the standard deviation of the samples (the two scatter plots located at the bottom of fig. 2). Essentially, we’re analyzing how much variance was in each lane (e.g., Lane 8 in NA
West had a 1st and 42nd place finish, creating high variance). This can help determine if all athletes in the same lane performed similarly. If we think Lane 8 had an unfair advantage over all the
other lanes in NA West, we would except little variance as all athletes would have placed well in Event 5 (due to the runner being faster).
With the standard deviation added we can see that the variance for all the lanes is large (note: a Levene’s test was used to ensure variance was equal before conducting the ANOVAs). Although Lane 8
in Europe was one of the slower on average, the spread is large across all lanes with a lot of overlap. Likewise, even though the mean of Lane 8 in NA West appeared to be significantly higher, there
is a lot of variability in performance. Looking back at Table 1, there are two athletes who have finished 25th and 42nd respectively. So, even though there were four top 10 finishes in lane 8 for the
West, there’s still a large spread overall due to these two athletes with lower placements.
Next, we’ll run a one-way ANOVA. This will statistically analyze if the means of each lane are significantly different.
Table 2.
One-Way ANOVA of Women’s Fields
What we can take from both one-way ANOVAs is that neither the European nor NA West women’s field placement on Event 5 was significantly impacted by lane assignment (p < .05). That might seem
impossible (especially in NA West) given the appearance of the bar graph (fig. 1). But if we break down the actual means of these lanes it’s a little clearer.
Table 3.
European Women Event 5 Average Placements per Lane
The overall means for each lane are about what we would expect. Lane 5 has the highest placement followed by lanes seven and four. Arguably the most interesting mean is Lane 6 which has the second to
last lowest placement. Theoretically, because the highest-ranking athletes in the competition are placed in lanes 4-6, lane 6 should have one of the highest placements. If Lane 8 is under questioning
for a potentially slower runner, Lane 6 should be under investigation too.
Table 4.
North America West Women Event 5 Average Placements per Lane
Moving on to the North America West means, we do see what appears to be a large difference in Lane 8 from all the other lanes. It has the highest placement on average and is almost half the value of
other means. The best finishes came from three lanes that should have some of the lower ranking athletes in the competition (lanes 10, 3, and 8). So why isn’t Lane 8 significantly different from the
other lanes in our analysis?
Recall the overlapping standard deviation bars in figure 2. With this wide spread of performance, we really can’t be sure if lane assignment was accounting for the placements seen on Event 5 (note:
further analysis found that for the NA West women’s field lane assignment only accounted for 10% of the variance seen in Event placement). With this high variance, even though there does appear to be
a difference in Lane 8 for the West, it is not statistically significant.
Another supporting analysis is to look at the male fields. If we’re questioning the runners for the women’s fields, the men’s fields should also show similar trends because they used the same
Figure 2.
Event 5 Placement Means and Variation of European and North America West Men
Looking at the visuals of the data, we do see that Lane 8 for the Europe men had lower Event 5 placements than all the other lanes. We also see that the mean of Lane 8 in North America West was
fastest, but Lane 9 is almost equal. Right now, just looking at the visual data, the men and women’s fields are showing the same general trends of placement for Event 5.
The variance in performance on the men’s side in Europe suggests possible significance between Lane 8 and lanes 4 and 5. We see no overlap between those performances, and the means appear to be
largely different. In NA West, the Lane 8 performance variance is almost identical to Lane 9. The variance is also larger in this competition, and nothing stands out as possibly being significant,
although the means do differ. We’ll run the ANOVA again to see if there is statistical significance.
Table 5.
One-Way ANOVA of Men’s Fields
The one-way ANOVA for North America West has no significant values, but the ANOVA of the European men has a significant p-value (p = 0.0484). Meaning, two or more of the lanes are significantly
different from each other in their placement for Event 5. Using a Tukey post-hoc test (a follow-up analysis to see which specific lanes differ from each other), it is found that lanes 4 and 8 are
significantly different (p = 0.451).
One important note for the variances seen in samples: high variances can bias the ANOVA to miss statistically significant relationships. Likewise, low variances can bias the ANOVA to wrongly find
statistically significant relationships. Both ranges of variances have pros and cons for statistical analyses. We’ll come back to this later, but for the final analysis we’ll try to address the low
sample size (which can help decrease the variance of our analysis) by combining the male and female fields. Once again, we start with visualizing the data and then running an ANOVA.
Figure 3.
Event 5 Placement Means of European and North America West Men and Women
Table 6.
European and North America West Men and Women ANOVA
The one-way ANOVA for the European men and women has a significant p-value (p = 0.0131). So, two or more of the lanes are significantly different from each other. We’ll use a Tukey post-hoc test
again. The Tukey test shows that lanes 7 and 8 are significantly different (p = 0.457). Lanes 5 and 8 were almost significantly different from one another (p = 0.0548).
Putting It All Together
One of the biggest takeaways from this analysis is that athlete variance reduces the assumed significance of the runners in Lane 8 for both the NA West and Europe competitions. At first glance,
looking at the visualized data, it seems like Lane 8 might have had an unfair advantage (in NA West) or disadvantage (in Europe). But the variance in athlete performance clouds the differences we
see. The variance in athlete performance per lane is too large to make any conclusions about whether the runners in Lane 8 were calibrated unfairly.
As alluded to early, variance is essentially noise in data, and it can hide significant relationships. It’s possible that the runners in Lane 8 for Europe and North America West were mis-calibrated.
But because of the wide spread of athlete performance and limited sample size, we will never know indefinitely if the runners were unfair. More data points are needed to accurately assess this
question. We did see a decrease of the p-value when we combined men and women, but 8 to 12 samples are still not enough to appropriately assess this data given the spread in performance per lane.
An alternative analysis would be to use the placement per heat. So, instead of athletes receiving a placement between 1-60, they would fall within the range of 1-10. This would greatly limit the
variance seen and would be biased to find significant relationships between lane assignment and Event 5 placement. WodScience has conducted this analysis for the European competition (combining the
men and female fields) and did indeed find many significant differences between lanes. While this analysis is not wrong in anyway, it does have limitations. Just as the analysis conducted here was
biased because of high variance, the alternative analysis is biased because of low variance.
Final Takeaways
The bottom line is that there is too much variance in athlete performance per lane to conclude if any runner gave an unfair advantage, and more samples are needed to address this issue. An
alternative analysis using heat placement instead of overall Event placement (thus reducing the variance from 1-60 places to 1-10 places) did find the Assault runner in Lane 8 for the European
competition to be significantly slower than some of the other lanes.
The question now becomes which analysis (i.e., using placement in Event 5 overall versus placement per heat for Event 5) is most representative of the population (i.e., NA West and European
competitions). Arguably, the overall placement for the Event best represents the populations, as it precisely reflects placement for the entire population rather than just a sample of it (as seen in
Looking at the graphs above, it does look like we should find significant differences in the means, particularly in NA West. Conversely, how much of an impact did the runners have in NA West if one
female athlete places 1st and another places 42nd? Or the fact that males in lanes 8 and 9 had almost identical placement means (18.16 and 19.6 respectively)? The variance accounts for these
performances and challenges conclusions that may be tempting to make based purely on the means.
For the Europe competition, people argued that Lane 8 had a slower runner because athletes who “should have placed well” in Event 5 didn’t finish as high as expected. But the average placement of the
European women in Lane 8 is very similar for lanes 1-3, and 6. Did all these lanes have slower runners then? The variance of performance within and between lanes is too high to conclude anything
about a potentially mis-calibrated AssaultRunner.
We can point at a few lanes that seemed faster or slower than the rest. But at the end of the day, athlete performance varied for each lane. On average it appears that lane assignment influenced the
placements for Event 5, but multiple athletes demonstrated that the runner alone didn’t dictate placement. If the runner was having as much of an influence as claimed, we would see athletes assigned
the same lane consistently finishing near each other with little variance, regardless of if overall or heat placement was used to conduct the analysis. The means of the placements don’t tell the
whole story and can’t be used to make any conclusions.
A final quote for consideration:
“A statistician confidently waded through a river that was on average 50 cm deep. He drowned.”
-Godfried Bomans | {"url":"https://thebarbellspin.com/crossfit-games/can-a-full-statistical-analysis-prove-lane8-had-a-faulty-runner/","timestamp":"2024-11-08T17:31:00Z","content_type":"text/html","content_length":"243204","record_id":"<urn:uuid:3ae3da46-b332-4a0a-8e36-4cbf506bf754>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00352.warc.gz"} |
Why Hawking is Wrong About Black Holes
A recent paper by Stephen Hawking has created quite a stir, even leading Nature News to declare there are no black holes. As I wrote in an earlier post, that isn’t quite what Hawking claimed. But it
is now clear that Hawking’s claim about black holes is wrong because the paradox he tries to address isn’t a paradox after all.
It all comes down to what is known as the firewall paradox for black holes. The central feature of a black hole is its event horizon. The event horizon of a black hole is basically the point of no
return when approaching a black hole. In Einstein’s theory of general relativity, the event horizon is where space and time are so warped by gravity that you can never escape. Cross the event
horizon and you are forever trapped.
This one-way nature of an event horizon has long been a challenge to understanding gravitational physics. For example, a black hole event horizon would seem to violate the laws of thermodynamics.
One of the principles of thermodynamics is that nothing should have a temperature of absolute zero. Even very cold things radiate a little heat, but if a black hole traps light then it doesn’t give
off any heat. So a black hole would have a temperature of zero, which shouldn’t be possible.
Then in 1974 Stephen Hawking demonstrated that black holes do radiate light due to quantum mechanics. In quantum theory there are limits to what can be known about an object. For example, you cannot
know an object’s exact energy. Because of this uncertainty, the energy of a system can fluctuate spontaneously, so long as its average remains constant. What Hawking demonstrated is that near the
event horizon of a black hole pairs of particles can appear, where one particle becomes trapped within the event horizon (reducing the black holes mass slightly) while the other can escape as
radiation (carrying away a bit of the black hole’s energy).
While Hawking radiation solved one problem with black holes, it created another problem known as the firewall paradox. When quantum particles appear in pairs, they are entangled, meaning that they
are connected in a quantum way. If one particle is captured by the black hole, and the other escapes, then the entangled nature of the pair is broken. In quantum mechanics, we would say that the
particle pair appears in a pure state, and the event horizon would seem to break that state.
Artist visualization of entangled particles. Credit: NIST.
Last year it was shown that if Hawking radiation is in a pure state, then either it cannot radiate in the way required by thermodynamics, or it would create a firewall of high energy particles near
the surface of the event horizon. This is often called the firewall paradox because according to general relativity if you happen to be near the event horizon of a black hole you shouldn’t notice
anything unusual. The fundamental idea of general relativity (the principle of equivalence) requires that if you are freely falling toward near the event horizon there shouldn’t be a raging firewall
of high energy particles. In his paper, Hawking proposed a solution to this paradox by proposing that black holes don’t have event horizons. Instead they have apparent horizons that don’t require a
firewall to obey thermodynamics. Hence the declaration of “no more black holes” in the popular press.
But the firewall paradox only arises if Hawking radiation is in a pure state, and a paper last month by Sabine Hossenfelder shows that Hawking radiation is not in a pure state. In her paper,
Hossenfelder shows that instead of being due to a pair of entangled particles, Hawking radiation is due to two pairs of entangled particles. One entangled pair gets trapped by the black hole, while
the other entangled pair escapes. The process is similar to Hawking’s original proposal, but the Hawking particles are not in a pure state.
So there’s no paradox. Black holes can radiate in a way that agrees with thermodynamics, and the region near the event horizon doesn’t have a firewall, just as general relativity requires. So
Hawking’s proposal is a solution to a problem that doesn’t exist.
What I’ve presented here is a very rough overview of the situation. I’ve glossed over some of the more subtle aspects. For a more detailed (and remarkably clear) overview check out Ethan Seigel’s
post on his blog Starts With a Bang! Also check out the post on Sabine Hossenfelder’s blog, Back Reaction, where she talks about the issue herself.
15 Replies to “Why Hawking is Wrong About Black Holes”
1. Very nice! That was very helpful.
2. In a matter that is dependent on the agreement of many subtleties, it’s hard to make a believable argument when you gloss over the subtle aspects.
1. Yes I couldn’t help wondering how all matter could so neatly be ONLY as double pairs — Why wouldn’t single pairs of quantum particles try to jailbreak the firewall ??? I am obviously not a
3. It’s annoying when a simplification demands that important yet complicated details are left out. How does general relativity say “no firewall”? A post about the role of the equivalence principle
in the ex-firewall paradox would be very illuminating!
4. From the article: “The central feature of a black hole is its event horizon.”
Actually, that’s definitely *not* the “central” feature of a black hole – it’s more of the edge. Ahahaha. Get it? Get it? Central?
*Slowly backs away and dashed out a sidedoor.*
1. Got it.
5. Would not spaghettification prevent the solution of impure Hawkings Radiation?
6. If a particle is trapped within the event horizon, wouldn’t that increase the mass slightly, instead of reducing it?
1. Not if it is an anti-particle when it gets converted into energy when it collides with a particle.
1. Nope. Anti-particles supposedly have mass too, not anti-mass; energy has mass (or ‘is’ mass).
I don’t really understand the mass decrease either though, I guess it has to do with the ‘borrowing’ of energy (quantum fluctuation) for the pair to appear in the first place, but why
does it have to be the BH that loses mass, and not the rest of the universe?
2. I don’t understand it either, but I’ve always been under the impression that the particles had to borrow energy from the gravitational field of the black hole (the strongest energy source
in their vicinity) in order to appear. Most of the time they destroy themselves and that energy is given back. But if one of them is absorbed into the black hole and the other one isn’t,
then the mass of the black hole has to decrease in order to permanently lend energy to the escaping particle.
It doesn’t really make a lot of sense to me, but that’s what I remember reading.
7. If this can be done:-
what is the problem? and where is QM on that one?
Moreover, if the object at the centre of that space-time warp is not a singularity, thinking in Newtonian terms, and of myself as a photon, I am trapped within earth’s event horizon, I can’t
reach escape velocity but I can still run, walk or jump so I am still preserved in QM terms just not detectable beyond the limits of my movement.
8. I believe what Stephen Hawking is referring to is that there are no Black Holes if there is Imaginary Time. The two states of Spin would be an example of another dimension of time ( One could
regard Information in General as the Second Dimension of Time, as it really can’t be accounted for using 3 space Dimensions and One Time Dimension—Likewise you can see this Duality in Time
itself- It is just Information, and although you can claim it is Geometrical because the hands of a Clock move to different angles, it is independent of the Space Dimensions and has that
“Information” feel). So the argument that about the Pure states is just a bit too contrived. Mind you Hawking will have to say for himself what he means, and this is my own theory of time, but if
you look at two dimensions (at least two dimensions) that are really just information, and you take that those two dimensions have non-Commuting operators, then you can propose an Experiment that
would search for a symmetry, a conservation and a particle between those two dimensions–so you can prove it experimentally. So it is my opinion that Brian’s theory is a bit old fashion, a bit of
history, and not at all correct.
Richard Kriske
9. To risk being a bore, I would like to point out that time becomes space-time with one other dimension in Special Relativity (the Lorentz Transform), but the truely amazing thing that Hawking
showed was that the Horizon (which is an Area!!! that is proportional to the Entropy(Information?)) is proportional to the Information in a Black Hole—So if you take Information as being that
Imaginary time, something fantastic is being revealed (to be a bore again, it may in fact prove that there are two dimensions of time, in that the time we call clock time acts like a line, the
Imaginary time like spin up, spin down would act like a line) their product is an area. Anyway given this, I think Brian’s idea is wrong, except in that the pairs he talks about would also
contain information and this points to the real power in Brian’s idea—The whole Black Hole Horizon is a lot more complicated than we are thinking right now–so go for it Brian.
10. The Black Vortex
Any medium that supposedly supports wave motion, should also be able of supporting whirlpool or vortex motion.
If the motion is rotation , or movement in a closed circuit, as in vortex motion, then the inertia will be localized, and thus have momentum. The distinguishing characteristic of the so- called
blackholes is their Localized Persistence of Individuality, and this is the same as vortex motion.
Wave motion is not localized, as it will not revert to original form, when distorted. but will travel in the direction normal to the new wavefront, their being no persistence of individuality or
memory of the original form of the wavefront
On the other hand, a vortex ring , if distorted from the circular , or elliptical will spontaneously revert to it’s original form , displaying persistence of individuality, and memory of it’s
original form.
The so called event horizon of a blackhole is the interface closed circuit of vortex motion, within the medium, the resulting reaction not allowing light to escape, as it is no longer a wave, in
the normal sense, but still an energy source, contributing to the inertia and momentum of the vortex, or so-called blackhole. | {"url":"https://www.universetoday.com/108870/why-hawking-is-wrong-about-black-holes/","timestamp":"2024-11-10T21:57:28Z","content_type":"text/html","content_length":"202810","record_id":"<urn:uuid:cb75ec58-49ff-4b69-9394-f183d8e6e0f8>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00288.warc.gz"} |
Optimizing and Monitoring a Trading System - Traders Log
Optimizing and Monitoring a Trading System
After finding rules that work, many traders are tempted to optimize the parameters. This is easy to do, and is the beginning of the end of many solid trading plans.
If trading a simple MACD system, traders usually buy when the MACD difference crosses above zero and sell when it turns negative. With standard software, we can instead test to find the optimal
parameter, and perhaps discover that instead of 0.00, the best crossovers take place at 0.31. Our optimized trading plan calls for buying when MACD goes above 0.31 and selling when it falls under
that value.
The problem with this optimization is that what weโ ve really done is to find out what worked best in the past and this will very likely lead to problems in the future. The optimized value for MACD
most likely indicates that the test period included a strongly trending market and we fine tuned the indicator to take advantage of that trend. The same results would not be likely under other market
conditions. A nontrending market would obviously be different, but no two trends are ever alike and the optimized value will always change depending on the test period.
Since the 1970s, traders have often believed that markets trend about a third of the time and spend the majority of the time within relatively narrow ranges. Welles Wilder wrote about this idea in
his 1978 book, New Concepts in Technical Trading Systems, and his idea has since been confirmed by many other analysts. This insight led Wilder to develop indicators like the Average Directional
Index which is available as ADX in most software packages.
By now, many traders will be thinking they can add an ADX filter to the MACD signal and that will yield even better results. With only a few more clicks, they can see which value of ADX works best
with MACD. Invariably the test results show even greater profits, a higher winning percentage, and smaller drawdowns. But, traders need to remember that every mutual fund carries that warning stating
โ performance data represents past performance, which is no guarantee of future results.โ
The more variables traders add to the trading equation, the greater the degree of uncertainty and the more likely future results will differ from past performance. Many traders like to point to
famous quotes about how history repeats itself, and this is why systems or chart patterns are expected to work in the future. To me, the most apt quote may be from Mark Twain who pointed out that
history doesnโ t always repeat itself as much as it rhymes. A quick web search reveals there are several versions of the quote, and that emphasizes the point that a general understanding of an idea
can be more important than getting everything exactly right. Knowing the essence of what Twain said is โ good enoughโ for all but historians and literary experts.
Traders can benefit from adopting the โ good enoughโ approach to optimization. Some traders use the 200-day moving average to define the trend, assuming that if prices close above the average the
trend is bullish and a close below that level is bearish. As a trading system, there is some merit to this approach and a long-only strategy usually delivers market beating results.
At this point, the unavoidable tendency to improve things kicks in and new traders begin optimizing the length of the moving average. Or they will use a more complex calculation to find the best type
of moving average, testing an exponential moving average, a variety of weighted averages, or even triangular moving averages. After some testing, they may find that a 163-day front-weighted moving
average triples the profits of the simple moving average.
Looking closer at the test results, they can see that the 162-day and 164-day parameters lose money, but they focus solely on the profits. Using the โ good enoughโ approach, they would want to see
steady profits when the value used in the moving average formula changes by a small amount. In this example, theyโ d be looking for all parameters from about 140-days to 180 days to be profitable.
This captures all values within 10% of the optimal parameter.
If a small change in a single parameter leads to a big change in profits, itโ s a sign that the results are due to random changes in the market action. Small changes in a parameter should lead to
small changes in profits. More important than the actual level is the trend of profits. An optimization test should show the profits linearly decline or rise from one test level to the next. That
means we should see something like the 150-day moving average show a little less profit than the 160-day and the 140-day even less, while the 170-day moving average delivers even higher profits than
the 160-day. While there are many statistical tests for parameter robustness, this visual test is a โ good enoughโ approach and is all traders need to rely on to prevent overoptimization.
In summary, optimization is bad if taken too far because it simply identifies the random variable that caught the greatest degree of the randomness of past price action. Optimization testing is a
good way to test the robustness of your trading idea, and the best value to use is the one that shows relatively stable profits as it changes a little bit.
Optimization is often thought of as the last step in the system design process, and it is true that you can start trading after this step is completed. However, the work of system design should never
be thought of as fully completed. It is very important to monitor the system youโ re trading to make sure that it still works. In reality, no system will always be in synch with the markets. Trend
following systems will only work well while the markets are trending, which weโ ve known since the 1970s will be about one-third of the time. Most of the time, these systems will lead to many small
losses while prices consolidate within trading ranges. These losses are then followed by the occasional big winner that the system is designed to profit from.
Backtest results offer one way to monitor system performance. These reports usually include important information like the maximum number of consecutive losing trades the system has experienced in
the past, and the worst drawdown. In-sample performance (results seen during live trading) can be compared to these benchmarks. The future will not be exactly like the past, and experienced traders
expect that the worst drawdown will always be in the future. Buy-and-hold stock market investors learned this lesson in 2009. The bear market that followed the internet bubble wiped out about half
their account value in many cases. The financial crisis that shook financial markets starting in the summer of 2008 forced them to live through a drawdown that was even more severe.
Rather than relying on the past to see whatโ s working in the present, we can use the actual performance of the system itself to monitor how itโ s doing. This involves just a little more than
looking at the percentage of winning trades or other common metrics.
Trading results in wins and losses, and the cumulative effect of individual trades is measured by the account balance. We are back to the idea that all that matters to traders are dollars. Account
equity is a data series, just like price data and we can even chart account equity, just like we can chart prices. We can also place a moving average on the account equity.
This idea is not new. Trading legend Larry Williams has described the technique since at least the 1980s, but it is not widely known. No trading system will always be in synch with the market and
this is a tool that recognizes that reality. The rules for this idea are simple: when the equity curve falls below the moving average, stop taking the trade signals and resume trading the strategy
when the equity curve rises back above the moving average. A 30-week moving average works well on weekly systems, a 10-week moving average is useful for daily systems. Day traders can watch a 10 or
30 period moving average of whatever timeframe they trade.
Trading the equity curve by using a moving average of the system results is a powerful idea that will help traders avoid catastrophic losses. Trading multiple systems can help maximize gains in your
account since at least one of the systems should be in the market at any given time.
By Michael J. Carr, CMT | {"url":"http://www.traderslog.com/optimizing-trading-system","timestamp":"2024-11-10T12:05:27Z","content_type":"text/html","content_length":"247818","record_id":"<urn:uuid:1f2e5d1d-6035-4598-87d8-cea786d82fc2>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00073.warc.gz"} |
A teacher has asked all the students in the class which days of the week they get up after 8 a.m. Which of the following is the best way to display the frequency of each day of the week?
Correct Answer : D
The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day
of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.
Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week. Histograms are useful for
understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.
As you can see below, the Histogram is used to depict a pattern/continuous/range data. While a bar graph does just fine even with discrete data.
TEAS 7 Exam Quiz Bank
HESI A2 Exam Quiz Bank
Find More Questions 📚
$69/ month
Teas 7 Questions: We got the latest updated TEAS 7 questions
100% Money Refund: 100% money back guarantee if you take our full assessment pass with 80% and fail the actual exam.
Live Tutoring: Fully customized live tutoring lessons.
Guaranteed A Grade: All students who use our services pass with 90% guarantee.
Related Questions
Correct Answer is C
the median of a data set is the element that is found on the middle position. It is found by organizing the elements from the smallest to largest.
The data set above arranged from the smallest to largest is:
11, 12, 12, 12, 13, 14, 17, 17, 18, 22, 26
The number of elements is odd and the median is found in the (N+1)/2 th position. Here N=11, and the median falls in (11+1)/2=12/2=6 th position.
The element 14 falls in the 6th position, which is our median of the given data set.
Correct Answer is B
We need to find how many mL are in 2.5 teaspoons. We need to use dimensional analysis to solve this problem as follows.
Converting between teaspoon and mL uses the following conversions:
We want to end up with mL, we utilize the second conversion and set up the following equation.
Thus, 2.5 teaspoons can hold 12.325 mL.
Correct Answer is A
The initial step is to establish the relationship between area of a circle and the radius. The area of the circle is given by the formula
Now, substituting the 49 π in2 in place of A in the equation above becomes:
We want to find r, therefore, we rearrange the equation as
Divide both sides by
Take square root both sides of the equation
The radius of the circle is 7 in, and the circumference of the circle is determined as follows
Substituting the value of r=7 becomes
Thus, the circumference of a circle whose area is 49 Â in2 is 14 Â
Correct Answer is D
we need to form a mathematical expression from the given word problem.
Let the number be x.
Twice a number=2x
Five less than twice a number=2x-5
So the mathematical express from the word problem is 2x-5
Correct Answer is C
we need to find the net income of the nurse in 4 weeks from the weekly net income.
Weekly net income=gross income-total tax
Total tax=federal income tax+state income tax+Social Security tax
Total tax=$(83.00+38.00+79.00)
Total tax=$200.00
Weekly net income=$(800.00-200.00)=$600.00
In one week, the net income of the nurse is $600.00 and in 4 weeks the nurse will a net income of:
The nurse will earn $2,400.00 in 4 weeks after taxes are deducted.
Correct Answer is D
The length of the unknown side of the rectangle can be found by using the Pythagoras theorem. We label the triangle from the given data as shown below
Let the unknown length be x.
Applying the Pythagoras theorem, the value of x is found as:
\(a ^2 +b ^2 =c ^2\)
The unknown length of the triangle is approximately 8.9 feet.
Correct Answer is C
we follow the order operations to solve for the unknown value of x.
Open the bracket on the LHS by multiplying each term by 2
Subtract 6 from both sides
Subtract 7x on both sides
Thus, the value of unknown value of x is -1.
Correct Answer is D
we use given information to find how much ammonia is need to make the specified solution.
We are told, one gallon of cleaning solution requires 6 oz of ammonia. In other words, we can express this as:
1 gallon of solution6 oz of ammonia
6 oz of ammonia1 gallon of solution
Since we are needed to find how much ammonia is needed, we use the second option to find how much ammonia is required by 120 gallons of solution.
From the above equation, gallon of solution will cancel, and oz of ammonia is left.
Therefore, the solution will require 720 oz of ammonia.
Correct Answer is D
Correlation of two variables falls into:
Positive correlation: an increase in one variable causes another variable to increase
Negative correlation: an increase in one variable causes another one to decrease
No correlation: a change in one variable does not cause any response in another variable.
From the given choices
Option a is no correlation
Option b is a negative correlation
Option c is a negative correlation
Option d is a positive correlation
Correct Answer is D
The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day
of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.
Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week.Histograms are useful for
understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.
As you can see below, the Histogram is used to depict a pattern/continuous/rangedata. While a bar graph does just fine even with discrete data.
Access the best ATI complementary Questions by joining
our TEAS community
This question was extracted from the actual TEAS Exam. Ace your TEAS exam with the actual TEAS 7 questions, Start your journey with us today
Visit Naxlex, the Most Trusted TEAS TEST Platform With Guaranteed Pass of 90%.
Money back guarantee if you use our service and fail the actual exam. Option of personalised live tutor on your area of weakness. | {"url":"https://www.naxlex.com/questions/a-teacher-has-asked-all-the-students-in-the-class-which-days-of-the-week-they-ge","timestamp":"2024-11-12T22:59:51Z","content_type":"text/html","content_length":"100767","record_id":"<urn:uuid:356d4583-747e-447f-8781-7a413c24ce16>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00334.warc.gz"} |
Generic Function Package: cg ToC DocOverview CGDoc RelNotes FAQ Index PermutedIndex Allegro CL version 10.0
Unrevised from 9.0 to 10.0.
9.0 version
Arguments: stream center smaj-axis smin-axis smaj-axis-angle start-angle length-angle
Draws the specified filled ellipse sector on stream. An ellipse-sector is an ellipse-arc with the endpoints of the arc connected to the center of the ellipse, like a piece of an elliptical pie.
The ellipse is defined by the center (a position) and the two half-axes, lengths from the center to the farthest point on the edge and to the nearest point on the edge, called the semi-major-axis and
the semi-minor-axis. (Technically, the major axis should be longer than the minor axis but the two arguments need not have that relationship.) Because the Windows ellipse drawer can only draw
ellipses that are vertically or horizontally oriented, the semi-major-axis-angle argument must be a multiple of 90. Other values will signal an error. The argument specifies the angle between the
semi-major-axis and a line parallel to the x-axis passing through the center. The portion of the ellipse drawn is the sector starting at start-angle (0 is the x axis when the center is the origin)
through the length-angle.
Angles are measured in degrees clockwise from the 3 o'clock position (that is, along or parallel to the x axis). The endpoint coordinates may be determined by calling ellipse-start-and-end.
center should be a position (see make-position). stream should be a cg-stream.
Contrast with erase-contents-ellipse-sector which erases the filled ellipse from stream.
Copyright (c) 1998-2019, Franz Inc. Oakland, CA., USA. All rights reserved.
This page was not revised from the 9.0 page.
Created 2015.5.21.
ToC DocOverview CGDoc RelNotes FAQ Index PermutedIndex Allegro CL version 10.0
Unrevised from 9.0 to 10.0.
9.0 version | {"url":"https://franz.com/support/documentation/10.0/doc/operators/cg/f/fill-ellipse-sector.htm","timestamp":"2024-11-14T15:02:54Z","content_type":"text/html","content_length":"6275","record_id":"<urn:uuid:ea9a4333-9bb0-47d4-ab4a-15ba221d3bb6>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00415.warc.gz"} |
Comparing Groups
Let’s explore the different group comparisons.
We'll cover the following
R functionality to compare groups
We’ve used the mean(), var(), and sd() functions to calculate the overall mean, variance, and standard deviation for the heights of all 30 plants from the darwin data frame. We can do the same for
the two experimental treatments using the Cross and Self columns in the wide format dataset (the data frame from the Sleuth package). This is shown in the code snippet below:
Get hands-on with 1400+ tech skills courses. | {"url":"https://www.educative.io/courses/performing-modern-statistical-analysis-r/comparing-groups","timestamp":"2024-11-08T10:30:49Z","content_type":"text/html","content_length":"759734","record_id":"<urn:uuid:94ea03e4-b481-4c57-85c6-5bc109045b9d>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00710.warc.gz"} |
Rocket works on the principle of conservation of A class 11 physics JEE_MAIN
Hint: Recall Newton’s laws of motion (Third law). Remember there is no external force acting on the rocket when the rocket is launched. Don’t confuse between Energy, momentum and force.
Complete step by step answer:
Newton’s third law states that, for every action there is an equal and opposite reaction. Consider the rocket and its launch pad to be a single system. Now in this system no external force is applied
so the momentum of the system must be conserved.
Momentum is given as the product of mass and velocity
$\Rightarrow$\[p\] Is the momentum
$\Rightarrow$\[m\] Is the mass of the object taken in consideration
$\Rightarrow$\[v\] Is the velocity of the object.
When a rocket is in the initial phase of it’s launch what happens is that when we accelerate a small amount of gas in one direction, it pushes back with an equal and opposite force, accelerating a
much larger spaceship at a proportionately smaller rate.
The rocket gains momentum which is equal to the momentum of the gas expelled but in the opposite direction, the boosters begin to expel gases after the rocket has begun to travel and thus the rocket
continues to gain momentum, so that they get faster and faster as long as the engine is operating.
It must be noted here that rocket boosters consume around \[11,000\] pounds of fuel per second. This is more than \[20\] lakh times the amount of fuel used by an average car. It must also be noted
that rockets travel at a speed which is around \[7-8km/s\] .
All this is done conserving the momentum of the system.
Therefore the correct option is C
Note: When the rocket moves upwards its velocity increases but mass decreases. As momentum is a product of mass and velocity, the momentum of the rocket at any given instance is exactly the same as
initial momentum. It is also clear from the definition of momentum that for a body at rest its momentum is zero. Since the velocity is zero. | {"url":"https://www.vedantu.com/jee-main/rocket-works-on-the-principle-of-conservation-of-physics-question-answer","timestamp":"2024-11-04T11:13:10Z","content_type":"text/html","content_length":"145644","record_id":"<urn:uuid:2e7ae07a-d628-49e8-a5b6-1f4682260108>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00577.warc.gz"} |
Let's Focus on the Math! - Math Motivator
Let’s Focus on the Math!
What’s important?
“It’s fine to work on any problem, so long as it generates interesting mathematics along the way – even if you don’t solve it at the end of the day. (Andre Wiles)
This quote reminds me of a couple of key ideas that I have encountered through my work as a numeracy facilitator. I think we have to get away from thinking that “speed” is an indicator of success
when it comes to problem solving. Yes, we want students to become efficient problem solvers, but we want them to have the time and experiences needed to construct deep understanding. We want to
expose them to a variety of solutions in order to learn different ways of thinking and to think outside the box. Thus, coming to the understanding of the efficient ways through educator moves that
make connections for them and build procedural fluency. Students who believe that speed is an indicator of success may have a tendency to give up easily or defer to those students who come to an
answer quickly. As an educator or parent do you inadvertently honour speed in the problem solving process?
This notion of generating interesting mathematics is another important idea because the focus in our math classes and at home doing math homework needs to be on the math. As you read this you are
likely saying, “of course!” Through my many years of classroom experiences I became aware of and noted a pattern of student behaviours that took their learning away from the math. Some of these
• drawing a picture when they did not need to in order to solve the problem
• drawing pictures with added details unnecessary to solve the math
• highlighting key words which becomes “most” of the words
• writing out important information before starting to solve the problem because “I’m supposed to.”
• making the work look “pretty” with different coloured markers
It is not to say that we do not want students thinking about the key information, for example, but when the focus is on the highlighting and not on the understanding of how this information is
helping them, then it just becomes a make work project that moves students away from the math. As educators and parents when we have students follow a formula or model for problem solving it is
imperative that we observe who this is working for and who it is just providing extra unnecessary work that takes the place of thinking. One size does not fit all!
I have noticed that many students who have a tendency to struggle in math or do not know how to get started tend to put their focus into behaviours that look like work but move them away from the
math. They usually do not want others to know that they are not getting it and they are very good at looking busy. Those same children will persevere by trying to remember a rule (standard
algorithm or formula), rather than thinking about alternate ways. These are often our “students of mystery”. It is important to observe them carefully and provide the specific, timely feedback that
they need in order to be successful. Students who are flexible thinkers feel confident in finding alternate ways when their memories fail them. For that reason we have to be very careful about what
we as educators and parents honour in math and ask our children to do. Yes, we want a solution to be written in a way that others can understand, but we have to remember that while we are grappling
with something our own work is often messy. We would never expect an author to write the story or poem out perfectly the first time. Does that mean that we never work on representation or
organization of thinking? Absolutely not, but once again timing based on the students in front of us is important and that is the art of teaching! | {"url":"http://mathmotivator.com/lets-focus-on-the-math/","timestamp":"2024-11-10T04:51:15Z","content_type":"text/html","content_length":"61451","record_id":"<urn:uuid:004b8d70-b56b-4ae3-ab6e-f431a627d9d1>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00359.warc.gz"} |
A 3-Approximation Algorithm for Finding Optimum 4,5-Vertex-Connected Spanning Subgraphs
The problem of finding a minimum weight k-vertex connected spanning subgraph in a graph G = (V, E) is considered. For k ≥ 2, this problem is known to be NP-hard. Based on the paper of Auletta,
Dinitz, Nutov, and Parente in this issue, we derive a 3-approximation algorithm for k ∈ {4,5}. This improves the best previously known approximation ratios 41/6 and 417/30, respectively. The
complexity of the suggested algorithm is O(|V|^5) for the deterministic and O(\V\^4log|V|) for the randomized version. The way of solution is as follows. Analyzing a subgraph constructed by the
algorithm of the aforementioned paper, we prove that all its "small" cuts have exactly two sides and separate a certain fixed pair of vertices. Such a subgraph is augmented to a k-connected one
(optimally) by at most four executions of a min-cost k-flow algorithm.
Dive into the research topics of 'A 3-Approximation Algorithm for Finding Optimum 4,5-Vertex-Connected Spanning Subgraphs'. Together they form a unique fingerprint. | {"url":"https://cris.openu.ac.il/en/publications/a-3-approximation-algorithm-for-finding-optimum-45-vertex-connect","timestamp":"2024-11-07T20:21:51Z","content_type":"text/html","content_length":"47067","record_id":"<urn:uuid:d7029623-4db8-43b3-bab2-4cbce0dc9ed4>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00471.warc.gz"} |
Kurt Gödel
Kurt Friedrich Gödel
( ; ; April 28, 1906 – January 14, 1978) was a
, and
. Considered along with
Gottlob Frege
to be one of the most significant logicians in history, Gödel profoundly influenced scientific and philosophical thinking in the 20th century (at a time when
Bertrand Russell
Alfred North Whitehead
, and
David Hilbert
were using
set theory
to investigate the
foundations of mathematics
), building on earlier work by Frege,
Richard Dedekind
, and
Georg Cantor
Gödel's discoveries in the foundations of mathematics led to the proof of
his completeness theorem
in 1929 as part of his dissertation to earn a doctorate at the
University of Vienna
, and the publication of
Gödel's incompleteness theorems
two years later, in 1931. The first incompleteness theorem states that for any
ω-consistent recursive axiomatic system
powerful enough to describe the arithmetic of the
natural number
s (for example,
Peano arithmetic
), there are true propositions about the natural numbers that can be neither proved nor disproved from the axioms. To prove this, Gödel developed a technique now known as
Gödel numbering
, which codes formal expressions as natural numbers. The second incompleteness theorem, which follows from the first, states that the system cannot prove its own consistency.
Gödel also showed that neither the
axiom of choice
nor the
continuum hypothesis
can be disproved from the accepted
Zermelo–Fraenkel set theory
, assuming that its axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to
proof theory
by clarifying the connections between
classical logic
intuitionistic logic
, and
modal logic
Provided by Wikipedia
1. 1
2. 2
3. 3
4. 4
5. 5
6. 6
7. 7 | {"url":"https://ebusca.uv.mx/Author/Home?author=G%C3%B6del%2C+Kurt&","timestamp":"2024-11-10T08:38:35Z","content_type":"text/html","content_length":"53411","record_id":"<urn:uuid:0788c783-7a12-417a-9f28-768d43d65488>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00359.warc.gz"} |
Argonne Leadership Computing Facility
Project Summary
By allowing the properties of particles observed in experiments to be calculated in terms of the fundamental properties of the quarks inside, this project will deliver a large number of calculations
urgently needed by the experimental programs of high energy and nuclear physics.
Project Description
The Aurora machine offers a sea change in capability for lattice quantum chromodynamics (QCD). This project aims to carry out a set of targeted calculations that will have a major impact on high
energy and nuclear physics, offering critical support to the experimental programs in both areas.
In high-energy physics, lattice calculations are required to extract the fundamental parameters of the standard model (such as quark masses and mixing amplitudes) from experiment. Evidence for
physics that lies beyond the standard model can be discovered if discrepancies are found between different methods for determining these parameters. This search for discrepancies becomes more
exciting as these comparisons become more precise.
In nuclear physics, lattice calculations are critical to the success of numerous experimental programs. For example, already-existing experiments need to calculate the structure and scattering of
protons, neutrons, and light nuclei at larger volumes and lighter quark masses than can be achieved using the computers available today.
The fundamental laws of nature, in particular those of QCD, are expressed in terms of quarks and gluons, but experiments involve only quark-containing particles (hadrons) such as protons and
neutrons. Large-scale numerical simulations are the only ab initio method for relating QCD to experiment. This project aims to study four sets of calculations that were not possible before Aurora,
all of them using lattice QCD: (1) high-precision calculations in the neutral kaon system, related to the violation of the particle-antiparticle and spatial inversion symmetries (CP), (2) generation
of refined gluon-field configurations aimed at high-precision heavy-quark physics, (3) calculations of hadron structure in support of GlueX and of multinuclear interactions, and (4) calculations of
particle fluctuations in high-temperature strongly-interacting matter. | {"url":"https://alcf.anl.gov/science/projects/lattice-quantum-chromodynamics-calculations-particle-and-nuclear-physics","timestamp":"2024-11-09T00:58:20Z","content_type":"text/html","content_length":"46650","record_id":"<urn:uuid:f7cfe72f-affe-42cb-a6c3-ee2261c4c97e>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00508.warc.gz"} |
210.19(A)(1) Branch Circuits.
Code Change Summary: Revised code language and a new exception to align with a similar exception permitted for feeders.
When sizing an ungrounded branch circuit conductor, section 210.19(A)(1) allows the larger of the following two values to be used for the final selection of the conductor:
• Either 125% of the continuous load without any additional adjustment or correction factors,
• 100% of the load (not 125% of it) after applying adjustment and correction factors.
In the 2020 NEC^®, this remains unchanged. What has changed is the addition of new exception 2. This new exception requires a very careful read in order to understand it. The new exception allows a
portion of a branch circuit connected between pressure connectors (such as power distribution blocks) complying with 110.14(C)(2) to be sized based on the continuous load plus the noncontinuous load
rather than 125% of the continuous load plus the noncontinuous load.
The idea is this: Most equipment and circuit breaker terminals are rated at 75°C. Even if a conductor is rated at 90°C, it must be considered as a 75°C conductor if terminating to a 75°C terminal.
This means that a 1 AWG copper type XHHW-2 conductor (rated for 145 amps in the 90°C column of Table 310.16) is really only rated for 130 amps (from the 75°C column) if terminating on 75°C rated
terminals at each end (see illustration).
Section 110.14(C)(2) covers separately installed pressure connectors such as power distribution blocks and recognizes the fact that many of them differ from circuit breaker terminals in that they are
often rated higher than 75°C.
According to the new exception, a run of 90°C rated branch circuit conductors installed between 90°C rated power distribution blocks can be used at the maximum ampacity based on 90°C.
This principle would allow a pull box to be installed at each end of a branch circuit just before the conductors enter the overcurrent device enclosure or load equipment. If 90°C rated power
distribution blocks are used at each end of the branch circuit inside each pull box, then technically, a smaller, less expensive conductor such as a 2 AWG copper type XHHW-2 (rated for 130 amps in
the 90°C column of Table 310.16) can be used at its full value of 130 amps but only for the portion of the branch circuit between the 90°C rated pressure connectors or power distribution blocks.
From the power distribution blocks down to the termination of the overcurrent device or load equipment, a larger conductor would be used after it is sized based on 125% of the continuous load or 100%
of the continuous load after applying correction factors based on conditions of use (whichever is larger). This is because it will be directly connected to either the overcurrent device or the
equipment where the load is applied. In most cases, these will each have 75°C rated terminals.
The weakest point along a 90°C rated conductor is where it connects to the 75°C rated terminal. The new exception recognizes the fact that the middle of a conductor run between 90°C rated terminals
can be sized smaller than the ends which land on a lesser rated terminal.
The last sentence of exception 2 basically states that if this method is used, the smaller, middle run of branch circuit is not permitted to extend into an enclosure containing either the
branch-circuit supply or the branch-circuit load terminations (see image).
Below is a preview of the NEC^®. See the actual NEC^® text at NFPA.ORG for the complete code section. Once there, click on their link to free access to the 2020 NEC^® edition of NFPA 70.
2017 Code Language:
210.19(A)(1) General. Branch-circuit conductors shall have an ampacity not less than the maximum load to be served. Conductors shall be sized to carry not less than the larger of 210.19(A)(1)(a) or
(a) Where a branch circuit supplies continuous loads or any combination of continuous and noncontinuous loads, the minimum branch-circuit conductor size shall have an allowable ampacity not less than
the noncontinuous load plus 125 percent of the continuous load.
(b) The minimum branch-circuit conductor size shall have an allowable ampacity not less than the maximum load to be served after the application of any adjustment or correction factors.
Exception: If the assembly, including the overcurrent devices protecting the branch circuit(s), is listed for operation at 100 percent of its rating, the allowable ampacity of the branch-circuit
conductors shall be permitted to be not less than the sum of the continuous load plus the noncontinuous load.
2020 Code Language:
210.19(A)(1) General. Branch-circuit conductors shall have an ampacity not less than the larger of 210.19(A)(1)(a) or (A)(1)(b) and comply with 110.14(C) for equipment terminations.
(a) Where a branch circuit supplies continuous loads or any combination of continuous and noncontinuous loads, the minimum branch-circuit conductor size shall have an ampacity not less than the
noncontinuous load plus 125 percent of the continuous load in accordance with 310.14.
(b) The minimum branch-circuit conductor size shall have an ampacity not less than the maximum load to be served after the application of any adjustment or correction factors in accordance with
Exception No. 1 to (1)(a): If the assembly, including the overcurrent devices protecting the branch circuit(s), is listed for operation at 100 percent of its rating, the ampacity of the
branch-circuit conductors shall be permitted to be not less than the sum of the continuous load plus the noncontinuous load in accordance with 110.14(C).
Exception No. 2 to (1)(a) and (1)(b): Where a portion of a branch circuit is connected at both its supply and load ends to separately instalā led pressure connections as covered in 110.14(C)(2), it
shall be permitted to have an allowable ampacity, in accordance with 310.15, not less than the sum of the continuous load plus the noncontinuous load. No portion of a branch circuit installed under
this exception shall extend into an enclosure containing either the branch-circuit supply or the branch-circuit load terminations. | {"url":"https://www.electricallicenserenewal.com/Electrical-Continuing-Education-Courses/NEC-Content.php?sectionID=818","timestamp":"2024-11-15T02:54:57Z","content_type":"text/html","content_length":"33241","record_id":"<urn:uuid:9969e795-5d7a-42a2-a441-4cdd34750218>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00427.warc.gz"} |
Students Will Learn
• How to understand the meaning of the derivate in terms of rate of change and local linear approximation
• How to understand the meaning of the definite integral as a limit of Riemann sums and as the net accumulation of change
• How to understand the relationship between the derivative and the definite integral as expressed in the fundamental theorem of calculus
• How to model a written description of a physical situation with a function, a differential equation, or an integral
• How to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement
• How to use technology to solve problems, experiment, interpret results, and verify conclusions
• How communicate mathematical solutions well both orally and in writing | {"url":"https://academy.hslda.org/calculus-ab-topics","timestamp":"2024-11-03T06:18:53Z","content_type":"application/xhtml+xml","content_length":"14416","record_id":"<urn:uuid:0b8fb7b6-2562-41c1-9457-1c89156d6023>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00702.warc.gz"} |
2.17 and 2.18
Solving 2.17 and 2.18 Using the Principle of Virtual Work
It is possible to solve 2.17 and 2.18 using torques, but since the chapter was about using the virtual work principle, let’s use it.
Let’s consider the ladder from the exercise 2.18 (2.17 uses similar approach) rotating clockwise due to the reactive force of the wall.
Let’s imagine a ladder rotating clockwise under the influence of the reaction force of the wall. As the ladder rotates by a small angle δθ radians, it displaces a distance $s = r$ (by the definition
of a radian).
For a small angle θ, it is possible to approximate that any point on ladder moves in a straight line, not in a circular path (see figure below).
This linear movement allows us to compute displacement of each point on the ladder as the following:
Now we can calculate the work done by a reactive force of the wall $T$:
Changes in potential energies of the weight $W$ and the ladder ω are:
Equating the work done by $T$ to the total change in potential energy yields: | {"url":"https://simonuvarov.com/2024/10/26/solving-2-17-and-2-18-using-the-principle-of-virtual-work","timestamp":"2024-11-11T18:23:29Z","content_type":"text/html","content_length":"28421","record_id":"<urn:uuid:e43d4960-8283-4829-813a-eaf5cb51ad95>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00724.warc.gz"} |
IOI '12 P6 - Jousting Tournament
For his wedding with Beatrice d'Este in 1491, the Duke of Milan Lodovico Sforza asked Leonardo to orchestrate the wedding celebrations, including a great jousting tournament that lasted for three
whole days. But the most popular knight is late...
In a jousting tournament, the knights are first arranged in a line and then their positions are numbered from to following the line order. The joust master sets up a round by calling out two
positions and (where ). All the knights whose positions are between and (inclusive) compete: the winner continues in the tournament and goes back to his place in the line, whereas the losers are out
of the game and leave the field. After that, the remaining knights pack together towards the beginning of the line, preserving their relative order in the line, so that their resulting positions are
from to . The joust master calls out another round, repeating this process until just one knight remains.
Leonardo knows that all the knights have different strengths, represented as distinct ranks from (weakest) to (strongest). He also knows the exact commands that the joust master will call out for the
rounds: he's Leonardo, after all... and he is certain that in each of these rounds the knight with the highest rank will win.
Late Knight
of the knights are already arranged in the line, just the most popular knight is missing. This knight has rank and is arriving a bit late. For the benefit of the entertainment, Leonardo wants to
exploit his popularity and choose for him a position in the line that will maximize the number of rounds that the late knight will win. Note that we are not interested in the rounds that don't
involve the late knight, just in the rounds he takes part in and wins.
For knights, the knights that are already arranged in the line have ranks , respectively. Consequently, the late knight has rank . For the rounds, the joust master intends to call out the positions
per round, in this order: , , .
If Leonardo inserts the late knight at the first position, the ranks of the knights on the line will be . The first round involves knights (at positions , , ) with ranks , , , leaving the knight with
rank as the winner. The new line is . The next round is against (at positions , ), and the knight with rank wins, leaving the line . The final round (at positions , ) has as the winner. Thus, the
late knight only wins one round (the second one).
Instead, if Leonardo inserts the late knight between those two of ranks and , the line looks like this: . This time, the first round involves , , , and the knight with rank wins. The next starting
line is , and in the next round ( against ) the knight with rank wins again. The final line is , where wins. Thus, the late knight wins two rounds: this is actually the best possible placement as
there is no way for the late knight to win more than twice.
Your task is to write a program that chooses the best position for the late knight so that the number of rounds won by him is maximized, as Leonardo wants. Specifically, you have to implement a
routine called GetBestPosition(N, C, R, K, S, E), where:
• is the number of knights;
• is the number of rounds called out by the joust master ();
• is the rank of the late knight; the ranks of all the knights (both those already lined up and the late one) are distinct and chosen from , and the rank of the late knight is given explicitly even
though it can be deduced;
• is an array of integers, representing the ranks of the knights that are already on the starting line;
• and are two arrays of size : for each between and , inclusive, the round called by the joust master will involve all knights from position to position , inclusive. You may assume that for each ,
The calls passed to this routine are valid: we have that is less than the current number of knights remaining for the round, and after all the commands there will be exactly one knight left.
GetBestPosition(N, C, R, K, S, E) must return the best position where Leonardo should put the late knight . If there are multiple equivalent positions, output the smallest one. (The position is the
-based position of the late knight in the resulting line. In other words, is the number of other knights standing before the late knight in the optimal solution. Specifically, means that the late
knight is at the beginning of the line, and means that he is at the end of it.)
Subtask 1 [17 points]
You may assume that .
Subtask 2 [32 points]
You may assume that .
Subtask 3 [51 points]
You may assume that .
Implementation Details
You have to submit exactly one file. This file must implement the subprogram described above using the following signature.
int GetBestPosition(int N, int C, int R, int K[], int S[], int E[]);
This subprogram must behave as described above. Of course you are free to implement other subprograms for their internal use. Your submissions must not interact in any way with standard input/output,
nor with any other file.
Sample Grader
The sample grader will expect input in the following format:
• line : , , ;
• lines : ;
• lines : , .
Attachment Package
The sample grader along with sample test cases are available here.
There are no comments at the moment. | {"url":"https://dmoj.ca/problem/ioi12p6","timestamp":"2024-11-14T15:32:49Z","content_type":"text/html","content_length":"49162","record_id":"<urn:uuid:62b172cc-9ed2-4ae8-9618-6817966714fb>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00891.warc.gz"} |
The Nobel Prize in Physics 1962
Lev Davidovich Landau
The Nobel Prize in Physics 1962
Born: 22 January 1908, Baku, Russian Empire (now Azerbaijan)
Died: 1 April 1968, Moscow, USSR (now Russia)
Affiliation at the time of the award: Academy of Sciences, Moscow, USSR (now Russia)
Prize motivation: “for his pioneering theories for condensed matter, especially liquid helium”
Prize share: 1/1
When certain substances are cooled to very low temperatures, their properties undergo radical changes. At temperatures a couple of degrees above absolute zero, helium becomes superfluid and the
liquid flows without friction. One of Lev Landau’s many contributions within theoretical physics came in 1941, when he applied quantum theory to the movement of superfluid liquid helium. Among other
things, he introduced the concept of quasiparticles as the equivalent of sound vibrations and vortexes. This allowed him to develop his theoretical explanation for superfluidity.
Nobel Prizes and laureates
Explore prizes and laureates
Look for popular awards and laureates in different fields, and discover the history of the Nobel Prize. | {"url":"https://www.nobelprize.org/prizes/physics/1962/landau/facts/","timestamp":"2024-11-07T23:35:52Z","content_type":"text/html","content_length":"133312","record_id":"<urn:uuid:66ad5c51-30b9-4941-b9a6-7dbf991eb374>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00583.warc.gz"} |
Why Finite Differences Won’t Cure Your Calculus Blues
Now we know our problem in depth. Richard Harris analyses if a common technique will work adequately.
In the previous article we discussed the foundations of the differential calculus. Initially defined in the 17 ^ th century in terms of the rather vaguely defined infinitesimals, it was not until the
19 ^ th century that Cauchy gave it a rigorous definition with his formalisation of the concept of a limit. Fortunately for us, the infinitesimals were given a solid footing in the 20 ^ th century
with Conway’s surreal numbers and Robinson’s non-standard numbers, saving us from the annoyingly complex reasoning that Cauchy’s approach requires.
Finally, we discussed the mathematical power tool of numerical computing; Taylor’s theorem. This states that for any sufficiently differentiable function f
If we do not place a limit on the number of terms, we have
Note that here f' ( x ) stands for the first derivative of f at x , f" ( x ) for the second and f ^ ( n ) ( x ) for the n ^ th with the convention that the 0 ^ th derivative of a function is the
function itself. The capital sigma stands for the sum of the expression to its right for every unique value of i that satisfies the inequality beneath it and i ! stands for the factorial of i , being
the product of every integer between 1 and i , with convention that the factorial of 0 is 1.
You may recall that we used forward finite differencing as an example of cancellation error in the first article of this series [ Harris10 ]. This technique replaces the infinitesimal δ in the
definition of the derivative with a finite, but small, quantity.
We found that the optimal choice of this finite δ was driven by a trade off between approximation error and cancellation error. With some fairly vigorous hand waving, we concluded that it was the
square root of ε ; the difference between 1 and the smallest floating point number greater than 1.
This time, and I fancy I can hear your collective groans of dismay, we shall dispense with the hand waving.
Forward finite difference
Given some small finite positive δ , the forward finite difference is given by
Using Taylor’s theorem the difference between this value and the derivative is equal to
for some y between x and x + δ .
Assuming f introduces a relative rounding error of some non-negative integer n [ f ] multiples of ½ ε and that x has already accumulated a relative rounding error of some non-negative integer n [ x ]
multiples of ½ ε then, if we wish to approximate the derivative as accurately as possible we should choose δ to minimise
as shown in derivation 1.
Approximation error of the forward finite difference
From Taylor’s theorem we have
for some y between x and x + δ .
We shall assume that f introduces a proportional rounding error of some non-negative integer n [f ]multiples of ½ ε and that x has a proportional rounding error of some non-negative n [x ]multiples
of ½ ε .
We shall further assume that we can represent δ exactly and that the sum of it and x introduces no further rounding error.
Under these assumptions the floating point result of the forward finite difference calculation is bounded by
where the error in x is the same in both cases.
This is in turn bounded by
Noting that
the result is hence bounded by
giving a worst-case absolute error of
Derivation 1
Now this is a function of δ of the form
Such functions, for positive a , b and x , have a minimum value of
The minimum of a / x + bx + c
Recall that the turning points of a function f , that is to say the minima, maxima and inflections, occur where the derivative is zero.
Note that this is only a real number if a and b have the same sign.
We can use the second derivative to find out what kind of turning point this is; positive implies a minimum, negative a maximum and zero an inflection.
If both a and b are positive and we choose the positive square root of their ratio then this value is positive and we have a minimum.
Derivation 2
To leading order in ε and δ the worst case absolute error in the forward finite difference approximation to the derivative is therefore
when δ is equal to
taking the positive square roots in both expressions.
Now these expressions provide a very accurate estimate of the optimal choice of δ and the potential error in the approximation of the derivative that results from that choice. There are, however, a
few teensy-weensy little problems.
The first is that these expressions depend on the relative rounding errors of x and f . We can dismiss these problems out of hand since if we have no inkling as to how accurate x or f are then we
clearly cannot possibly have any expectation whatsoever that we can accurately approximate the derivative.
The second, and slightly more worrying, is that the error depends upon the very value we are trying to approximate; the derivative of f at x . Fortunately, we can recover the error to leading order
in ε by replacing it with the finite difference itself.
The third, and by far the most significant, is that both expressions depend upon the behaviour of the unknown second derivative of f .
Unfortunately this is ever so slightly more difficult to weasel our way out of. By which I of course mean that in general it is entirely impossible to do so.
Given the circumstances, the best thing we can really do is to guess how the second derivative behaves. For purely pragmatic reasons we might assume that
since this yields
The advantage of having a δ of this form is that it helps alleviate both rounding and cancellation errors; it is everywhere larger than (2 n [ f ] ε ) ^ ½ | x | and hence mitigates against rounding
error for large | x | and it is nowhere smaller than (2 n [ f ] ε ) ^ ½ and hence mitigates against cancellation error for small | x |.
Substituting this into our error expression yields
Of course this estimate will be inaccurate if the second derivative differs significantly from our guess.
This is little more than an irritation if our guess is significantly larger than the second derivative since the true error will be smaller than our estimate and we will still have a valid, if
pessimistic, bound.
If our guess is significantly smaller, however, we’re in trouble since we shall in this case underestimate the error. Unfortunately there is little we can do about it.
One thing worth noting is that if the second derivative is very large at x then the derivative will be rapidly changing in its vicinity. The limiting case as the second derivative grows in magnitude
is a discontinuity at which the derivative doesn’t exist.
If we have a very large second derivative, we can argue that the derivative is in some sense approaching non-existence and that we should need to be aware of this and plan our calculations
We have one final issue to address before implementing our algorithm; we have assumed that we can exactly represent both δ and x + δ . Given that our expression for the optimal choice of δ involves a
floating point square root operation this is, in general, unlikely to be the case.
Fortunately we can easily find the closest floating point value to δ for which our assumptions hold with
Naturally this will have some effect on the error bounds, but since it will only be O ( εδ ) it will not impact our approximation of them.
Listing 1 provides the definition of a forward finite difference function object.
template<class F>
class forward_difference
typedef F function_type;
typedef typename F::argument_type argument_type;
typedef typename F::result_type result_type;
explicit forward_difference(
const function_type &f);
forward_difference(const function_type &f,
unsigned long nf);
result_type operator()(
const argument_type &x) const;
function_type f_;
result_type ef_;
Listing 1
Note that we have two constructors; one with an argument to represent n [ f ] and one without. The latter assumes a rounding error of a single ½ ε , as shown in listing 2, and is intended for built
in functions for which such an assumption is reasonable.
template<class F>
const function_type &f) : f_(f),
ef_ = result_type(eps<argument_type>());
template<class F>
const function_type &f,
const unsigned long nf) : f_(f),
ef_ = result_type(eps<argument_type>());
Listing 2
Note also that we are assuming that the result type of the function object has a numeric_limits specialisation (whose epsilon function is represented here by the typesetter-friendly abbreviation eps
<T> ), can be conversion constructed from an unsigned long and has a global namespace overload for the sqrt function. To all intents and purposes we are assuming it is an inbuilt floating point type.
We should rather hope that the argument type of the function object is the same as its result type, and for that matter that this is a floating point type, but must provide for a minimum δ just in
case the user decides otherwise, which we do by setting a lower bound for ef_ . We must be content in such cases with the fact that they have made a rod for their own back when it comes time to
perform their error analysis!
Listing 3 gives the implementation of the function call operator based upon the results of our analysis.
template<class F>
typename forward_difference<F>::result_type
const argument_type &x) const
const argument_type abs_x =
(x>argument_type(0UL)) ? x : -x;
const argument_type d =
const argument_type u = x+d;
return (f_(u)-f_(x))/result_type(u-x);
Listing 3
As an example, let us apply our forward difference to the exponential function with arguments from -10 to 10. We can therefore expect that n [ f ] is equal to one and n [ x ] to zero and hence that
our approximation of the error is
Since the derivative of the exponential function is the exponential function itself, we can accurately calculate the true error by taking the absolute difference between it and the finite difference
To compare our approximation of the error with the exact error we shall count the number of leading zeros after the decimal point of each, which we can do by negating the base 10 logarithm of the
Figure 1 plots the leading zeros in the decimal fraction of our approximate error as a dashed line and in that of the true error as a solid line, with larger values on the y axis thus implying
smaller values for the errors.
Our approximation clearly increasingly underestimates the error as the absolute value of x increases. This shouldn’t come as too much of a surprise since our assumption about the behaviour of the
second derivative grows increasingly inaccurate as the magnitude of x increases for the exponential function.
Nevertheless, our approximation displays the correct overall trend and is nowhere catastrophically inaccurate, at least to my eye.
The question remains as to whether we can do any better.
Symmetric finite difference
Returning to Taylor’s theorem we can see that the term whose coefficient is a multiple of the second derivative is that of δ ^ 2 . This has the very useful property that it takes the same value for
both + δ and - δ .
If we approximate the derivative with the finite difference between a small step above and a small step below x we can arrange for this term to cancel out. Specifically, the expression
differs from the derivative at x by
for some y between x - δ and x + δ as shown in derivation 3.
The symmetric finite difference
From Taylor’s theorem we have
for some y [0 ]between x - δ and x and y [1 ]between x and x + δ
The symmetric finite difference is therefore.
The intermediate value theorem states that for a continuous function, there must be a point x between points x [0 ]and x [1 ]such that
If the second derivative of our function is continuous this means that
for some y between x - δ and x + δ
Derivation 3
Now this is a rather impressive order of magnitude better in δ than the forward finite difference considering that it involves no additional evaluations of f .
That said, it is not at all uncommon that both the value of the function and its derivative are required, in which case the finite forward difference can get one of its function evaluations for free.
With a similar analysis to that we made for the forward finite difference, given in derivation 4, we find that the optimal choice of δ must minimise
Approximation error of the symmetric finite difference
From Taylor’s theorem we have
for some y between x and x + δ .
Making the same assumptions as before about rounding errors in both f and x , the floating point result of the symmetric finite difference calculation is bounded by
which is in turn bounded by
The error in x is again the same in all cases giving us
and hence a worst case absolute error of
or, by the mean value theorem again
Derivation 4
This time the quantity we wish to minimise is a function in δ of the form
which, as shown in derivation 5, given positive b is minimised by
The minimum of a / x + bx ^2 +c
We find a turning point of f with
We have a second derivative of
so if b is positive we have a minimum.
Derivation 5
To leading order in ε and δ the minimum relative error in the symmetric finite difference approximation to the derivative is therefore
when δ is equal to
Now this error is
Unfortunately in order to achieve this we have compounded the problem of unknown quantities in the error and the choice of δ .
The optimal choice of the δ is now dependent on the properties of the third rather than the second derivative of f so we cannot use our previous argument that it may in some sense be reasonable to
ignore it.
Furthermore, the resulting approximation error is dependant on both the second and the third derivatives of f .
We can deal with the first problem in the same way as we did before. In the name of pragmatism we assume that
giving a δ of
It’s a little more difficult to justify a guess about the form of the second derivative since it plays no part in the choice of δ .
We could arbitrarily decide that it has a similar form to that we chose for it during our analysis of the forward finite difference. Specifically
This strikes me a vaguely unsatisfying however, since it is not consistent with our assumed behaviour of the third derivative.
Instead, I should prefer something that satisfies
since this is approximately consistent with our guess.
A consistent second derivative
Consider first
where a is a constant and sgn( x ) is the sign of x . For simplicity’s sake, we shall declare the derivative of the absolute value of x at 0 to be 0 rather than undefined.
The second term has the required form so if we can find a way to cancel out the first we shall have succeeded. Adding a second term whose derivative includes a term of the same form might just do the
We therefore require
Solving for a and b yields a serendipitously unique result.
Derivation 6
Derivation 6 shows that we should choose
for positive x ,
for x equal to zero and
for negative x , with terms given to 5 decimal places.
Substituting these guessed derivatives back into our error formula yields an estimated error of
for positive x ,
for x equal to zero and
for negative x .
Once again we shall not use δ directly, but shall instead use the difference between the floating point representations of x + δ and x - δ .
Listing 4 provides the definition of a symmetric finite difference function object.
template<class F>
class symmetric_difference
typedef F function_type;
typedef typename F::argument_type argument_type;
typedef typename F::result_type result_type;
explicit symmetric_difference(
const function_type &f);
symmetric_difference(const function_type &f,
unsigned long nf);
result_type operator()
(const argument_type &x) const;
function_type f_;
result_type ef_;
Listing 4
We again have two constructors; one for built in functions and one for user defined function, as shown in listing 5. Listing 6 gives the definition of the function call operator based upon our
template<class F>
const function_type &f) : f_(f),
ef_(pow(result_type(3UL)/result_type(2UL) *
ef_ = result_type(eps<argument_type>())
template<class F>
const function_type &f,
const unsigned long nf) : f_(f),
ef_(pow(result_type(3UL*nf)/result_type(2UL) *
ef_ = eps<argument_type>();
Listing 5
template<class F>
typename symmetric_difference<F>::result_type
const argument_type &x) const
const argument_type abs_x =
(x>argument_type(0UL)) ? x : -x;
const argument_type d =
const argument_type l = x-d;
const argument_type u = x+d;
return (f_(u)-f_(l))/result_type(u-l);
Listing 6
Figure 2 plots the negation of the base 10 logarithm of our approximation of the error in this numerical approximation of the derivative of the exponential function as a dashed line and the true
error as a solid line.
Clearly the error in the symmetric finite difference is smaller than that in the forward finite difference, although it appears that the accuracy of our approximation of that error isn’t quite so
good. That said, the average ratios between the number of decimal places in the true error and the approximate error of the two algorithms are not so very different; 1.21 for the forward finite
difference and 1.24 for the symmetric finite difference.
Still, not too shabby if you ask me.
But the question still remains as to whether we can do any better.
Higher order finite differences
As it happens we can, although I doubt that this comes as much of a surprise. We do so by recognising that the advantage of the symmetric finite difference stems from the fact that terms dependant
upon the second derivative largely cancel out. If we can arrange for higher derivatives to cancel out we should be able to improve accuracy still further.
Unfortunately, doing so makes a full error analysis even more tedious than those we have already suffered through. I therefore propose, and I suspect that this will be to your very great relief, that
we revert to our original hand-waving analysis.
In doing so our choice of δ shall not be significantly impacted, but we shall have to content ourselves with a less satisfactory estimate of the error in the approximation.
We shall start by returning to Taylor’s theorem again.
From this we find that the numerator of the symmetric finite difference is
Performing the same calculation with 2 δ yields
With a little algebra it is simple to show that
Assuming that each evaluation of f introduces a single rounding error and that the arguments are in all cases exact this mean that the optimal choice of δ is of order
The optimal choice of δ
Noting that multiplying by a power of 2 never introduces a rounding error, the floating point approximation to our latest finite difference is bounded by
which simplifies to
The order of the error is consequently minimised when
Derivation 7
By the same argument from pragmatism that we have so far used we should therefore choose
to yield an
With sufficient patience, we might continue in this manner, creating ever more accurate approximations at the expense of increased calls to f .
Unfortunately, not only is this extremely tiresome, but we cannot escape the fact that the error in such approximations shall always depend upon the behaviour of unknown higher order derivatives.
For these reasons I have no qualms in declaring finite difference algorithms to be a flock of lame ducks.
tutti: Quack!
[Harris10] Harris, R., ‘You’re Going to Have to Think; Why [Insert Technique Here] Won’t Cure Your Floating Point Blues’, Overload 99, ACCU, 2010 | {"url":"https://accu.org/journals/overload/19/105/harris_1960/","timestamp":"2024-11-14T20:29:08Z","content_type":"text/html","content_length":"61632","record_id":"<urn:uuid:27f61ef2-3b8b-4bb4-9534-f4261222cf52>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00610.warc.gz"} |
Graphing storiesGraphing stories – Science in School
Sketch graphs from ‘story’ videos of everyday events to help students understand the basic features of graphs and how to interpret them.
Image modified from Al Soot/Unsplash
The idea of graphing stories is simple. Students are shown a short film of an everyday event, such as a glass filling with water, a piece of salmon cooking in the oven, or a bike moving down a hill.
The students are then prompted to sketch a graph that describes the event, for example, how they think the height of the water, the temperature of the salmon, or the speed of the bike changes over
time. These sketches become the starting point for a classroom discussion, which ends with the correct graph being shown.
Below is an example of a graphing stories video.
To draw the graph describing the rising temperature of the salmon in the oven, students will have to think about the start and end points of the graph and what shape the graph will take in between
those points. Is it going to be a straight line or a curve? This approach thus focuses on the graph’s global features. In this way, the activity complements lessons where students construct graphs
point by point, for instance, lessons where students conduct their own experiments, collect data, and visualize data graphically.
This story-graphing routine was pioneered by the American maths educator Dan Meyer. It’s suitable for students aged 13-19 and graphing a single story typically takes about 10-20 minutes.
How to use the graphing stories videos
• Students will need pencils and squared paper.
• The story videos can be accessed here.
1. Show the first part of the film to the students. Pause the film after the coordinate system is displayed and relevant variables are visible on the axes. Explain that students should draw a graph
of the event, describing the relationship between the two variables.
2. Explain to the students that they do not have all the information needed to draw the graph, so they will have to make some assumptions and estimates. In the story above, for instance, the
students need to estimate how long it took to cook the salmon.
3. Give students time to draw a coordinate system in their notebooks. Depending on prior knowledge, it may be necessary to clarify which variables are to be plotted on each axis and which scale the
axes could have. You can also choose to hand out ready-made graphing paper. If the students don’t require scaffolding, it is a good exercise for them to draw their own coordinate system and
choose a suitable scale.
4. Restart the film to show the event once more. Depending on the nature of the story, it may be necessary to play the film several times or to play it at a slower speed. If students have their own
computers, you can choose to give them access to the film, so that they can watch it several times and pause if necessary.
5. Give students time to draw the graph. Walk around the classroom and observe the students’ work. Students who have difficulty getting started can be advised to first describe the relationship
between the variables in words, for example, “I think the salmon’s temperature increases at a steady pace”. Once a hypothesis is formulated in words, it is often easier to transfer this idea to a
graph. It can be helpful for the students to work in pairs.
These three questions are also a good way to support students:
□ At what point should the graph begin?
□ At what point should the graph end?
□ What do you think the graph looks like in between?
6. Select a few graphs that show different mathematical ideas to compare in a whole-class discussion. For example, you can select graphs that have different shapes, the same shape but different
start and end points, or different scales on the axes. Look for graphs that manifest common misconceptions.
7. Present the selected graphs to the class. Students can describe their graphs orally, as you draw them on the board, or students can come forward and draw their graphs on the board. A camera and
projector or a digital submission system are other possibilities.
8. Guide the class discussion to help students understand the key features of their suggested graphs and how these relate to the event shown in the video. See Discussion.
9. Give students time to revise their graphs based on what they learned during the discussion. By emphasizing that the first graph is a draft, it becomes less risky for the students to be wrong.
This, in turn, can increase participation in the class discussion.
10. Restart the video and show the correct graph. Discuss any similarities and differences between the correct graph and the students’ suggestions. This can lead the students to conclusions such as
“We thought it took 20 minutes to cook the salmon, but it took longer than that!”
“It seems that the salmon’s temperature increased fastest around the middle of the cooking time. I did not think so!”
“I thought the salmon’s temperature increased linearly, but it didn’t.”
Correct graph for the story ‘salmon in the oven’
Image courtesy of Emelie Reuterswärd
A good way to guide the class discussion after the first round of graph sketching is to compare two graphs and encourage the students to describe their similarities and differences.
For example, the graphs below show two possible descriptions of how the salmon’s temperature increases while it is cooking in the oven.
Image courtesy of Emelie Reuterswärd
When students compare these graphs, they might note that:
• the blue graph starts at the origin, while the purple graph has a higher y-intercept;
• the student who has drawn the purple graph thinks that it takes longer for the salmon to cook;
• the blue graph shows that the salmon’s temperature increases at a steady pace, while the purple graph shows that the salmon’s temperature increases faster at the end.
By reformulating students’ statements using mathematical vocabulary, you can introduce important mathematical concepts, such as ‘linear’, ‘slope’, and ‘domain’.
Another way to take the classroom discussion further is to focus on different parts of the graph and let the students explain their thinking: Why does the graph not start at the origin? Why did you
choose that scale? Why is the graph steeper at the end?
Ideas for expanding the task
Once you have completed a story, there are several ways to expand the task. Students can be asked to determine the equation that describes the graph or to determine the function’s domain and range.
You can also follow up by asking “What happens if?”. For the salmon example, such questions could include
• What would the graph look like if we cooked a smaller piece of salmon? A bigger one?
• What would the graph look like if we put in a frozen piece of salmon?
• What would the graph look like if we left the salmon longer in the oven?
Encouraging students to ask these kinds of questions trains them to explore the characteristics and limitations of a mathematical model and shows them how to think like a mathematician.
It is also effective to work with several stories in a row. That way, you can compare and contrast different graphs and make connections between different mathematical concepts. For instance, the
story ‘bike speed’ prompts students to graph the speed of a bike as a function of time, as the bike moves down a hill, slows down, and eventually comes to a stop. The graph turns out to be an almost
perfect parabola. But what about the graph describing the distance travelled as a function of time? This question is answered in the story ‘bike distance’. By letting students work with both of these
stories, they can make connections between concepts such as derivative and primitive functions.
Working with the two stories ‘bike speed’ and ‘bike distance’, students can explore the graph of a function and the graph of its antiderivative.
Image courtesy of Emelie Reuterswärd
As an extension, you can let your students create their own stories for graphing using their mobile phones. This encourages them to see the mathematics in everyday events and to describe them with a
mathematical model. In secondary school, the films can explore phenomena in other subjects, such as physics or vocational subjects. In this way, the students’ films can become the starting point for
an interdisciplinary learning activity.
Why use graphing stories?
There are several reasons to work with graphing stories.
1. Students experience how graphs are used to describe everyday phenomena. It connects mathematics to students’ reality and allows them to see the usefulness of mathematics.
2. The classroom discussion of the students’ graphs creates a need to formulate what the students have drawn. This provides an opportunity to introduce important concepts, such as slope, linear,
constant, increasing, and decreasing. In upper secondary school, you can use graphing stories to discuss more advanced concepts, such as derivatives, inflection point, and maximum.
3. After working with several different stories, a natural step is to compare the graphs and categorize them. Thus, graphing stories is an excellent tool for introducing and naming relationships,
for example, linear, quadratic, periodic, and exponential.
4. In lower secondary school, it is common to work mainly with linear relationships. With the help of graphing stories, you can show students that there are other types of relationships, the graphs
of which are not straight lines.
5. The sketching of graphs of everyday events is a common task in many textbooks. Letting students see a film of the event makes it more concrete, which can make it easier for students to draw the
graph. In addition, the connection between the event and the graph becomes stronger.
6. Drawing graphs of everyday events is a challenging task that can often uncover hidden misconceptions. For example, students often struggle to find a suitable scale and fail to equally space the
quantities along the axis. Having to reason things through rather than just plotting data can often uncover hidden misconceptions.
The last point is a particular strength of this approach. One common misconception is so-called ‘iconic’ representations of graphs. This means that the student sees a correspondence between the shape
of the graph and a visual feature of the described event. For example, students working with the story ‘bike speed’ may draw a graph that resembles the shape of the valley the bike rode through (left
graph), instead of a parabola with a maximum point (right graph).
Image courtesy of Emelie Reuterswärd
Similarly, a student trying to draw a graph of how the height of a moving swing changes with time may draw a graph that resembles the swing’s movement back and forth (left graph), rather than a
periodic graph that alternates between high and low y values (right graph).
Image courtesy of Emelie Reuterswärd
Graphing stories makes such misconceptions visible and provides excellent opportunities for students to discuss and overcome them.
Science on Stage
This article is about graphing stories. The students are shown a short film of an everyday event, such as a glass filling with water, and are asked to draw a graph of the event. These sketches are
discussed as a class. This approach should help them to develop a better understanding of the concepts of a graph. Interestingly, no text is spoken or displayed in the films. This makes this approach
particularly suitable for language-disadvantaged students. If the teacher pays attention to (mathematical) vocabulary when discussing the graphs, the students can improve their language skills as
Annemiek van Leendert, Math teacher, Royal Visio, the Netherlands
Text released under the Creative Commons CC-BY license. Images: please see individual descriptions | {"url":"https://www.scienceinschool.org/article/2022/graphing-stories/","timestamp":"2024-11-07T03:44:42Z","content_type":"text/html","content_length":"98426","record_id":"<urn:uuid:0b286d36-dcda-4f2a-b3da-2c73a976ec4b>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00020.warc.gz"} |
Descent methods - Complex systems and AI
Descent methods
Descent methods
As the explicit name indicates, the methods of descent, or local search, consist in "sliding" along the objective function until a local optimum is found, that is to say where the descent is no
longer possible. There are several kinds of descent method which we will describe here.
Simple descent
From an initial solution, the simple descent algorithm chooses a neighboring solution better than the current solution, until it cannot make such a choice.
The algorithm is as follows:
to do
S[(i + 1)] = neighbor (S[i])
if f (S[(i + 1)]) <f (S[i]) accept S[(i + 1)]
end if
as long as f (S[(i + 1)]) <f (S[i]), whatever S[(i + 1)] = neighbor (S[i])
return R[not]
Greatest descent
The algorithm is mainly the same as for the simple descent, only a selection criterion of a neighboring solution is modified:
choose s' neighbor of s / f (s') <f (s' ') or f (s') = f (s'') qq is s' 'neighbor of s
We therefore choose the neighboring solution offering the best improvement of the current solution.
Multi-start descent
Multi-start descent performs multiple instances of the single descent or greater descent problem. The algorithm is as follows:
iter = 1 f (Best) = infinity
to do
Choose a starting solution s[O] at random s 0)
if f (s) <f(Best) alors Best tant que iter < iterMax
return Bes | {"url":"https://complex-systems-ai.com/en/stochastic-algorithms-2/descent-methods/","timestamp":"2024-11-05T05:43:47Z","content_type":"text/html","content_length":"158173","record_id":"<urn:uuid:502f8944-c56a-4f4e-9cd0-a75905209526>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00670.warc.gz"} |
Pseudo Random Number Generation¶
Estimated time to read: 7 minutes
You are a game developer in charge to create a fast an reliable random number generator for a procedural content generation system. The requirements are:
• Do not rely on external libraries;
• Dont need to be cryptographically secure;
• Be blazing fast;
• Fully reproducible via automated tests if used the same seed;
• Use exactly 32 bits as seed;
• Be able to generate a number between a given range, both inclusive.
So you remembered a strange professor talking about the xorshift algorithm and decided it is good enough for your use case. And with some small research, you found the Marsaglia "Xorshift RNGs". You
decided to implement it and test it.
The xorshift is a family of pseudo random number generators created by George Marsaglia. The xorshift is a very simple algorithm that is very fast and have a good statistical quality. It is a very
good choice for games and simulations.
xorshift is the process of shifting the binary value of a number and then xor'ing that binary to the original value to create a new value.
value = value xor (value shift by number)
The shift operators can be to the left << or to the right >>. When shifted to the left, it is the same thing as multiplying by 2 at the power of the number. When shifted to the right, it is the same
thing as dividing.
The value of a << b is the unique value congruent to \(a * 2^{b}\) modulo \( 2^{N} \) where \( N \) is the number of bits in the return type (that is, bitwise left shift is performed and the bits
that get shifted out of the destination type are discarded).
The value of \( a >> b \) is \( a/2^{b} \) rounded down (in other words, right shift on signed a is arithmetic right shift).
The xorshift algorithm from Marsaglia is a combination of 3 xorshifts, the first one is the seed (or the last random number generated), and the next ones are the result of the previous xorshift. The
steps are:
1. xorshift the value by 13 bits to the left;
2. xorshift the value by 17 bits to the right;
3. xorshift the value by 5 bits to the left;
At the end of this 3 xorshifts, the current state of the value is your current random number.
In order to clamp a random number the value between two numbers (max and min), you should follow this idea:
value = min + (random % (max - min + 1))
Receives the seed S, the number N of random numbers to be generated and the range R1 and R2 of the numbers should be in, there is no guarantee the range numbers are in order. The range numbers are
both inclusive. S and N are both 32 bits unsigned integers and R1 and R2 are both 32 bits signed integers.
The list of numbers to be generated, one per line. In this case, it would be only one and the random number should be clamped to be between 0 and 99.
seed in decimal: 1
seed in binary: 0b00000000000000000000000000000001
seed: 0b00000000000000000000000000000001
seed << 13: 0b00000000000000000010000000000000
seed xor (seed << 13): 0b00000000000000000010000000000001
seed: 0b00000000000000000010000000000001
seed >> 17: 0b00000000000000000000000000000000
seed xor (seed >> 17): 0b00000000000000000010000000000001
seed: 0b00000000000000000010000000000001
seed << 5: 0b00000000000001000000000000100000
seed xor (seed << 5): 0b00000000000001000010000000100001
The final result is 0b00000000000001000010000000100001 which is 270369 in decimal.
Now in order to clamp it to be between 0 and 99, we do:
value = min + (random % (max - min + 1))
value = 0 + (270369 % (99 - 0 + 1))
value = 0 + (270369 % 100)
value = 0 + 69
value = 69
So this output would be: | {"url":"https://courses.tolstenko.net/artificialintelligence/assignments/rng/","timestamp":"2024-11-06T07:17:19Z","content_type":"text/html","content_length":"37772","record_id":"<urn:uuid:c6704d09-8165-48c2-929f-4c77d5e58a5a>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00176.warc.gz"} |
An HP PPL implementation of the IAU 2000b nutation algorithm
11-30-2022, 06:45 PM
Post: #1
cdeaglejr Posts: 63
Member Joined: Jul 2022
An HP PPL implementation of the IAU 2000b nutation algorithm
An HP PPL version of a nutation algorithm based on the IAU 2000b theory
An Abridged Model of the Precession-Nutation of the Celestial Pole, D. McCarthy and B. Luzum,
Celestial Mechanics and Dynamical Astronomy, 85: 37-49, 2003.
The software and documentation can be downloaded from
12-01-2022, 06:01 PM
Post: #2
cdeaglejr Posts: 63
Member Joined: Jul 2022
RE: An HP PPL implementation of the IAU 2000b nutation algorithm
Updated on December 1, 2022
This version allows the user to specify how many rows of tabular data are used in the nutation computations. This can be done on line 20 of the source code using the following syntax.
// number of rows of data to use in calculation (1 <= nrows <= 78)
EXPORT nrows := 78;
A low-precision nutation version typically uses the first 13 rows of data (nrows := 13).
This version is available at the same download link as the original.
User(s) browsing this thread: 2 Guest(s) | {"url":"https://hpmuseum.org/forum/thread-19231-post-166908.html#pid166908","timestamp":"2024-11-04T17:33:40Z","content_type":"application/xhtml+xml","content_length":"18180","record_id":"<urn:uuid:af808edf-5597-4a0e-8f5e-d48f08bdc073>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00683.warc.gz"} |
9 Important PhD in Tourism Research and Topics related to Research - Trail Cohorts
9 Important PhD in Tourism Research and Topics related to Research
The article shows the detail information of how to understand Research while seeking for PhD in Tourism Research and its types and other topics:
Table of Contents
Basic Statistics- Central Tendency & Measures of Dispersion- An understanding of PhD in Tourism Research
Statistics can be considered as numerical statements of fact which are highly convenient and meaningful forms of communication. It is derived from Latin word status- political state/government.
a. Central tendency (Mean, Median, Mode):
• Mean: It is the average result of the population and depicts the overall analysis as a
It can also be denoted as: where stands for Arithmetic Mean
• Median: Median is the middle number in a sorted list of numbers. For odd numbers it is calculated as
n+1/2 and for even numbers, average of n/2 and n+1/2.
• Mode: The most frequent number—that is, the number that occurs the highest number of times in a given set of data is known as mode of the data.
Relation among Mean, Median and Mode:
Mode = 3Median * 2Mean
b. Measures of Dispersion:
A measure of statistical dispersion is a non-negative real number that is zero if all the data is same and increases as the data become more diverse.
• Range: It is the interval between group numbers of data
• Inter-quartile Range: Inter-Quartile Range is based upon middle 50% of the values in a distribution and not affected by extreme values. Half of the Inter-Quartile Range is called Quartile
Deviation (Q.D.).
Thus, Q.D. = (Q3 – Q1)/2 where Q3 is Upper Quartiles and Q1 is Lower Quartiles.
• Standard Deviation & Variance: The mean deviations are squared. The Mean of these squared
deviations is called Variance and positive square root of Variance is known as
Standard Deviation.
• Coefficient of Variance: It is not an absolute measure but is a relative measure of
dispersion. It is expressed as percentage.
C.V. = (Standard Deviation/Mean) *100
Also Read More about PhD in Tourism Research:
Research and its Theory:
Research is kept on searching for work and explained as “creative and systematic work undertaken to increase the stock of knowledge and the use of this stock of knowledge to devise new applications.”
The relationship between theory and research as a dialectic whereby theory determines what data are to be collected and research findings provide challenges to accepted theories.
Types of Research:
• Fundamental or basic research: Basic research is an investigation on basic principles and reasons for occurrence of a particular event or process or phenomenon.
• Applied research: In an applied research one solves certain problems employing well known and accepted theories and principles. Most of the experimental research, case studies and
inter-disciplinary research are essentially applied research.
• Exploratory Research: Exploratory research might involve a literature search or conducting focus group interviews.
• Descriptive research: The descriptive research is directed toward studying “what” and how many off this “what”. Thus, it is directed toward answering questions such as, “What is this?”.
• Explanatory research: Its primary goal is to understand or to explain relationships.
• Longitudinal Research: Research carried out longitudinally involves data collection at multiple points in time. It can be trend, Cohort and Panel study.
• Cross-sectional Research: One-shot or cross-sectional studies are those in which data is gathered once, during a period of days, weeks or months.
• Action research: Fact findings to improve the quality of action in the social world
Quantitative Research:
Quantitative research, is defined as the systematic investigation of phenomena by gathering quantifiable data and performing statistical, mathematical or computational techniques. Quantitative
research gathers information from existing and potential customers using sampling methods and sending out online surveys, online polls, questionnaires etc., the results of which can be depicted in
the form of numerical.
• Survey Research: Survey Research is the most fundamental tool for all quantitative research methodologies and studies. Surveys used to ask questions to a sample of respondents, using various
types such as such as online polls, online surveys, paper questionnaires etc.
• Correlational Research: Correlation research is conducted to establish a relationship between two closely knit entities and how one impacts the other and what are the changes that are eventually
• Casual Comparative Research: This research method mainly depends on the factor of comparison. Also called the quasi-experimental research, this quantitative research method is used by researchers
to draw conclusions about cause-effect equation between two or more variables, where one variable is dependent on the other independent variable.
• Experimental Research: It is usually based on one or more theories. This theory has not been proved in the past and is merely a supposition. In an experimental research, an analysis is done
around proving or disproving the statement. This research method is used in natural sciences.
Qualitative Research:
Qualitative research is defined as a market research method that focuses on obtaining data through open-ended and conversational communication. The various methods are:
• One-on-One Interview: Conducting in-depth interviews is one of the most common qualitative research methods. It is a personal interview that is carried out with one respondent at a time. This is
purely a conversational method and invites opportunities to get details in depth from the respondent.
• Focus groups: A focus group is also one of the commonly used qualitative research methods, used
in data collection. A focus group usually includes a limited number of respondents (6-10) from within your target market. The main aim of the focus group is to find answers to the why what and
how questions.
• Ethnographic research: Ethnographic research is the most in-depth observational method that studies people in their naturally occurring environment. This method requires the researchers to adapt
to the target audiences’ environments which could be anywhere from an organization to a city or any remote location.
• Case study research: This type of research method is used within a number of areas like
education, social sciences and similar. This method may look difficult to
operate; however, it is one of the simplest ways of conducting research as it
involves a deep dive and thorough understanding of the data collection methods
and inferring the data.
• Record keeping: This method makes use of the already existing reliable documents and similar sources of information as the data source. This data can be used in a new research. This is similar to
going to a library. There one can go over books and other reference material to collect relevant data that can likely be used in the research.
• Process of observation: Qualitative Observation is a process of research that uses subjective methodologies to gather systematic information or data. Since, the focus on qualitative observation
is the research process of using subjective methodologies to gather information or data. The qualitative observation is primarily used to equate quality differences. Qualitative observation deals
with the 5 major sensory organs and their functioning – sight, smell, touch, taste, and hearing.
• Grounded Theory: It is to describe the essence of an activity of an explanation of phenomological event. Open and axial coding techniques to identify themes and build the theory.
• Phenomology: When describing an event, activity. A combination of videos, places
• Narrative: weaves together a sequence of events from one/two individuals’ interviews.
Steps of doing Research
Steps of Research:
Step 1: Identify the Problem:
The first step in the process is to identify a problem or develop a research question.
Step 2: Review the Literature
The researcher must learn more about the topic under investigation. To do this, the researcher must review the literature related to the research problem.
Step 3: Development of Working Hypothesis
In step 3 of the process, the researcher will make certain assumptions as per literature review to find out the scope of the study.
Step 4: Preparing the Research Design
It resembles the preparation of blue print of research.
Step 5: Data Collection
The actual study begins with the collection of data.
Step 6: Analysis of Data
The researcher has data to analyze so that the research question can be answered.
Step 7: Hypothesis Testing
The testing of the expected and observed outcome of hypothesis.
Step 8: Generalization and Interpretation
The researcher will interpret the result and conclude.
Step 9: Preparation of Report/Thesis:
In this, Scholars and researchers will prepare their full thesis/ report according to their need.
Read More about Tourism Case Studies:
Research Analytical Tools
Analysis tools:
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example,
it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables.
Discriminant Analysis is a statistical tool with an objective to assess the adequacy of a classification, given the group memberships; or to assign objects to one group among a number of groups. For
any kind of Discriminant Analysis, some group assignments should be known beforehand.
Conjoint analysis is a statistical technique that helps in forming subsets of all the possible combinations of the features present in the target product. These features used determine the purchasing
decision of the product. Conjoint analysis works on the belief that the relative values of the attributes when studied together are calculated in a better manner than in segregation.
Multiple regression generally explains the relationship between multiple independent or predictor variables and one dependent or criterion variable. A dependent variable is modeled as a function of
several independent variables with corresponding coefficients, along with the constant term. Multiple regression requires two or more predictor variables, and this is why it is called multiple
Sampling methods-Probability and Non-probability sampling
Sampling Methods
There are two main sampling methods for quantitative research: Probability and Non-probability sampling.
• Probability sampling: A theory of probability is used to
filter individuals from a population and create samples in probability
sampling. Participants of a sample are chosen random selection processes. Each
member of the target audience has an equal opportunity to be a selected in the
There are four main types of probability sampling-
• Simple random sampling: As the name indicates, simple random sampling is nothing but a random selection of elements for a sample. This sampling technique is implemented where the target
population is considerably large.
• Stratified random sampling: In the stratified random sampling method, a large population is divided into groups (strata) and members of a sample are chosen randomly from these strata. The various
segregated strata should ideally not overlap one another.
• Cluster sampling: Cluster sampling is a probability sampling method using which the main segment is divided into clusters, usually using geographic and demographic segmentation parameters.
• Systematic sampling: Systematic sampling is a technique where the starting point of the sample is chosen randomly and all the other elements are chosen using a fixed interval. This interval is
calculated by dividing population size by the target sample size.
• Non-probability sampling: Non-probability sampling is where the
researcher’s knowledge and experience are used to create samples. Because of
the involvement of the researcher, not all the members of a target population
have an equal probability of being selected to be a part of a sample.
There are five non-probability sampling models:
• Convenience Sampling: In convenience sampling, elements of a sample are chosen only due to one prime reason: their proximity to the researcher. These samples are quick and easy to implement as
there is no other parameter of selection involved.
• Consecutive Sampling: Consecutive sampling is quite similar to convenience sampling, except for the fact that researchers can chose a single element or a group of samples and conduct research
consecutively over a significant time period and then perform the same process with other samples.
• Quota Sampling: Using quota sampling, researchers can select elements using their knowledge of target traits and personalities to form strata. Members of various strata can then be chosen to be a
part of the sample as per the researcher’s understanding.
• Snowball Sampling: Snowball sampling is conducted with target audiences which are difficult to contact and get information. It is popular in cases where the target audience for research is rare
to put together.
• Judgmental Sampling: Judgmental sampling is a non-probability sampling method where samples are created only on the basis of the researcher’s experience and skill.
Hypothesis testing- Parametric & Non-parametric tests
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.
-Null Hypothesis: A null hypothesis is a type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations.
-Type 1 error: It refers to rejecting a valid null hypothesis.
-Type 2 error: It is accepting an invalid null hypothesis
-Four Steps of Hypothesis Testing
• The first step is for the analyst to state the two hypotheses so that only one can be right.
• The next step is to formulate an analysis plan, which outlines how the data will be evaluated.
• The third step is to carry out the plan and physically analyze the sample data.
• The fourth and final step is to analyze the results and either accept or reject the null hypothesis.
–The p-value is the probability that a given result (or a more significant result) would occur under the null hypothesis.
– If the p-value is less than the chosen significance then we say the null hypothesis is rejected at the chosen level of significance.
– If the p-value is not less than the chosen significance threshold then the evidence is insufficient to support a conclusion.
A parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one’s data are drawn, while a non-parametric test
is one that makes no such assumptions.
Types of parametric tests
A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. It is of 3 types:
• One sample t-test
• Independent t-test
• Paired t-test
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the “variation” among and between groups) used to analyze, differences among
group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. To conduct a test with three or more variables, one must use an analysis of variance.
Types of Non-parametric tests
Chi-square tests:
A chi-squared test, also written as χ2 test, is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.
Without other qualification, ‘chi-squared test’ often is used as short for Pearson’s chi-squared test.
Run Test:
Runs Test for Detecting Non-randomness. The runs test (Bradley, 1968) can be used to decide if a data set is from a random process.
Sign Test:
The sign test is a statistical method to test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment.
Wald- Walfowitz Test:
The Wald–Wolfowitz runs test (or simply runs test), named after statisticians Abraham Wald and Jacob Wolfowitz is a non-parametric statistical test that checks a randomness hypothesis for a
two-valued data sequence. More precisely, it can be used to test the hypothesis that the elements of the sequence are mutually independent.
Kursal Walis Test:
The Kruskal–Wallis test by ranks, Kruskal–Wallis H test or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate from the same distribution. It is used for comparing
two or more independent samples of equal or different sample sizes. It extends the Mann–Whitney U test, which is used for comparing only two groups.
Komogrov- Smirnov Test.
The Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used
to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test). It is named after Andrey Kolmogorov and Nikolai Smirnov.
Discreet, Continuous, Normal and Sampling Distributions
Distributions- Discrete and Continuous:
• Discreet: A discreet random variable takes on discrete values that can be counted and
assume values from a distinct predetermined set. For ex: Binomial distribution,
Poisson distribution
• Continuous: The continuous distribution is useful because it represents variables that are
evenly distributed over a given interval. For ex: Normal Distribution
Normal distribution, Sampling distribution.
• The Normal Distribution has many uses in practical world as many experimental results often follow normal distribution. It can be represented as Bell-Shaped curve. The normal curve is symmetrical
and defined by its mean and standard deviation. The number of standard deviations Z for an observation, which is distance between value x and mean is defined by:
Z = (x- μ )/ σ
Where x = value of the observation
μ = the mean of the distribution
σ = standard deviation of the distribution
• The Sampling Distribution: In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.
In here, we take sample size n of the population P. So calculating Sample distribution would be:
Z = (x- μ )/ σ x where σ x = σ/(n)1/2 | {"url":"https://ugcnettourism.in/phd-in-tourism-research-and-topics-related-to-research/","timestamp":"2024-11-13T10:49:22Z","content_type":"text/html","content_length":"111774","record_id":"<urn:uuid:54663f45-2eb5-4b7b-8329-b6258d4cd885>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00615.warc.gz"} |
Top Rated
Pre-Algebra Learning and Tutorial Software
PRE-ALGEBRA is a highly acclaimed
self-study software program designed to help students learn and master pre-algebra.
The program is based on a new understanding of the ways in which students grasp math concepts and build proficiency in problem-solving skills. The result is a program that transforms math learning in
pre-algebra, and lays a solid foundation for algebra and future math courses.
PRE-ALGEBRA is a dynamic interactive learning program designed for students at all levels of ability.
Students receive personalized on-demand coaching and hints as they learn.
Parents seeking homeschool pre-algebra tutorial and learning software will find the program to be perfectly suited to their needs.
Schools seeking
curriculum-based pre-algebra teaching and review software
will find the program to be ideal.
Why has PRE-ALGEBRA been so successful in helping students learn and master pre-algebra? Highly interactive lessons that engage students. Stunning graphics that bring the concepts of math to life and
help students discover the patterns that underlie pre-algebra and mathematics as a whole. Carefully chosen practice problems that reinforce the concepts of pre-algebra and show its many applications.
And personalized lessons tailored to each student's abilities.
PRE-ALGEBRA is also available in a version aligned to Common Core math Grade 8 standards, which includes complete coverage of math concepts and applications.
PRE-ALGEBRA is research-based and has been acclaimed for its educational excellence and flexibility. It can be used for self-study and to supplement classroom instruction in high school and middle
school math classes. The program also contains diagnostic and assessment tests that measure student skills and provide a study plan customized for each student.
Examples and pre-algebra problem solving exercises progress gradually from the simpler to the more challenging, allowing students to build their skills and confidence. Detailed step by step
explanations are provided for each problem.
Designed by math educators and in accordance with math curriculum standards, the program is also effective when used as software for remedial and developmental math teaching.
• Award-winning, curriculum-based pre-algebra courseware developed by math educators
• Provides dynamic, interactive pre-algebra lessons that are ideal for self-study, and as a supplement to classroom instruction
• Demonstrated success in boosting students' math skills and comprehension, and proficiency in problem solving
• Network versions contain student record-keeping, grading, and performance analysis features
Adding and Subtracting Whole Numbers
• Place Value
• Ordering Numbers
• Rounding Numbers
• Adding Whole Numbers
• Subtracting Whole Numbers
• Word Problems
Multiplying and Dividing Whole Numbers
• Multiplying By 1-Digit Numbers
• Multiplying By Whole Numbers
• Dividing By 1 and 2 Digit Numbers
• Dividing By Whole Numbers
• Word Problems
Other Operations Using Whole Numbers
• Factoring Whole Numbers
• Square Roots of Perfect Squares
Adding and Subtracting Fractions and Mixed Numbers
• Fractions and Mixed Numbers
• Finding Equivalent Fractions
• Comparing and Ordering Fractions
• Adding Fractions
• Adding Fractions and Mixed Nos.
• Subtracting Fractions
• Subtracting Fractions and Mixed Nos.
Multiplying and Dividing Fractions and Mixed Numbers
• Multiplying Fractions
• Multiplying Fractions and Mixed Nos.
• Dividing Fractions
• Dividing Fractions and Mixed Nos.
• Word Problems
Operations With Decimals
• Place Value and Decimal Numbers
• Comparing and Rounding Decimal Nos.
• Adding Decimal Numbers
• Subtracting Decimal Numbers
• Multiplying Decimal Numbers
• Dividing Decimal Numbers
• Word Problems
Positive and Negative Numbers
• The Number Line
• Addition
• Subtraction
• Multiplication
• Division
• Positive and Negative Exponents
• Scientific Notation
Expressions and Formulas
• Variables and Expressions
• Like Terms
• Simplifying Expressions
• Solving Equations
• Translating Words into Expressions
• Solving Word Problems
• Percent Problems Using Proportions
• Word Problems Involving Percent
Ratio and Proportion
• Ratios and Rates
• Solving Proportions
• Measurement
• Word Problems
Customer Ratings 4.8 / 5 stars (9 reviews)
The MathTutor pre-algebra program is simply wonderful. Our daughter is understanding and enjoying math after years of struggling. Ms. Rachel Clarins
Detroit, MI
Thank you for your wonderful software! Math has always been a liability for me and I did poorly in pre-algebra when I was in high school (years ago). I've taken your pre-algebra course and feel
prepared for the math courses I'll be taking when I returning to college this fall. Mrs. R. Shipley
Tacoma, WA
The MathTutor series is remarkable. We purchased pre-algebra and the other titles and we're so glad our son's teacher recommended it. My only wish is for a version in Italian. Mr. Carlo Signorelli
Asheville, NC
The graphics and animation in pre-algebra are stunning. The tutorials are superb and far more effective than anything else I've tried. Troy Goodman
Huntington, NY
I felt my son had the potential to do well in math, but he seemed to lack motivation. We purchased your pre-algebra program and we're thrilled with the results. Now he does his math homework first
and he's getting and A. We're very pleased! Robert Hollis
Fort Wayne, IN
In elementary school our son did poorly in math, and we worried because he wanted to be an engineer. Pre-Algebra is a wonderful program. It gave him confidence and his grades are better than we ever
expected. Madeline Long
Riverside, CA
I work at a tutoring lab and have heard students comment on how much your Pre-Algebra program has helped them. We are planning to purchase all of the remaining programs in your series. Thank you for
an excellent software program. Ms. Clarissa Bragg
Flushing, NY
Our daughter has flourished in pre-algebra since we purchased your program. She is officially the math whiz in our household! She's looking forward to the more advanced math classes to come and I'm
sure we will be purchasing the other programs in your series. We are so glad we learned about your software from another family. Ms. Denise Herrera
Boulder, CO
Our son has raved about your PRE-ALGEBRA program, and we've told other parents how much it's helped him. It's hard to believe but he's actually working ahead of his class. Your software program is
wonderful. Mr. Julius Zimmerman
Sulphur, LA | {"url":"https://www.mathtutor.com/software/pre-algebra-lessons.html","timestamp":"2024-11-04T12:12:08Z","content_type":"text/html","content_length":"34492","record_id":"<urn:uuid:10ac679b-b861-4441-bd35-76af3061d542>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00268.warc.gz"} |
Fractal Architectures
The Square Roots 2, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 60in
The Square Roots 1, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 60in
The Square Roots 3, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 60in
The Square Roots Installation, from The Fractal Architectures series, Mixed Media, L144 x W16 x H120 inches
The Square Roots Sculpture, from The Fractal Architectures series, Mixed Media, L40 x H51 x W40 inches
Wallpaper edition for The Square Roots, from The Fractal Architectures series
The Matryoshka Dolls 1, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 60in
The Matryoshka Dolls 2, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 80in
The Matryoshka Dolls 3, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 60in
Self Portrait, from The Fractal Architectures series, C-print, 40in x 80in & 30in x 60in
The Matryoshka Doll Sculpture, from The Fractal Architectures series, Mixed Media, L85 x H48 x W 34 inches
Wallpaper edition for The Matryoshka Dolls, from The Fractal Architectures series
Building the image – The Fractal Architectures series is divided into two chapters: The Matryoshka Dolls and The Square Roots. The hyper-realistic models, conceived for the unique point of view of
the camera, are built in the toy scale of 1/24 to life size and above, following a fractal logic. Within the interlocked spaces, a foot, a thumb or a face appear to reveal the multiple scales
incorporated in the model. Young characters unfold within these fractal architectures, which are at once their toy, their home, their childhood, their adulthood, the space between their past and
their future.
Fractal Geometry – The conception of each model begins with a simple geometric figure; the circle for the Matryoshka Dolls and the square for the Square Roots. These elementary forms repeat at
different scales to create an intricate pattern, which weaves together the infinitely small and the infinitely big. This never-ending fractal motif spreads across the wallpaper, and is the basis of
the model’s floor plan and interior design. For example, the wallpaper for the Matryoshka series is made up of nested dolls woven in a circular dance, each impregnated with this repeating pattern.
Similarly in the model, the circular archetype puts everything in rotation; the hardwood floor grows in concentric circles, the doors bend in arches, and the staircase swirls to the higher alcoves.
The walls undulate organically, folding and refolding in a womb-like interior where the exterior seems to no longer exist.
Laetitia Soulier
The red and winding spaces of Laetitia Soulier’s “Matryoshka Dolls” series allude to the intricate worlds of David Lynch, as well as Piranèse’s deceptive architecture. We find on the one hand, an
atmosphere of oneiric complexity, flushed with color and steeped in mystery; and on the other, mathematical structures, rooms replete with nooks and crannies. The hypnotic geometric motifs play
rhythms on the wall and yet time appears to be suspended.
In one of the photographs, part of a face peers out of an arched doorway; its out of scale size hints at a higher realm. A spiral staircase winds upward like a strand of DNA, reaching toward some
mysterious hereafter. Among the elements that govern this oscillation between the real and the imaginary is a game of reminiscences and repetitions. This fractal logic acts as a structural lattice
that delineates these worlds, which nest one within the other like Russian dolls. The artist illuminates the dynamic interplay between a universe entirely fabricated from an elementary figure – such
as a circle or a square – and a complex reality, which is ever changing, and ever expanding. The “Matryoshka Dolls” project is based upon an initial motif, that is continually reshuffled,
reconfigured and displayed anew. A simple geometric figure, reiterated like a leitmotif, serves as the basis for almost everything in these fictive spaces. It explores the semiotics of the circle, in
The Matryoshka Dolls series, or of the square, in The Square Roots series.
The fractal nature of these photographs is based not so much on formal manipulations as it is on the logic of the work as a whole. Fractals juxtapose two distinct realities through the use of a
singular and indivisible entity, in this case the circle or the square into an endlessly divisible mathematical space. We recognize a fractal only by virtue of its tendency to express two
contradictory forces, which nevertheless feed off each other to produce a single system. Thus, an initial movement creates a macroscopic layer, an entire space that appears to break down
indefinitely, allowing us over time to glimpse a global coherence, a structural momentum. This movement is mirrored at the microscopic level by the uninterrupted advancement of a corresponding
element. Far from a dualistic dialectic, this fractal logic combines two distinct realities to clear the way for a third path, permitting a greater whole to come together with a momentum that takes a
cyclical or spiral form.
This is what we see, in the photographs from “Square Roots.” We are thrown into the heart of a fully formed reality, into “the big picture”; a boy sits on the stairs, while small hands play behind
him, and he contemplates the steps of the grown man above him. But the structure of the photograph draws us into the compartments, which, like so many places and inward moments, represent the stages
at which we gain understanding of ourselves and of the world.
Using fractals, to connect the whole to its parts, Soulier’s work reveals the movement of life itself. Just as a spiral combines expanding and contracting forces, the viewer simultaneously perceives
an image and it’s construction. If fractal dynamics are what enable this nesting of realities, the “Fractal Architectures” series does not aim at the reproduction of a preexisting world, but of a
world, which is building itself. More precisely, what fractal motion seems to produce, through these contrary movements is an image in which we cannot tell whether we are on the side of construction
or deconstruction. To use an expression from Deleuze and Guattari from A Thousand Plateaus, this “zone of indiscernibility,” interrogates the fabric of all acts of creation. By dismantling and
recycling the materials from one model after the photograph is made and using it for the next construction. Like Nietzsche’s eternal return, Soulier’s work questions this very moment, which
consolidates the birth of the self and its relation to the world, before its dissolution and reintegration.
Julien Verhaeghe | {"url":"http://laetitiasoulier.com/fractal-architectures/","timestamp":"2024-11-08T14:33:06Z","content_type":"text/html","content_length":"48147","record_id":"<urn:uuid:9e8258ce-4b5b-4bdd-88b7-b889e5c73907>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00352.warc.gz"} |
Mastering Logistic Regression A Comprehensive Guide for Beginners - Deepaira.io
Mastering Logistic Regression: A Comprehensive Guide for Beginners
Logistic regression, a cornerstone technique in machine learning, empowers us to predict the probability of an event occurring based on a set of independent variables. Its applications span diverse
fields, from healthcare and finance to marketing and customer segmentation. In this comprehensive blog post, we will delve into the concepts, implementation, and key considerations of logistic
regression, equipping you with the knowledge to leverage its capabilities effectively.
Key Takeaways and Benefits:
• Understand the fundamentals of logistic regression and its applications
• Gain insights into the probability-based nature of logistic regression
• Learn how to interpret logistic regression coefficients
• Implement logistic regression using Python/R code snippets
• Enhance predictive modeling accuracy with logistic regression
Understanding Logistic Regression:
Logistic regression is a statistical model that predicts the probability of a binary outcome (yes/no, true/false) based on a set of independent variables. Unlike linear regression, which predicts
continuous outcomes, logistic regression produces a probability value between 0 and 1. This probability represents the likelihood of the event occurring given the values of the independent variables.
Implementation Steps:
1. Data Preparation: Prepare your dataset by ensuring it is clean, free of missing values, and scaled appropriately.
2. Model Training: Train the logistic regression model using a training dataset. The model learns the relationship between the independent variables and the probability of the binary outcome.
3. Model Evaluation: Evaluate the performance of the trained model using a holdout dataset. Calculate metrics such as accuracy, precision, recall, and F1 score to assess the model’s predictive
4. Model Interpretation: Interpret the logistic regression coefficients to understand the impact of each independent variable on the probability of the event occurring. Positive coefficients
indicate a positive relationship, while negative coefficients indicate a negative relationship.
5. Model Deployment: Deploy the trained model to make predictions on new data. Use the model to assign probabilities to new observations and classify them into the appropriate binary outcome.
Code Snippets:
import numpy as np
import pandas as pd
from sklearn.linear_model import LogisticRegression
# Load the data
data = pd.read_csv('data.csv')
# Create the logistic regression model
model = LogisticRegression()
# Fit the model to the training data
model.fit(data[['x1', 'x2']], data['y'])
# Predict probabilities for new data
probabilities = model.predict_proba(new_data[['x1', 'x2']])
# Load the data
data <- read.csv('data.csv')
# Create the logistic regression model
model <- glm(y ~ x1 + x2, data = data, family = 'binomial')
# Predict probabilities for new data
probabilities <- predict(model, newdata = new_data, type = 'response')
Congratulations on mastering logistic regression! By understanding its key concepts and implementation steps, you’re equipped to tackle its applications in various domains. Stay tuned for more
exciting topics in our series.
Next Steps:
Ready to explore more advanced techniques? Join us in our next post on K-Nearest Neighbors (KNN). Don’t forget to share your newfound knowledge with your network and invite them to join us on this
educational journey! | {"url":"https://deepaira.io/mastering-logistic-regression-a-comprehensive-guide-for-beginners/","timestamp":"2024-11-08T17:04:44Z","content_type":"text/html","content_length":"90520","record_id":"<urn:uuid:e540cace-38d3-4612-9359-cdd346df7b23>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00530.warc.gz"} |
Retracing Intermediate Quantities in the Mortality Model of Rohde et al 2004
This note was motivated by and part of my goal to better understand Rohde et al's modeling work in the 2004 paper "Modelling the recent common ancestry of all living humans". My initial current steps
are described in this blog post.
In this post, I am focussing on the mortality model used in Rohde et al's work. There were a few more steps than I had realized (relative to my own unfamiliarity with actuarial methods), and I wanted
to dive in a little bit.
The goal is to verify for myself the following statement from Rohde et al. for their model:
"...the death rate, β, was raised to 12.5 for the purposes of the model. This produces an average life span of 51.8 for those who reach maturity."
Based on the derivation below for the needed quantities, I am currently getting 51.866.
Note: This is a work-in-progress. I could be off-by-one in the equations below based on the interpretation of "death at age s" vs "death by age s" kind of thing.
Mortality Model in Rohde et al
In Rohde's model, the probability $p(s)$ that an individual (referred to as a "sim" in their paper) dies at age $s$ (in years), conditional on not having died before age $s$, is assumed to follow a
"discrete Gompertz-Makeham form":
$p(s) = \alpha + (1-\alpha) \exp\{ (s - maxAge)/\beta \} $
"Survival Tree" for Mortality Model
given that one die not die before age $s$
($p(s)$ defined in the text)
where the parameters and the values used are shown in the following table.
Parameter Definition Rohde et al 2004
$\alpha$ Accident rate 0.01
$maxAge$ Maximum Lifespan 100
$\beta$ Death Rate 12.5
While in Rohde's model you can use this formula to determine the probability that a "sim" of a given age dies, you can also calculate other summary statistics without need for simulation.
But you have to be careful.
This is because when calculating any statistics, you must first specify at what age are you are starting.
The "survival tree" figure above, inspired by that in the Wikipedia page on life expectancy, shows how the mortality probabilities are used sequentially.
If a sim has lived to age $s$, then the expected lifespan given that they have lived to that age $s$ is
$$ \begin{align*} Expected\ Lifespan\ if\ live\ to\ s &= \sum_{k=s}^{MaxAge} k\ *\ prob(die\ at\ age\ k\ given\ that\ survive\ to\ age\ s) \\ &= \sum_{m=0}^{MaxAge-s} (s+m)\ *\ prob(die\ at\ age\
(s+m)\ given\ that\ survive\ to\ age\ s) \\ &= s * \sum_{m=0}^{MaxAge-s} prob(die\ at\ age\ (s+m)\ given\ that\ survive\ to\ age\ s) \\ & \ \ \ \ + \sum_{m=0}^{MaxAge-s} m \ *\ prob(die\ at\ age\
(s+m)\ given\ that\ survive\ to\ age\ s) \\ &= s + \sum_{m=0}^{MaxAge-s} m \ *\ prob(die\ at\ age\ (s+m)\ given\ that\ survive\ to\ age\ s) \end{align*} $$
where the sum that is multiplied by $s$ sums to one because the sim must die at one of those ages.
The (simple) pattern for the needed probabilities can be obtained by referring to the "survival tree" figure. For example,
$$ \begin{align*} prob(die \ at\ age\ s\ given\ that\ did\ not\ die\ before\ age\ s) &= p(s) \\ prob(die \ at\ age\ s+1\ given\ that\ survive\ to\ age\ s) &= (1-p(s)) * p(s+1) \\ prob(die \ at\ age\
s+2\ given\ that\ survive\ to\ age\ s) &= (1-p(s)) * (1-p(s+1)) * p(s+2) \\ prob(die \ at\ age\ s+3\ given\ that\ survive\ to\ age\ s) &= (1-p(s)) * (1-p(s+1)) * (1-p(s+2)) * p(s+3)\\ &\vdots \\ \end
{align*} $$
or, more generally $$prob(die\ at\ age\ s+m\ given\ that\ survive\ to\ age\ s) = p(s+m) * \prod_{n=0}^{m-1} (1-p(s+n)) $$ which can be used to obtain the simple-to-calculate
$$ $$Expected\ Lifespan\ if\ live\ to\ s = s + \sum_{m=0}^{MaxAge-s} m\ *\ p(s+m) * \prod_{n=0}^{m-1} (1-p(s+n)) \label{\eqnum}$$ $$
Obviously, one could remove the first term in the sum.
After a bit of tedious thrashing, I think this might be correct. Note that this rederivation is I'm sure a trivial thing for those familiar with actuarial concepts and techniques.
Checking Average Lifespan Reported in Rohde et al
So now I can use the formula for expected lifespan above to check the following statement in Rohde et al for the mortality model used:
"...the death rate, β, was raised to 12.5 for the purposes of the model. This produces an average life span of 51.8 for those who reach maturity."
When using the parameter values reported in Rohde et al in the equation for expected lifespan for those who reach maturity ($s=16$), I get a value of 51.866. Is that the same as 51.8? I don't know if
he truncated instead of rounded, or I am wrong. It seems pretty close.
Note that as for my running of the population model itself, the average lifespans for those reaching maturity in a given simulation is consistently slightly higher than 51.8. This could be due to any
number of trivial issues with my implementation, and I hope to be looking at that later.
Postscript: An Alternative Form?
I also noticed that the following equation seems to yield the same result for expected lifespan. There must be some simple algebraic collapsing going on.... or I am wrong.
$$ $$Expected\ Lifespan\ if\ live\ to\ s = s + \sum_{m=0}^{MaxAge-s} \prod_{n=0}^{m} (1-p(s+n))$$ $$
No comments: | {"url":"https://www.nowherenearithaca.com/2015/10/retracing-intermediate-quantities-in.html","timestamp":"2024-11-12T19:18:46Z","content_type":"application/xhtml+xml","content_length":"86988","record_id":"<urn:uuid:e6e89928-63de-4e06-be12-a63b080ab27f>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00768.warc.gz"} |
4th Grade OSTP Math Worksheets: FREE & Printable
Are you planning to improve your student's skills specifically in the math section of the 4th-grade OSTP exam? Our 4th-grade OSTP math worksheets are what you need!
The Oklahoma State Testing Program (OSTP) is a standardized test designed to determine the academic achievement of students in grades 3-8.
One of the biggest challenges for 4th-grade students to succeed in the exam is facing the math section of the OSTP exam.
The solution we have to this problem is a 4th-grade OSTP math worksheet! This is probably all that a 4th-grade student needs to pass the 4th-grade OSTP math test.
These 4th-grade OSTP math worksheets consist of the most up-to-date exercises and all questions are categorized by topic.
In addition, our 4th-grade OSTP math worksheets are free and printable and will be available to you with a simple click whenever you want.
IMPORTANT: COPYRIGHT TERMS: These worksheets are for personal use. Worksheets may not be uploaded to the internet, including classroom/personal websites or network drives. You can download the
worksheets and print as many as you need. You can distribute the printed copies to your students, teachers, tutors, and friends.
You Do NOT have permission to send these worksheets to anyone in any way (via email, text messages, or other ways). They MUST download the worksheets themselves. You can send the address of this page
to your students, tutors, friends, etc.
Related Topics
The Absolute Best Book to Ace the 4th Grade OSTP Math Test
Original price was: $29.99.Current price is: $14.99.
4th Grade OSTP Mathematics Concepts
Place Values
Numbers Operations
Rounding and Estimates
Fractions and Mixed Numbers
Data and Graphs
A Perfect Practice Book to Help Students Prepare for the OSTP Grade 4 Math Test!
Original price was: $26.99.Current price is: $14.99.
4th Grade OSTP Math Exercises
Place Values and Number Sense
Adding and Subtracting
Multiplication and Division
Mixed Operations
Data and Graphs
Ratios and Rates
Three-Dimensional Figures
Fractions and Mixed Numbers
Looking for the best resource to help you succeed on the OSTP Math test?
The Best Books to Ace the OSTP Math Test
Original price was: $29.99.Current price is: $14.99.
Original price was: $29.99.Current price is: $14.99.
Related to This Article
What people say about "4th Grade OSTP Math Worksheets: FREE & Printable - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet. | {"url":"https://www.effortlessmath.com/blog/4th-grade-ostp-math-worksheets-free-printable/","timestamp":"2024-11-05T22:10:03Z","content_type":"text/html","content_length":"110343","record_id":"<urn:uuid:a780b74e-9bc9-4096-b22e-60993f23b028>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00293.warc.gz"} |
Surface Pro 4 and Academic Note Taking
March 6, 2016
I’ve been looking for a way to take digital notes for a while. I started out with an Asus Transformer TF101 and planned to use a capacitive stylus. I quickly realized that stylus/tablet combo didn’t
have the necessary precision and there really wasn’t any good software on android to handle something as precise as note taking. Later, I moved on to the Nvidia Shield Tablet. It suffered from the
same problem as the Transformer: not enough precision and no useful software.
Anyhow, I was going to get a Thinkpad X1 Yoga until a friend suggested I check out the SP4 and I was blown away. In particular, the precision, accuracy, and speed of the stylus was astounding. I
ended up getting the Core i5 / 8gb ram 256gb ssd variant.
I’ve been using the desktop version of OneNote 2016 for taking notes, however, I also wanted to do some more artistic stuff. The problem that I ran into, however, is that the stylus’s pressure
sensitivity features don’t work in some 3rd-party programs (I had problems with Gimp, Inkscape, and Krita).
Fixing Pressure Sensitivity
So there were two parts of getting the pressure sensitivity fixed: updating pen drivers, updating C++ redistributables. To update the pen drivers get the Wintab x64 from Microsoft. Next we’ll need
several C++ redistributables: x64 C++ 2010, x64 C++ 2012, x64 C++ 2013. Make sure to get the 64bit versions of each. From there, if you’re using Gimp, go to “Edit” ⇒ “Input Devices” ⇒ “Microsoft
device Stylus”. Change the mode to “Screen”. Do the same for “Microsoft device Eraser” and “Microsoft device Puck”.
Note Taking
I’ve been using a combination of OneNote 2016 and Drawboard PDF. I’ve had problems with OneNote importing PDFs directly so any time I want to take notes on a PDF, I either have to send the PDF to
OneNote’s send-to-onenote “printer” or I use Drawboard. The printer seems to be slow and I suspect it’s because I’m using the onedrive cloud sync features. Drawboard’s circle menu is a good way to
store frequently-used features such as several pens, an eraser, and an undo button. Annotations done in drawboard don’t show up
Categories: Computers, | {"url":"https://theodorelindsey.io/blog/2016/03/06/SurfacePro4.html","timestamp":"2024-11-11T03:46:56Z","content_type":"text/html","content_length":"6418","record_id":"<urn:uuid:f0291fe2-0b3b-4e80-85d1-3c04a4f73fa2>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00312.warc.gz"} |
what happens in high speed of ball mill
WEBSep 12, 2020 · The milling method used is central milling. The average chip thickness is known (see code position 10 in the name of the insert): mm. In the chart we see that for an ae/Dc ratio
of 20/100 (=20%) C1 has a value of 1; for an entering angle of 90°, C2 also equals 1. This means that the feed to be used equals x 1 x 1 = mm/tooth.
WhatsApp: +86 18838072829
WEBJan 28, 2024 · Demerits: 1. High Energy Consumption: Ball mills often require high energy input for the grinding process, making them less energyefficient compared to some other milling
techniques. 2. Wear and Tear: The grinding media and liners experience wear, requiring regular maintenance and replacement. 3.
WhatsApp: +86 18838072829
WEBAug 12, 2021 · When the vessel's rotational speed is too high, the centrifugal force acting on the balls exceeds the gravity force, and the balls will be stuck to the vessel's inner surface.
... The result revealed that the energy required by a ball mill, highpressure homogenizer and twin screw extruder were,, and 5 kWh/kg of biomass, ...
WhatsApp: +86 18838072829
Highenergy ball milling. Highenergy ball milling is a mechanical deformation process that is frequently used for producing nanocrystalline metals or alloys in powder form. This technique belongs
to the comminution or attrition approach introduced in Chapter 1. In the highenergy ball milling process, coarsegrained structures undergo ...
WhatsApp: +86 18838072829
WEBNov 16, 2023 · Ball milling was carried out using a Fritsch Pulverisette 5 planetary ball mill with tungsten carbide lined grinding vials and 10 mm diameter WC balls with a balltopowder weight
ratio (BPR) of 10:1 for 20 hours of duration. The milling operation was carried out in a toluene medium with a constant rotation speed of 300 rev/min.
WhatsApp: +86 18838072829
WEBResult #1: This mill would need to spin at RPM to be at 100% critical speed. Result #2: This mill's measured RPM is % of critical speed. Calculation Backup: the formula used for Critical Speed
is: N c = (D ) where, Nc is the critical speed,in revolutions per minute, D is the mill effective inside diameter, in feet.
WhatsApp: +86 18838072829
WEBMilling was then performed in 80% ethanol for 30–120 minutes using a highenergy ball mill. The mechanical treatment resulted in a reduction of the fibre length and diameter, probably due to
degradation of the cellulose amorphous regions. Fibrillation was helped by the wet environment, which facilitated the intrafibre swelling.
WhatsApp: +86 18838072829
WEBNov 1, 2020 · Planetary ball mill Retsch PM100 was operated at 300 rpm. Vessel for the ball milling was a stainlesssteel jar of 50 mL volume. g of graphite powder Gr (Alfa Aesar, 99%) was
mixed with g of potassium perchlorate KClO 4 (Fisher Scientific 99%) and mL of deionized water (DI). Powder to balls ratio was 1:20.
WhatsApp: +86 18838072829
WEBThe Planetary Ball Mill PM 100 is a powerful benchtop model with a single grinding station and an easytouse counterweight which compensates masses up to 8 kg. It allows for grinding up to 220
ml sample material per batch. The extremely high centrifugal forces of Planetary Ball Mills result in very high pulverization energy and therefore short ...
WhatsApp: +86 18838072829
WEBDownload. The PM 400 is a robust floor model with 4 grinding stations and accepts grinding jars with a nominal volume from 12 ml to 500 ml. It processes up to 8 samples simultaneously which
results in a high sample throughput. The extremely high centrifugal forces of Planetary Ball Mills result in very high pulverization energy and therefore ...
WhatsApp: +86 18838072829
WEBOct 17, 2022 · Low speed: At low speed, the mass of balls will slide or roll up one over another and will not produce a significant amount of size reduction. High Speed: At highspeed balls are
thrown to the cylinder wall due to centrifugal force and no grinding will occur. Normal speed: At Normal speed balls are carried almost to the top of the mill .
WhatsApp: +86 18838072829
WEBJan 1, 2000 · Kato [2] investigated the use of polycrystalline cubic boron nitride (PCBN) ball nose end mills and the effect of cutting environment on tool life when machining lnconel 718. A
length cut of 900 m with a maximum flank wear of mm was reported at a cutting speed of 90 m/min. This was obtained using 50 bar high pressure .
WhatsApp: +86 18838072829
WEBJan 1, 1998 · In order to sustain a cascading charge profile the mill must be run beyond the critical speed. It is found that at 95 rpm the charge profile and the power draw are comparable. "
[hus this speed was maintained throughout all the experiments. ... the rate of production of fines is quite high in a cascading mill compared to the ball mill and it is ...
WhatsApp: +86 18838072829
WEBJan 1, 2013 · The ball nose end milling tests were carried out on a Matsuura FX5 vertical high speed machining centre with a maximum spindle speed of 20,000 rpm rated at 15 kW, with a feed
rate of up to 15 m/min. For tests involving Ti–45Al–8Nb–, three blocks were prepared including one with dimensions 220 mm × 80 mm × 60 mm which was .
WhatsApp: +86 18838072829
WEBSome highenergy planetary ball mills have been developed by Russian scientists, and these have been designated as AGO mills, such as AGO2U and AGO2M. The high energy of these mills is derived
from the very high rotation speeds that are achievable. For example, Salimon et al. used their planetary ball mill at a rotation speed of 1235 rpm ...
WhatsApp: +86 18838072829
WEBFeb 6, 2023 · For a ball mill to function, critical speed must be attained. Critical speed refers to the speed at which the enclosed balls begin to rotate along the internal walls of the ball
mill. If a ball mill fails to reach critical speed, the balls will remain stationary at the bottom where they have little or no impact on the material. Ball Mills vs ...
WhatsApp: +86 18838072829
WEBDec 3, 2001 · Following a brief introduction of high speed machining (HSM) and the machinability of Inconel 718, the paper details experimental work using TiAlN and CrN coated tungsten carbide
ball end mills, operating at cutting speeds up to 150. m/min. Inconel 718 is one of a family of nickel based superalloys that are used extensively for .
WhatsApp: +86 18838072829
WEBJul 5, 2017 · Effects of Ball Milling Velocity and Ball Volume Fraction. EDEM as a powerful software enables to collect data from the dynamic behavior of the entire ball milling simulation
process. In order to explore the milling efficiency of the models, the average speed of balls, the maximum speed of balls, and the magnitude of torque on .
WhatsApp: +86 18838072829
WEBFeb 4, 2022 · End Mill Edge Chipping Causes. End mill edge chipping is commonly seen within aggressive and rigid machining. Machinists will find this when their feed rate is too aggressive in
both the continued machining and on initial cut. Aggressive DOC is another common cause of tool chipping. Solutions. Edge chipping is an easily solved issue for .
WhatsApp: +86 18838072829
WEBBall mill diameter, media size and mill revolutions per minute (rpm) control the process of powder mixing and particle size reduction (Upadhyaya, 1998). For given mill size and media, too low
an rpm extends the process time, whereas too high an rpm leads to poor cascading of media, leading to inefficient particle size reduction.
WhatsApp: +86 18838072829
WEBAir speed in mill – Open circuit : to m/sec – Closed circuit : to m/sec ... Agglomeration and ball coating Cause:Temperature too high tendency of the material forming agglomerates/coating on
grinding media and liner platesGrinding efficiency will be reduceTemperature outlet mill range 110120 C. Test dimension
WhatsApp: +86 18838072829 | {"url":"https://www.lacle-deschants.fr/11/13-3058.html","timestamp":"2024-11-05T22:41:07Z","content_type":"application/xhtml+xml","content_length":"20953","record_id":"<urn:uuid:a16a0ed9-e2d2-4d5f-a176-502d93baddca>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00322.warc.gz"} |
Understanding "E=mc²" Idiom: Meaning, Origins & Usage - CrossIdiomas.com
Understanding the Idiom: "E=mc²" - Meaning, Origins, and Usage
Idiom language: English
Etymology: After the formula of mass–energy equivalence, an important principle discovered by the German-born theoretical physicist Albert Einstein (1879–1955).The formula entered the popular
consciousness after it was included in the opening pages of the Smyth Report (1945), a widely read document that explained the United States’ nuclear weapons program to the public for the first time.
Its appearance alongside a portrait of the (already well known) Einstein on a Time magazine cover the following year consolidated its fame.
The Origins of “E=mc²”
The origins of this famous equation can be traced back to Einstein’s work in physics during the early 20th century. He was attempting to reconcile two seemingly incompatible theories: Newtonian
mechanics and Maxwell’s equations for electromagnetism. In doing so, he developed a new framework for understanding space and time that would become known as special relativity.
Einstein’s Breakthrough
One key insight that Einstein had was that energy could be thought of as a form of mass. This led him to develop the equation “E=mc²”, which states that energy is equal to mass times the speed of
light squared. This simple formula has profound implications for our understanding of how matter behaves at high speeds or in extreme conditions.
Origins and Historical Context of the Idiom “E=mc²”
The idiom “E=mc²” is widely recognized as one of the most famous equations in physics. It represents the relationship between energy (E), mass (m), and the speed of light squared (c²). However, to
fully understand its significance, it is important to explore its origins and historical context.
In 1905, Albert Einstein published a paper titled “Does the Inertia of a Body Depend Upon Its Energy Content?” This paper introduced the concept that mass and energy are interchangeable, which led to
the development of his famous equation. At this time, Einstein was working as a patent clerk in Switzerland and did not have access to sophisticated laboratory equipment or resources. Instead, he
relied on thought experiments and mathematical calculations.
The equation itself was not immediately recognized for its significance. It wasn’t until later experiments confirmed its accuracy that it became widely accepted by physicists around the world. The
equation also played a crucial role in developing nuclear technology during World War II.
Today, “E=mc²” has become synonymous with Einstein’s groundbreaking work in theoretical physics. It continues to be studied and applied in various fields such as particle physics, cosmology, and even
popular culture.
The Importance of Context
To truly appreciate the impact of “E=mc²”, it is important to consider its historical context. At the time when Einstein developed this equation, there were many scientific breakthroughs happening
across Europe. The field of physics was rapidly evolving thanks to advancements in technology such as X-rays and radioactivity.
Additionally, political tensions were high due to events like World War I looming on the horizon. Many scientists fled their home countries due to persecution or fear for their safety during this
time period.
All these factors contributed to an environment where new ideas could flourish but also faced significant challenges. Einstein’s work on “E=mc²” was not immediately embraced by the scientific
community, and it took years of experimentation and research to confirm its validity.
Usage and Variations of the Idiom “E=mc²”
The idiom “E=mc²” has been widely used in various fields, including physics, engineering, and even popular culture. Its significance lies in its representation of the relationship between energy and
mass, which has greatly influenced scientific research and technological advancements.
Variations in Scientific Applications
In physics, “E=mc²” is commonly used to explain the conversion of matter into energy. This principle is utilized in nuclear power plants and weapons, where a small amount of matter can produce a
large amount of energy through nuclear fission or fusion reactions. The equation also plays a crucial role in understanding black holes and the behavior of particles at high speeds.
Engineering applications include calculations for the design and operation of particle accelerators, as well as spacecraft propulsion systems that utilize nuclear reactions for energy production.
Cultural References
Besides its scientific applications, “E=mc²” has also made appearances in popular culture. It has been referenced in movies such as Back to the Future and The Simpsons Movie. Additionally, it has
been adapted into various forms such as T-shirts with witty slogans or artwork featuring Einstein’s famous formula.
The idiom has become synonymous with intelligence or knowledge due to its association with Albert Einstein – one of history’s greatest scientists who developed this theory during his lifetime.
Synonyms, Antonyms, and Cultural Insights for the Idiom “E=mc²”
Phrase Meaning
Einstein’s equation A mathematical formula that expresses the relationship between energy (E) and mass (m)
The theory of relativity A scientific concept developed by Albert Einstein that explains how time and space are relative to each other based on an observer’s perspective
The equivalence of mass and energy A concept stating that mass can be converted into energy and vice versa at a fixed rate according to Einstein’s equation.
Word/Expression Opposite Meaning
Inertia Resistance or reluctance to change or move forward. In contrast, E=mc² represents a transformative idea about the nature of matter and energy.
Cultural Insights:
Nuclear Energy The energy released by splitting atoms, which is based on the principles outlined in E=mc². This concept has had a significant impact on global politics and environmental
Pop Culture References The equation has been referenced in various movies, TV shows, songs, and other forms of media to symbolize intelligence or scientific breakthroughs. | {"url":"https://crossidiomas.com/emc/","timestamp":"2024-11-05T20:18:53Z","content_type":"text/html","content_length":"184061","record_id":"<urn:uuid:e330f059-178b-456f-a5d5-7f0741e1700a>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00598.warc.gz"} |
Accelerating Quantum Algorithms for Solar Energy Prediction with NVIDIA CUDA-Q and NVIDIA cuDNN | NVIDIA Technical Blog
Improving sources of sustainable energy is a worldwide problem with environmental and economic security implications. Ying-Yi Hong, distinguished professor of Power Systems and Energy at Chung Yuan
Christian University in Taiwan, researches hybrid quantum-classical methods. These approaches leverage quantum computing to solve challenging problems in power systems and sustainable energy.
Solar irradiance prediction is a key focus of Professor Hong’s research group. The goal is to use geographical and historical data to forecast the power generation of photovoltaic farms, enabling
power utilities to optimally schedule traditional fossil fuel-based power generation.
Professor Hong and his student, Dylan Lopez have used the NVIDIA CUDA-Q platform to predict solar irradiance through calculations run by hybrid quantum neural networks (HQNNs). This work was recently
published in the paper, Solar Irradiance Forecasting Using a Hybrid Quantum Neural Network: A Comparison on GPU-Based Workflow Development Platforms.
This work on HQNN made use of CUDA-Q interoperability with the NVIDIA cuDNN library to achieve a 2.7x model training speedup and a 3.4x reduction in test set error compared to other leading quantum
What is a hybrid quantum neural network?
Classical neural networks (NNs) are trainable machine learning (ML) models built from layers of mathematical operations that resemble the connectivity of neurons in the brain. Each layer is made up
of neurons which are connected to neurons in adjacent layers through trainable weights. A standard NN consists of an input layer to receive the raw data, hidden layers that apply various
transformations, and an output layer that produces a final prediction.
An NN is an ML model trained with a data set to find the optimal parameters that minimize a cost function. The trained model can then make predictions based on new data in a process known as
inference. NNs have proved remarkably capable when modeling complex systems.
An HQNN shares the same objective, but instead replaces one or more layers of the traditional NN with a parameterized quantum circuit within a so-called “quantum layer.” A quantum layer consists of a
few important sublayers (Figure 1).
Figure 1. A standard quantum layer within a hybrid quantum neural network
First, the input data is encoded into the quantum circuit with an encoding layer. Then, a set of parameterized single qubit gates act on each qubit. The structure of these gates is generally called
an ansatz. Next, an entangling layer is applied with a cascade of controlled NOT (CNOT) gates. Finally, a quantum circuit is measured and the measurement results are either used to compute a cost
function or are fed forward as inputs to another layer.
HQNNs are a promising approach because the unique properties of quantum entanglement allow the opportunity for a more expressive model that can capture complex patterns with fewer trainable
parameters. However, many challenges remain, particularly regarding the best way to encode classical data into a quantum circuit.
A CUDA-Q HQNN for solar irradiance
HQNNs require CPUs, GPUs, and QPUs all working in concert (Figure 2). Data preprocessing takes place on a traditional CPU, GPUs run the classical layers of the HQNN, and the QPU runs the circuits
that compose the quantum layers. Professor Hong and Dylan used the CUDA-Q development platform to construct and train an HQNN with data from the National Solar Radiation Database including a
multitude of weather related features from across Taiwan.
Figure 2 shows a typical HQNN workflow. Most of the workflow is accelerated with CUDA and additional acceleration is realized using the cuDNN and cuQuantum libraries.
Figure 2. A typical HQNN workflow
A classical NN was implemented in PyTorch, with the NN layers designed using Bayesian optimization as described in the Methodology section of the paper. The resulting architecture served as the
classical component of an HQNN, where a final dense layer was replaced with a quantum layer (Figure 3).
Figure 3. The HQNN is similar to the NN design with the final (magenta) layer replaced by a quantum layer. Both NNs process data with various weather features to generate corresponding predictions
Working together, NVIDIA CUDA-Q, CUDA, and cuDNN tools were able to accelerate the whole workflow in this HQNN. CUDA-Q ensures acceleration of both the quantum and classical layers in the network,
enabling quantum and classical resources to work together seamlessly. The PyTorch training is automatically accelerated with CUDA.
Two NVIDIA libraries provide even further acceleration for specific tasks. cuDNN ensures highly efficient NN operations like convolution, while in cases where the quantum layers are simulated (rather
than running on actual quantum hardware), cuQuantum accelerates all quantum circuit simulations.
CUDA-Q improves HQNN speed and accuracy
Professor Hong and Dylan trained their HQNN model to predict solar irradiance for all four seasons of the year using two NVIDIA RTX 3070 GPUs. They compared their results to a classical baseline and
benchmarked the impact of different simulators and methods of accelerating the classical NN part of the hybrid workflow. The data suggests the importance of using GPU acceleration and CUDA-Q to
realize the greatest performance gains.
Figure 4. CUDA-Q is optimized to leverage CUDA and other libraries like cuDNN for accelerating hybrid quantum-classical applications such as HQNNs
The utility of the GPU is made clear for simulating both the quantum and the classical parts of an HQNN. Regardless of the simulator, GPU-accelerated quantum circuit simulations lowered the epoch
latency (time for each training step) by at least 3x. The classical NN steps could also be accelerated with CUDA or CUDA plus cuDNN (Figure 4, left).
CUDA-Q is uniquely optimized to take advantage of the GPU better than any other simulator. Compared to other leading GPU simulators, when CUDA and cuDNN accelerated the classical NN steps, CUDA-Q was
2.7x faster (Figure 4, left) and trained a model that was 3.4x more accurate (Figure 4, right) in terms of the test set RMSE.
Professor Hong and Dylan were able to successfully predict the seasonal solar irradiance in Taiwan with competitive accuracy to classical approaches. Professor Hong noted that the outcomes of this
study indicate that “CUDA-Q provides a great means to stage hybrid quantum operations for energy research during the NISQ-era and beyond. Accelerating both the classical and quantum tasks allows us
to explore best-case and worst-case solutions for integrating HPCs and quantum computers in solution pipelines.”
Get started with CUDA-Q
CUDA-Q is a platform for hybrid quantum-classical computing, not just a quantum simulator. CUDA-Q orchestrates all aspects of a hybrid CPU, GPU, and QPU workflow enabling acceleration of the quantum
and classical components of the HQNN presented in this work. Code developed on the CUDA-Q platform has longevity and is designed to seamlessly scale as accelerated quantum computers scale to solve
practical problems.
To get started with CUDA-Q, check out the following resources: | {"url":"https://developer.nvidia.com/blog/accelerating-quantum-algorithms-for-solar-energy-prediction-with-nvidia-cuda-q-and-nvidia-cudnn/","timestamp":"2024-11-14T18:40:12Z","content_type":"text/html","content_length":"219219","record_id":"<urn:uuid:c819094d-1372-4375-9582-a8f8f03d9527>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00647.warc.gz"} |
ECCC - Reports tagged with metric embeddings
Parikshit Gopalan, Salil Vadhan, Yuan Zhou
We give two new characterizations of ($\F_2$-linear) locally testable error-correcting codes in terms of Cayley graphs over $\F_2^h$:
\item A locally testable code is equivalent to a Cayley graph over $\F_2^h$ whose set of generators is significantly larger than $h$ and has no short linear dependencies, but yields a ... more >>> | {"url":"https://eccc.weizmann.ac.il/keyword/18333/","timestamp":"2024-11-07T02:49:30Z","content_type":"application/xhtml+xml","content_length":"19458","record_id":"<urn:uuid:f6328ff8-f623-436a-a29d-04e56ce8d773>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00420.warc.gz"} |
spatial quality Archives - Vastu Solutions
We have introduced the 12 Laws of Success for Healthy Living and Building and mentioned the 12 Vasati laws in earlier posts. Here in part I, we explore the First of the Four Geometric Laws.
1. The Effect of Proportions
2. The Effect of measures
3. Energy Lines and Energy Spots in Space
4. Energy Quality of Grid Fields
• The first four Energetic Laws of Vasati describe the energy fields that pervade a plot of land, house and room. However the quality of any given energy field is also influenced by its geometry.
• The First and Second geometrical Vasati Laws describe in which way proportions and measures influence spatial quality. The physical laws of vibration and resonance underlie these two laws which
indicate the proportions and measurements required to create harmonic vibration fields.
• The third and fourth geometrical Vasati laws describe the inner geometry of the energy fields being created. Every field that is limited is space possesses an inner interference pattern that
contains especially prominent points, lines and planes.The significance and quality of these geometrical elements within a room and building are demonstrated by the third and fourth geometrical
laws which we will cover in the posts to follow.
Energy Quality of Grid Fields: Space is divided into 81 different fields of qualitative energy that are arranged in 5 concentric rings.
First Geometrical law
The first geometrical Vasati law is the effects of proportions. This rules that only in orderly shaped rooms with mainly whole number proportions, i.e. side ratios, can harmonious energy fields be
created. Many of us are familiar with the law if whole number intervals from acoustics and music. Intervals like 1:2 (octave), 2:3 (fifth) or 3:4 (fourth) are perceived as harmonious while even
slight deviations from the pure intervals diminish the clarity and purity of the sound. Correspondingly Vasati prefers whole number side ratios like 4:4 (square) or 4:5.
Besides the proportions that are derived from the quartering of the side length, side ratios like 4:6 and 4:7 create harmonious room energies as well, because the room
is being structured with number four, respectively eight. The quality that is achieved with a certain proportion corresponds to the musical tone quality of the corresponding interval. We will address
the utility of harmonious proportions in Vasati in more detail for future posts.
• Proportions in Vasati: Proportions is the ratio between two lines. The eyes see a link between them and develop a qualitative impression that corresponds to the sound quality of a musical
interval. Just as ones inner ear perceives specific sound intervals as harmonious or as dissonant, the eyes similarly see certain line ratios as harmonious or disharmonious.
Although this perception is subjective and to a certain extent dependant upon a person’s cultural background, there are universal laws of
nature that depict the qualitative effect of proportions or intervals on living systems. These laws are summarised by the notion of harmonics. Harmonics help to
establish harmony or union and an opening or channel for the descension of the cosmic pulse from the spiritual to the material dimension. The ‘numerical’ quality and denomination is the agent or
language for this harmony.
• Ragas ..to be continued… | {"url":"https://vastusolutions.co.uk/tag/spatial-quality/","timestamp":"2024-11-14T17:30:09Z","content_type":"text/html","content_length":"52158","record_id":"<urn:uuid:1cf0051d-78ae-41bd-9376-cbb6cdf49c3f>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00726.warc.gz"} |
ti reliability test
January 1, 2021 In Uncategorized
ti reliability test
Accelerated stress testing is used to provide estimates of component reliability performance under use conditions and to assist in identifying opportunities for improving the reliability performance
of the component. A test can be split in half in several ways, e.g. Preconditioning . As the materials degrade and reach wear-out, the fail rate keeps increasing with time. The following is common
terminology related to reliability of semiconductor products: The bathtub curve is typically used as a visual model to illustrate the three key periods of product failure rate and not calibrated to
depict a graph of the expected behavior for a particular product family. For more about MSL, please see our MSL ratings application note. During the useful life phase, the fail-rate is constant. The
three sections of the bathtub curve – early fail, useful life, and wear-out – often have different shapes for failure distributions, as illustrated in the figure. Scope Note: Accuracy, consistency,
and stability of the results from a test or other measurement technique for a given population (Note: Prior to Mar80, "Reliability" was not restricted by a Scope Note, and many items indexed by
"Reliability" should have been indexed with "Test Reliability") Category: Measurement. Frequently, a manufacturer will have to demonstrate that a certain product has met a goal of a certain
reliability at a given time with a specific confidence. First Online: 02 August 2014. Measurements are gathered from a single rater who uses the same methods or instruments and the same testing
conditions. standards for short-circuit reliability testing. If the two halves of th… Test Reliability. EAG’s reliability testing techniques help our clients understand design and failure issues,
leading to product improvement and better qualification. Click on the specific part number to see the moisture level of the part. There are three primary phases of semiconductor product lifetime: For
a given sample size n, there will be m failures after t hours Probability density function f(t): The initial measurement may alter the characteristic being measured in Test-Retest Reliability in
reliability analysis. (tm – tm-1) ]/m = tm/m. It could change without notice. I assume that the reader is familiar with the following basic statistical concepts, at least to the extent of knowing and
understanding the definitions given below. The probability of survival to time t. Expressed another way, it is the fraction of units surviving to time t. Total fraction failing and surviving must add
to 1. Thank you very much for your support. It is the average time for a failure to occur. The product is known to follow an exponential distribution. Thermal Shock . See TI's Terms of Sale for more
information. HTOL is used to determine the reliability of a device at high temperature while under operating conditions. Using TI products outside limits stated in TI's official published
Specifications may void TI's warranty. first half and second half, or by odd and even numbers. For more information, visit our reliability testing page. ABSTRACTThe reliability and validity of the
T-test as a measure of leg power, leg speed, and agility were examined. Our holistic approach to quality permeates every aspect of the company’s supply chain from process technology and design … It
is rare to have enough short-term and long-term failure information to actually model a population of products with a calibrated bathtub curve, so estimations are made using reliability modeling.
However, the reliability in a test retest situation is the same as in Rater 1. It is the average time for a failure to occur. MTTF (Mean Time To Fail) = (t1+t2+t3+….tm)/m. Our world-class test center
in Caro, MI is a NEMA Class 1 Div 1 rated fuel lab, and facilitates our R&D team to test pumps and modules in extreme temperatures, adverse conditions, and with over 50 different fuel blends. A
reliability test plan is the high level plan that calls out all of the reliability testing that is to be performed on a product, including Design Verification Tests (DVT), Highly Accelerated Life
Tests (HALT), Reliability Demonstration Tests (RDT), Accelerated Life Tests (ALT), and On-Going Reliability Tests (ORT). 2. (9), we get: So a total of 1944.89 hours of testing is needed. Test-Retest
Reliability is sensitive to the time interval between testing. MTTF is … reliability) by 5 items, will result in a new test with a reliability of just .56. David, I am calculating both reliability
tests, but struggling with the re-test one. MTTF (Mean Time To Fail) = (t1+t2+t3+….tm)/m. For example, differing levels of anxiety, fatigue, or motivation may affect the applicant's test results.
Half the fails happen before T50; the other half after T50. Temperature Humidity Bias/Biased Highly Accelerated Stress Test (BHAST) These definitions are all expressed in the context of educational
testing, although the statistical concepts are more general. Environmental factors. Probability distributions are graphical or mathematical representations of the failing fraction of units with time.
How many samples were used for the Reliability Test? Table 1summarizes the qualification tests that are part of Maxim’s reliability program. Durability Test of a TI-83 Plus Testing the screen and
waterproofing of this calculator. DEFINITION. In practice, the fail probabilities are modeled by a 3-parameter Weibull Distribution: η,β,γ, are parameters to be determined by stress-testing units to
failure. They are discussed in the following sections. We test for durability, reliability and performance, noise, vibration and harshness, and more. 8:06. There, it measures the extent to which all
parts of the test contribute equally to what is being measured. Quality, reliability & packaging data download. Area f(t).Δt can also predict the expected number of fails at a specific time t. TI
Thinks Resolved LMT01-Q1: Qestion for Reliability Test Report. In a large number of cases, only two parameters are necessary for modeling reliability, and the Weibull distribution simplifies to: β is
known as the ‘Weibull Slope’ and η is called the ‘Characteristic Life’ of the distribution. To accurately assess the reliability of TI’s products, we use accelerated stress test conditions during
qualification testing. Moisture sensitivity level (MSL) determines the floor life before the board mounting once its dry bag has been opened. The profile shape of this distribution is represented
mathematically by a Probability Distribution Function (PDF). The resulting test scores arc correlated and this correlation coefficient provides a measure of stability, that is, it indicates how
stable the test results are over a period of time. T50 (Median Time To Fail) = Time for 50 percent of units to fail. A total of 304 college-aged men (n = 152) and women (n = 152), selected from
varying levels of sport participation, performed 4 tests of sport skill ability: (a) 40-yd dash (leg speed), (b) counter-movement vertical jump (leg power), (c) hexagon test (agility), and (d)
T-test. For specific information regarding a device’s MSL rating, please visit the moisture sensitivity level tool. Customers are solely responsible to conduct sufficient engineering and additional
qualification testing to determine whether a device is suitable for use in their applications. The Reliability Development/Growth (RD/GD) test attempts to achieve certain reliability goals by
identifying deficiencies and systematically eliminating them … Maxim’s product reliability test program meets EIA-JEDEC standards and most standard OEM reliabili-ty test requirements. Results: The
Finkelstein´s and Eichhoff´s tests revealed False Positives, of 46,7% and 53,3% respectively. The percentage of agreement for the WHAT test was fair (0.210.40) and for the Eichhoff test, moderate
(0.41 0.60). This function represents the probability of failure at a specific time t, as f(t).Δt Also, the accuracy of any projection is … Every organization in TI works together to ensure quality
and to deliver reliable products, and we are committed to continuously improving our products and process technologies toward that end. This calculator works by selecting a reliability target value
and a confidence value an engineer wishes to obtain in the reliability calculation. probability of fail at time t, given that the unit has survived untill then. Reliability Testing Tutorial: What is,
Methods, Tools, Example Design of Reliability Tests. For device-specific MTBF/FIT data, please see TI’s MTBF/FIT estimator. Quality and reliability data provided by TI, such as MTBF and fit rate
data, is intended to facilitate an estimate of the part’s performance to spec, based solely on the part’s historical observations. To estimate reliability by means of the test-retest method, the same
test is administered twice to the same group of pupils with a given time interval between the two administrations of the test. It represents the cumulative number of failures up to a given time ‘t’.
The test is usually run over an extended period of time according to the JESD22-A108 standard. Our techniques include: Moisture/Reflow Sensitivity Classification . Based on definition of f(t), F(t),
R(t) and l(t), previously described, When the failure-rate l(t) is constant, reliability function becomes an exponential distribution. X-ray exposures over these limits, however, may cause damage to
the device and should be avoided. In a past issue of the Reliability Edge (see Cumulative Binomial for Test Design and Analysis), an article was presented on the cumulative binomial distribution and
how it can be applied towards test design. Operating hours – If ‘n’ operated for ‘t’ hours before the failure-count ‘m’ was noted, then. All TI products undergo qualification and reliability testing
or qualification by similarity justification prior to release. Before releasing products, we require that three consecutive manu-facturing lots from a new process technology suc- cessfully meet the
reliability test requirements. TI does not typically specify acceptable x-ray levels on the device datasheet. These values are calculated by TI’s internal reliability testing. This is used commonly
for reliability modeling. of some statistics commonly used to describe test reliability. SPSS Statistics Test Procedure in SPSS Statistics. You can use TI’s Reliability Estimator to get a FIT rate
for most TI parts. Authors; Authors and affiliations; Shichun Qu; Yong Liu; Chapter. This is done by comparing the results of one half of a test with the results from the other half. It should not be
interpreted that any performance levels reflected in such data can be met if the part is operated outside appropriate conditions or the conditions described. TROPICAL Puerto Rican STREET FOOD TOUR |
Piñones, Puerto Rico - Duration: 13:32. Texas Instruments is making most of its high-reliability (HiRel) semiconductor products immediately available for online purchase on TI.com, helping aerospace
and defense companies quickly get the authentic TI products they need for their next-generation space-grade and military-grade designs.. TI is committed to delivering high quality and reliable
semiconductor solutions that meet our customers’ needs. 2.2k Downloads; Abstract. I will have a look on this link. You use it when you are measuring something that you expect to stay constant in your
sample. MTBF is the average time between successive failures. Test Your Brain power - Duration: 8:06 s life are calculated via the data taken understand. ’ needs Parts of the T-test as a histogram or
by odd and even numbers billion operating.! And most standard OEM reliabili-ty test requirements the floor life before the board mounting once its bag... Not get exactly the same test score every
time he or she takes the test is usually run an. Reliability testing or qualification by similarity justification prior to release, but struggling with the results of half. Half, or motivation may
affect the applicant 's test results degree to which all Parts of part... ; the other half after T50 levels on the available resources, one failure is allowed the. T2- t1 ) + ( t3 – t2 ) … ( t3 – t2
) … to sufficient. Test scores are consistent from one test administration to the JESD22-A108 standard it measures the extent which! Visit the moisture sensitivity level tool TI does not typically
specify acceptable x-ray on. 0.41 0.60 ) state at the time of testing usually run over an period! Continuous short-circuit condition the context of educational testing, although the statistical
concepts are more general Duration! The same methods or instruments and the same test score every time he or she takes test... Been opened specify acceptable x-ray levels on the specific part number
“ OPA333 ” into search! In the reliability of TI ti reliability test s internal reliability testing Tutorial: What is being measured in test-retest is... Units to fail ) = [ t1 + ( t2- t1 ) + ( t2-
t1 ) + ( –! Testing or qualification by similarity justification prior to release suitable for use in their applications reliability and reliability. As psychometric tests and questionnaires agility
were examined from the other half T50. Standard OEM reliabili-ty test requirements to accelerate the failure mechanisms that are to! Value an engineer wishes to obtain in the test is usually run over
an extended period of time to. Cessfully meet the reliability test program meets EIA-JEDEC standards and most standard OEM reliabili-ty test requirements then. Of failure at time t, i.e speed, and
other information of. Carefully chosen to accelerate ti reliability test failure mechanisms that are expected to occur under normal conditions... The failing fraction of units to fail measuring
something that you expect to stay constant in Your.... Qualification testing to determine whether a device at high temperature while under operating conditions x-ray over! After T50 sensitivity level
tool designed to help engineers: Cumulative Binomial, Exponential Chi-Squared and Non-Parametric.!, processes, products and packages meets industry standards, Non-Parametric Binomial Exponential!
Testing conditions the floor life before the board mounting once its dry bag has been opened Waloddi... Consecutive manu-facturing lots from a new process technology suc- cessfully meet the
reliability terminology.. Known as number of units to fail ) = [ t1 + t2-. To What is, methods, Tools, Example of some statistics commonly to. These questions about MSL, please visit the moisture
level of the failing fraction of units to fail ) (... Test administration to the time interval Between testing = time for a failure to.... From the other half after T50 ti reliability test for use in
their applications it is same... Stated in TI 's warranty is constant outside limits stated in TI 's warranty EIA-JEDEC! Time of testing is needed uses the same as mttf ( Mean time to fail ) = t1!
And Non-Parametric Bayesian 50 percent of units failing per billion ti reliability test hours reliability testing page were samples... Failing per billion operating hours ti reliability test, and
click search reliability target value and a confidence value an wishes... Test Your Brain power - Duration: 8:06 test requirements Failures in time number. When you are measuring something that you
expect to stay constant in Your sample time. Time Between fails ) = ( t1+t2+t3+….tm ) /m as in rater 1 more information, visit our testing! Agility were examined the failure mechanisms that are
expected to occur value an engineer wishes to obtain in the test. One failure is allowed in the test both reliability tests, but with. Before the board mounting once its dry bag has been opened level
tool measurement... In SPSS statistics using the reliability terminology page individual who does not get the! 'S warranty units to fail ) = [ t1 + ( t3 – t2 ) … reliability in a,. Calculating both
reliability tests, but struggling with the re-test one describe test reliability % and 53,3 % respectively processes... Of failing units per Million shipped Liu ; Chapter life before the board
mounting once its bag! That three consecutive manu-facturing lots from a single rater who uses the test! Products, we require that three consecutive manu-facturing lots from a new ti reliability test
technology cessfully. /M = tm/m can be influenced by a person 's psychological or physical state at time! Get a FIT rate for most TI Parts also known as number of failing units per,... Failing per
billion operating hours PDF ) industry standards technology suc- cessfully meet the reliability TI... Are expected to occur under normal use conditions of smart-power switches when in. Weibull++, as
shown below from a single rater who uses the same testing conditions use TI ’ s,... Qualification testing for most TI Parts device datasheet the context of educational testing, although statistical.
The available resources, one failure is allowed in the context of educational testing, although statistical... Target value and a confidence value an engineer wishes to obtain in the reliability
calculation testing is needed the method! Consecutive manu-facturing lots from a single rater who uses the same methods or and! Solely responsible to conduct sufficient engineering and additional
qualification testing T50 is the average time for a failure to.! To delivering high quality and reliable semiconductor solutions that meet our customers ’ needs life before the board mounting its.
The board mounting once its dry bag has been opened is the conditional probability of at... Sufficient engineering and additional qualification testing Exponential Chi-Squared and Non-Parametric
Bayesian or mathematical representations of the T-test a... Can use TI ’ s products, we require that three consecutive manu-facturing lots from a new technology! Failure to occur under normal use
conditions Tutorial: What is being in... For device-specific MTBF/FIT data, please visit the moisture level of the failing fraction of units with time -! Cause damage to the time to fail ) = [ t1 +
t3. Lmt01-Q1: Qestion for reliability test, i.e What is, methods,,... Before releasing products, we use accelerated stress test conditions are carefully to... Cumulative Binomial, Non-Parametric
Binomial, Exponential Chi-Squared and Non-Parametric Bayesian delivering high quality reliable... Who uses the same as in rater 1 measures of a test with the results of one half a! High quality and
reliable semiconductor solutions that meet our customers ’ needs to What is being measured test-retest. Mttf ( Mean time to fail ) = time for a failure to occur is sensitive to the datasheet... Of
failure at time t, i.e testing is needed is done by comparing the results one... ( PDF ) survived untill then data taken to understand these questions JESD22-A108.... Same test score every time he or
she takes the test contribute equally to is. ( t1+t2+t3+….tm ) /m single rater who uses the same methods or instruments and the as... Allowed in the context of educational testing, although the
statistical concepts are more general to conduct engineering! In Weibull++, as shown below to obtain in the test by odd and even numbers, moderate ( 0.60! Performance can be carried out in SPSS
statistics using the reliability of our designs, processes, and... Circuit, detailed test conditions during qualification testing, as shown below being. In Weibull++, as shown below same testing
conditions reliability and test-retest reliability was studied a. Use it when you are measuring something that you expect to stay constant in Your.... And affiliations ; Shichun Qu ; Yong Liu ;
Chapter be avoided the... We get: So a total of 1944.89 hours of testing is needed test contribute equally to What is methods. Use it when you are measuring something that you expect to stay in... Of
leg power, leg speed, and more and should be avoided use conditions MSL determines. ) = time for a failure to occur and even numbers time t, that... Ti part number “ OPA333 ” into the search box, and
other information ; authors and affiliations ; Qu. In time, number of units failing per billion operating hours, we use accelerated test!, may cause damage to the device and should be avoided
motivation may the! Phase, the fail rate keeps increasing with time % and 53,3 % respectively different reliability definitions... Thinks Resolved LMT01-Q1: Qestion for reliability test Report same
test score every time he or she takes the contribute! S MSL rating, please see our MSL ratings application note at time t, i.e or instruments and same.: What is, methods, Tools, Example of some
statistics commonly used determine. Selecting a reliability target value and a confidence value an engineer wishes to obtain in the reliability page... Conditional probability of failure at time t,
i.e MSL ratings application note stay constant in Your.... Being measured representations of the failing fraction of units with time qualification tests that are expected to occur under use...
Whether a device at high temperature while under operating conditions authors and ;... For Example, differing levels of anxiety, fatigue, or motivation may affect the 's.
World Health Organization President 2020, Sign In To Comodo One, James Rodriguez Fifa 20 Potential, Isle Of Man Lockdown, Wolf Of Wall Street Brad, Crib Dimensions In Feet, Ashok Dinda Ipl 2020 Team
List, Dublin To Westport, Easyjet Flights From Luton To Isle Of Man,
No Comments
Post a Comment | {"url":"https://thebutlerdiditcleaning.com/planes-disney-khtmym/a96e54-ti-reliability-test","timestamp":"2024-11-13T22:28:14Z","content_type":"text/html","content_length":"48359","record_id":"<urn:uuid:6b1f1ebc-a3f3-47b3-8940-30862173b7d2>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00026.warc.gz"} |
Koko Eating Bananas LeetCode Solution
Difficulty Level Medium
Frequently asked in Adobe Airbnb Amazon Apple DoorDash Facebook GoogleViews 1950
Problem Statement
Koko Eating Bananas LeetCode Solution – Koko loves to eat bananas. There are n piles of bananas, the i^th pile has piles[i] bananas. The guards have gone and will come back in h hours.
Koko can decide her bananas-per-hour eating speed of k. Each hour, she chooses some pile of bananas and eats k bananas from that pile. If the pile has less than k bananas, she eats all of them
instead and will not eat any more bananas during this hour.
Koko likes to eat slowly but still wants to finish eating all the bananas before the guards return.
Return the minimum integer k such that she can eat all the bananas within h hours.
Test Case 1:
piles = [3, 6, 7, 11]
h = 8
Let’s understand the solution, as we are going to be using Binary Search we have given an Array [3,6,7,11] And we have to eat every single pile of bananas in less than or equal to hours = 8. If we
are not able to do that Guard will kill KOKO [just a joke]
As we know that the potential rate that we’re eating bananas at k is going to be between 1 that’s the minimum it could possibly be. The max it could possibly be is going to be whatever the max in our
input array is and that is 11. So, then we’re going to initialize a range like this k = [1,2,3,4,5,6,7,8,9,10,11] the entire range we have. Going all the way from 1 to the max value 11.
So, in other words, we’re going to have a left pointer at the minimum and a right pointer at the maximum. Then we compute the middle by taking the average of left & right / 2 i.e. 1 + 11 / 2 = 6. So,
our middle will be here at 6 in other words that k we’re trying is going to be here at this rate that we’re going to eat bananas at the rate of 6.
Now let’s check can we eat all the piles of bananas at the rate of 6. Let’s check it.
If you see that we just eat all piles of bananas in 6 hours is that a good value. Well, it is less than or equal to 8 hours, but still, we have to find the minimum possible k value. This might be the
solution but less try is there any smaller k value than 6.
So, we decrement our right pointer to mid – 1 because there might be the best possible solution available.
So, once again we compute the middle by taking the average of left & right / 2 i.e. 1 + 5 / 2 = 3 our k is here at 3 value
Now let’s check can we eat all the piles of bananas at the rate of 3. Let’s check it.
If you see that we just eat all piles of bananas in 10 hours but if you see we went over 8 hours we took too long to eat all the bananas. So, eating at a rate of 3 didn’t work.
Let’s start searching to the right of our range we increment our left pointer to mid + 1 but remember when we shift our right pointer from the last position to mid -1 we just consider that this range
will not work. And that’s how Binary search work!
So, once again we compute the middle by taking the average of left & right / 2 i.e. 4 + 5 / 2 = 4 our k is here at the 4 value
Now let’s check can we eat all the piles of bananas at the rate of 4. Let’s check it.
If you see that we just eat all piles of bananas in 8 hours. So, we were able to eat all bananas in less than or equal to 8 hours if we had a rate of 4. Let’s compare this with our current result.
So, far we find a value of 6 we update this 6 and we can say there is a smaller rate we can use i.e. 4.
Code for Koko Eating Bananas
Java Program
class Solution {
public int minEatingSpeed(int[] piles, int h) {
int left = 1;
int right = 1000000000;
while(left <= right){
int mid = left + (right - left) / 2;
if(canEatInTime(piles, mid, h)) right = mid - 1;
else left = mid + 1;
return left;
public boolean canEatInTime(int piles[], int k, int h){
int hours = 0;
for(int pile : piles){
int div = pile / k;
hours += div;
if(pile % k != 0) hours++;
return hours <= h;
C++ Program
class Solution {
int minEatingSpeed(vector<int>& piles, int h) {
int left = 1;
int right = 1000000000;
while(left <= right){
int mid = left + (right - left) / 2;
if(canEatInTime(piles, mid, h)) right = mid - 1;
else left = mid + 1;
return left;
bool canEatInTime(vector<int>& piles, int k, int h){
int hours = 0;
for(int pile : piles){
int div = pile / k;
hours += div;
if(pile % k != 0) hours++;
return hours <= h;
Complexity Analysis for Koko Eating Bananas LeetCode Solution
Time Complexity:- O(N * log(M)) where N is no of piles & M is the range of K (left to right)
Space Complexity:- O(1) as not using any extra space | {"url":"https://tutorialcup.com/leetcode-solutions/koko-eating-bananas-leetcode-solution-2.htm","timestamp":"2024-11-14T23:21:06Z","content_type":"text/html","content_length":"111067","record_id":"<urn:uuid:221e666d-b334-4cbe-9eaa-03c42f0c20ad>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00635.warc.gz"} |
Series G RG Frame
Part # Description Stock Level
RGC25T96WP53 The Eaton RGC25T96WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316032E The Eaton RGC316032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC316033E The Eaton RGC316033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC316035E The Eaton RGC316035E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC316036E The Eaton RGC316036E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC316038E The Eaton RGC316038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC316039E The Eaton RGC316039E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC316T61WP44 The Eaton RGC316T61WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T62WP44 The Eaton RGC316T62WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T63WP44 The Eaton RGC316T63WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T64WP44 The Eaton RGC316T64WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T65WP44 The Eaton RGC316T65WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T66WP44 The Eaton RGC316T66WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T91WP44 The Eaton RGC316T91WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T92WP44 The Eaton RGC316T92WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T93WP44 The Eaton RGC316T93WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T94WP44 The Eaton RGC316T94WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T95WP44 The Eaton RGC316T95WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC316T96WP44 The Eaton RGC316T96WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320032E The Eaton RGC320032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC320033E The Eaton RGC320033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC320035E The Eaton RGC320035E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC320036E The Eaton RGC320036E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC320038E The Eaton RGC320038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC320039E The Eaton RGC320039E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC320T61WP49 The Eaton RGC320T61WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T62WP49 The Eaton RGC320T62WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T63WP49 The Eaton RGC320T63WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T64WP49 The Eaton RGC320T64WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T65WP49 The Eaton RGC320T65WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T66WP49 The Eaton RGC320T66WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T91WP49 The Eaton RGC320T91WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T92WP49 The Eaton RGC320T92WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T93WP49 The Eaton RGC320T93WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T94WP49 The Eaton RGC320T94WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T95WP49 The Eaton RGC320T95WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC320T96WP49 The Eaton RGC320T96WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325032E The Eaton RGC325032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC325033E The Eaton RGC325033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC325035E The Eaton RGC325035E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC325036E The Eaton RGC325036E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC325038E The Eaton RGC325038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC325039E The Eaton RGC325039E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC325T61WP53 The Eaton RGC325T61WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T62WP53 The Eaton RGC325T62WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T63WP53 The Eaton RGC325T63WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T64WP53 The Eaton RGC325T64WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T65WP53 The Eaton RGC325T65WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T66WP53 The Eaton RGC325T66WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T91WP53 The Eaton RGC325T91WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T92WP53 The Eaton RGC325T92WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T93WP53 The Eaton RGC325T93WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T94WP53 The Eaton RGC325T94WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC325T95WP53 The Eaton RGC325T95WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGC416032E The Eaton RGC416032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC416033E The Eaton RGC416033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC416038E The Eaton RGC416038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC420032E The Eaton RGC420032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC420033E The Eaton RGC420033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC420038E The Eaton RGC420038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC425032E The Eaton RGC425032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC425033E The Eaton RGC425033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGC425038E The Eaton RGC425038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGFCT160A The RGFCT160A is a External Neutral Sensor by Eaton with a RG Frame and 3 Poles. The RGFCT160A has 1600 Amperes. Available, Call For Quote
RGFCT200A The RGFCT200A is a External Neutral Sensor by Eaton with a RG Frame and 3 Poles. The RGFCT200A has 2000 Amperes. Available, Call For Quote
RGFCT250A The RGFCT250A is a External Neutral Sensor by Eaton with a RG Frame and 3 Poles. The RGFCT250A has 2500 Amperes. Available, Call For Quote
RGH316032E The Eaton RGH316032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH316033E The Eaton RGH316033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH316035E The Eaton RGH316035E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH316036E The Eaton RGH316036E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH316038E The Eaton RGH316038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH316039E The Eaton RGH316039E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH316T61WP44 The Eaton RGH316T61WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T62WP44 The Eaton RGH316T62WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T63WP44 The Eaton RGH316T63WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T64WP44 The Eaton RGH316T64WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T65WP44 The Eaton RGH316T65WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T66WP44 The Eaton RGH316T66WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T91WP44 The Eaton RGH316T91WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T92WP44 The Eaton RGH316T92WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T93WP44 The Eaton RGH316T93WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T94WP44 The Eaton RGH316T94WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T95WP44 The Eaton RGH316T95WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH316T96WP44 The Eaton RGH316T96WP44 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320032E The Eaton RGH320032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH320033E The Eaton RGH320033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH320035E The Eaton RGH320035E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH320036E The Eaton RGH320036E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH320038E The Eaton RGH320038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH320039E The Eaton RGH320039E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH320T61WP49 The Eaton RGH320T61WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T62WP49 The Eaton RGH320T62WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T63WP49 The Eaton RGH320T63WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T64WP49 The Eaton RGH320T64WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T65WP49 The Eaton RGH320T65WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T66WP49 The Eaton RGH320T66WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T91WP49 The Eaton RGH320T91WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T92WP49 The Eaton RGH320T92WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T93WP49 The Eaton RGH320T93WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T94WP49 The Eaton RGH320T94WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T95WP49 The Eaton RGH320T95WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH320T96WP49 The Eaton RGH320T96WP49 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325032E The Eaton RGH325032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH325033E The Eaton RGH325033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH325035E The Eaton RGH325035E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH325036E The Eaton RGH325036E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH325038E The Eaton RGH325038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH325039E The Eaton RGH325039E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH325T61WP53 The Eaton RGH325T61WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T62WP53 The Eaton RGH325T62WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T63WP53 The Eaton RGH325T63WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T64WP53 The Eaton RGH325T64WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T65WP53 The Eaton RGH325T65WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T66WP53 The Eaton RGH325T66WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T91WP53 The Eaton RGH325T91WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T92WP53 The Eaton RGH325T92WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T93WP53 The Eaton RGH325T93WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T94WP53 The Eaton RGH325T94WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T95WP53 The Eaton RGH325T95WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH325T96WP53 The Eaton RGH325T96WP53 has a 612 Volt-Amperes Power Consumption @ 24 Vac and No Terms Modification. Available, Call For Quote
RGH416032E The Eaton RGH416032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH416033E The Eaton RGH416033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH416038E The Eaton RGH416038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH420032E The Eaton RGH420032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH420033E The Eaton RGH420033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH420038E The Eaton RGH420038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH425032E The Eaton RGH425032E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH425033E The Eaton RGH425033E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGH425038E The Eaton RGH425038E has a 612 Volt-Amperes Power Consumption @ 24 Vac and Imperial Tapped Line/Load Conductor Terminations. Available, Call For Quote
RGK3160KSE The RGK3160KSE is a Molded Case Switch by Eaton with a RG Frame and 3 Poles. The RGK3160KSE has 1600 Amperes. Available, Call For Quote
RGK3200KSE The RGK3200KSE is a Molded Case Switch by Eaton with a RG Frame and 3 Poles. The RGK3200KSE has 2000 Amperes. Available, Call For Quote
RGK4160KSE The RGK4160KSE is a Molded Case Switch by Eaton with a RG Frame and 4 Poles. The RGK4160KSE has 1600 Amperes. Available, Call For Quote
RGK4200KSE The RGK4200KSE is a Molded Case Switch by Eaton with a RG Frame and 4 Poles. The RGK4200KSE has 2000 Amperes. Available, Call For Quote | {"url":"https://www.distcache.org/buy/eaton-cutler-hammer/series-g-rg-frame","timestamp":"2024-11-12T22:10:25Z","content_type":"application/xhtml+xml","content_length":"142006","record_id":"<urn:uuid:1b0186a7-2863-40b9-96bf-71b227e814e8>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00803.warc.gz"} |
Reactor Cooling
Execution time limit is 2 seconds
Runtime memory usage limit is 64 megabytes
A group of young scientists in a developing country has decided to construct a nuclear reactor to produce enriched plutonium. As the computer expert in this team, your role is to design the reactor's
cooling system.
The cooling system is comprised of a network of pipes connecting various nodes. Liquid flows through these pipes, and each pipe has a predetermined flow direction. The nodes in the cooling system are
numbered from 1 to N. The system must be configured so that, for every node, the volume of liquid entering the node per unit time is equal to the volume exiting it. Specifically, if f_ij units of
liquid flow from node i to node j per unit time (with f_ij = 0 if there is no pipe from i to j), then for each node i, the following condition must be satisfied:
Each pipe has a capacity c_ij. Additionally, to ensure adequate cooling, at least l_ij units of liquid must flow through each pipe per unit time. Therefore, for the pipe from node i to node j, it
must hold that l_ij ≤ f_ij ≤ c_ij.
You are provided with a description of the cooling system. Your task is to determine how the liquid can be directed through the pipes to meet all the specified conditions.
The first line of the input file contains the numbers N and M – the number of nodes and pipes (1 ≤ N ≤ 200). The following M lines describe the pipes. Each line contains four integers i, j, l_ij, and
c_ij. Any two nodes are connected by at most one pipe; if there is a pipe from i to j, there is no pipe from j to i, and no node is connected to itself by a pipe. The constraints are 0 ≤ l_{ij }≤ c_
{ij }≤ 10^5.
If a solution exists, output the word YES on the first line of the output file. Then, output M numbers representing the amount of liquid that should flow through each pipe, in the order the pipes are
listed in the input file. If no solution exists, output NO.
Submissions 152
Acceptance rate 13% | {"url":"https://basecamp.eolymp.com/en/problems/2093","timestamp":"2024-11-04T13:24:47Z","content_type":"text/html","content_length":"246467","record_id":"<urn:uuid:6610bc05-df7f-4d8b-83fc-79e2f14efa34>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00871.warc.gz"} |
A vector with n elements that contains the response variable.
Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.
Data Types: single| double
Data matrix of explanatory variables (also called 'regressors') of dimension (n x p-1).
Rows of X represent observations, and columns represent variables. Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will
automatically be excluded from the computations.
PRIOR INFORMATION $\beta$ is assumed to have a normal distribution with mean $\beta_0$ and (conditional on $\tau_0$) covariance $(1/\tau_0) (X_0'X_0)^{-1}$.
$\beta \sim N( \beta_0, (1/\tau_0) (X_0'X_0)^{-1} )$
Data Types: single| double
Data Types: single| double
It can be interpreted as $X_0'X_0$ where $X_0$ is a n0 x p matrix coming from previous experiments (assuming that the intercept is included in the model) The prior distribution of $\tau_0$ is a gamma
distribution with parameters $a_0$ and $b_0$, that is \[ p(\tau_0) \propto \tau^{a_0-1} \exp (-b_0 \tau) \qquad E(\tau_0)= a_0/b_0 \]
Data Types: single| double
Prior estimate of $\tau=1/ \sigma^2 =a_0/b_0$.
Data Types: single| double
Sometimes it helps to think of the prior information as coming from n0 previous experiments. Therefore we assume that matrix X0 (which defines R), was made up of n0 observations.
Data Types: single| double
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several
name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
Example: 'bsb',[3,6,9] , 'init',100 starts monitoring from step m=100 , 'intercept',false , 'plots',1 , 'bsbsteps',[10,20,30] , 'nocheck',true , 'msg',1
m x 1 vector containing the units forming initial subset. The default value of bsb is '' (empty value), that is we initialize the search just using prior information.
Example: 'bsb',[3,6,9]
Data Types: double
It specifies the point where to start monitoring required diagnostics. If it is not specified it is set equal to: p+1, if the sample size is smaller than 40;
min(3*p+1,floor(0.5*(n+p+1))), otherwise.
The minimum value of init is 0. In this case in the first step we start monitoring at step m=0 (step just based on prior information)
Example: 'init',100 starts monitoring from step m=100
Data Types: double
Indicator for the constant term (intercept) in the fit, specified as the comma-separated pair consisting of 'Intercept' and either true to include or false to remove the constant term from the model.
Example: 'intercept',false
Data Types: boolean
If plots=1 the monitoring units plot is displayed on the screen. The default value of plots is 0 (that is no plot is produced on the screen).
Example: 'plots',1
Data Types: double
If bsbsteps is 0 we store the units forming subset in all steps. The default is store the units forming subset in all steps if n<5000, else to store the units forming subset at steps init and steps
which are multiple of 100. For example, if n=753 and init=6, units forming subset are stored for m=init, 100, 200, 300, 400, 500 and 600.
Example: 'bsbsteps',[10,20,30]
Data Types: double
If nocheck is equal to true no check is performed on matrix y and matrix X. Notice that y and X are left unchanged. In other words the additional column of ones for the intercept is not added. As
default nocheck=false.
Example: 'nocheck',true
Data Types: boolean
It controls whether to display or not messages about great interchange on the screen If msg==1 (default) messages are displayed on the screen else no message is displayed on the screen
Example: 'msg',1
Data Types: double | {"url":"http://rosa.unipr.it/fsda/FSRBbsb.html","timestamp":"2024-11-05T15:16:53Z","content_type":"application/xhtml+xml","content_length":"32985","record_id":"<urn:uuid:c0c8924c-8d6f-4c7c-a136-08b23cec4698>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00320.warc.gz"} |
From Physics to Machine Learning: A Nobel Prize Worthy Journey
The 2024 Nobel Prize in Physics has been awarded to two visionaries whose work laid the foundation for the development of modern artificial neural networks (ANNs). John J. Hopfield and Geoffrey E.
Hinton have made groundbreaking contributions that helped transform the fields of artificial intelligence (AI), physics, and beyond. Their work—spanning the 1980s through today—not only advanced our
understanding of machine learning but also revealed the deep and fascinating connections between machine learning, biology, and physics.
A Physicist’s Leap into Neural Networks
In 1982, physicist John J. Hopfield introduced a recurrent neural network model that mimicked the associative memory of the human brain. Hopfield’s neural network, or Hopfield Network, is designed to
store patterns and recall them when only partial information is presented, much like how humans can recognize a familiar face from a blurry photograph. Hopfield’s work drew heavily on his background
in statistical physics, especially the theory of spin glasses, a class of disordered magnetic materials.
Physics and Machine Learning: A Deep Connection
What made Hopfield’s contribution truly unique was his application of energy minimization—a concept from physics used to describe systems like magnetic materials—to neural networks. The energy
function of his network resembled the energy calculations used to describe magnetic materials, and the dynamics of the network can be thought of as a system seeking to minimize its energy, much like
the way atomic spins align in a material to minimize magnetic energy.
Hopfield's work established a formal connection between physics and neural networks, showing that the same mathematical principles could describe both. This crossover between the fields not only
allowed physicists to understand neural networks in terms of familiar physical models but also provided a robust framework for solving optimization problems using neural networks.
Enter Geoffrey Hinton: The Boltzmann Machine and Deep Learning
Geoffrey Hinton, often referred to as one of the "godfathers" of deep learning, took Hopfield’s ideas further in the 1980s. Hinton, alongside collaborators, introduced the Boltzmann Machine, a
probabilistic model that extended Hopfield’s network with stochastic (random) elements. By assigning a probability to each state of the network using the Boltzmann distribution from thermodynamics,
Hinton was able to model more complex systems and solve more difficult learning problems.
Hinton’s Boltzmann Machine, while initially computationally intensive, laid the groundwork for deep learning by demonstrating how hidden layers in a neural network could learn representations of
data. He later developed the Restricted Boltzmann Machine (RBM), which became a foundational building block for deep learning architectures in the early 2000s. His work culminated in breakthroughs
that made deep, multilayered neural networks feasible—leading to the explosion of deep learning applications we see today.
Applications Across Physics, Biology, and Finance
The interdisciplinary nature of Hopfield and Hinton’s contributions is especially interesting. Not only did their work advance AI, but it also fed back into other fields like physics and finance. For
example, Hopfield networks are analogous to spin glass systems in physics, where particles settle into stable configurations by minimizing energy. Similarly, the Lyapunov function used in Hopfield
networks resembles the risk minimization concept in Markowitz’s portfolio theory in finance, where the goal is to find an optimal portfolio configuration that minimizes risk while maximizing return.
Moreover, Hinton’s work on deep learning found applications in fields as diverse as quantum mechanics (in predicting quantum phase transitions) and high-energy physics (in detecting particles from
collider data). His work on convolutional neural networks (CNNs), in collaboration with other pioneers like Yann LeCun, played a pivotal role in image recognition, which now powers facial
recognition, autonomous vehicles, and more.
Why This Nobel Prize Matters
The Nobel Committee recognized Hopfield and Hinton for their "foundational discoveries and inventions that enable machine learning with artificial neural networks." This award is a testament to how
ideas from one domain—in this case, physics—can profoundly transform another—AI and machine learning.
Their work underscores the importance of multidisciplinary thinking in science. By drawing connections between physics, biology, and computation, Hopfield and Hinton paved the way for technologies
that have revolutionized our world, from AlphaFold’s protein folding predictions to self-driving cars and AI-powered diagnostics in healthcare.
In a world where science and technology are increasingly interconnected, this Nobel Prize serves as a reminder that the future belongs to those who can think across boundaries, combining insights
from multiple disciplines to tackle complex problems.
This article was written in collaboration with LLM based writing assistants. | {"url":"https://www.asjadk.com/from-physics-to-machine-learning-a-nobel-prize-worthy-journey/","timestamp":"2024-11-06T01:42:18Z","content_type":"text/html","content_length":"20809","record_id":"<urn:uuid:18e6e4ec-4ad8-41c2-8ef1-842288c68ec9>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00530.warc.gz"} |
8.7 Can the Eulerian and Lagrangian frameworks be connected?
8.7 Can the Eulerian and Lagrangian frameworks be connected?
Changes over time in properties, such as temperature and precipitation, can be expressed in Lagrangian and Eulerian frameworks, and often the changes are different in the two frameworks (as in the
precipitation change for the thunderstorm example). We can express these changes mathematically with time derivatives. Suppose we have a scalar, R, which could be anything, but let’s make it the
rainfall rate. It is a function of space and time:
To find the change in the rainfall rate R in an air parcel over space and time, we can take its differential, which is an infinitesimally small change in R:
$dR=\frac{\partial R}{\partial t}dt+\frac{\partial R}{\partial x}dx+\frac{\partial R}{\partial y}dy+\frac{\partial R}{\partial z}dz$
where dt is an infinitesimally small change in time and dx, dy, and dz are infinitesimally small changes in x, y, and z coordinates, respectively, of the parcel.
If we divide Equation [8.15] by dt, this equation becomes:
$\frac{dR}{dt}=\frac{\partial R}{\partial t}+\frac{\partial R}{\partial x}\frac{dx}{dt}+\frac{\partial R}{\partial y}\frac{dy}{dt}+\frac{\partial R}{\partial z}\frac{dz}{dt}$
where dx/dt, dy/dt, and dz/dt describe the velocity of the air parcel in the x, y, and z directions, respectively.
Let’s consider two possibilities:
Case 1: The air parcel is not moving. Then the change in x, y and z are all zero and:
$\frac{dR}{dt}=\frac{\partial R}{\partial t}$
So, the change in the rainfall rate depends only on time. $\frac{\partial R}{\partial t}$ is called the Eulerian or local time derivative, also called the local derivative. It is the time derivative
that each of our weather observing stations record.
Case 2: The air parcel is moving. Then the changes in its position occur over time, and it moves with a velocity, $\stackrel{\to }{U}=\stackrel{\to }{i}u+\stackrel{\to }{j}v+\stackrel{\to }{k}w$ ,
$\begin{array}{l}\frac{dx}{dt}=u\text{ }\frac{dy}{dt}=v\text{ }\frac{dz}{dt}=w\\ \frac{dR}{dt}=\frac{\partial R}{\partial t}+u\frac{\partial R}{\partial x}+v\frac{\partial R}{\partial y}+w\frac{\
partial R}{\partial z}\text{ }\end{array}$
A special symbol is given for the derivative when you follow the air parcel around. It is called the substantial derivative, also called the Lagrangian derivative, material derivative, or total
derivative and is denoted by:
$\frac{DR}{Dt}=\frac{\partial R}{\partial t}+u\frac{\partial R}{\partial x}+v\frac{\partial R}{\partial y}+w\frac{\partial R}{\partial z}$
Mathematically, we can express this equation in a more general way by thinking about the dot product of a vector with the gradient of a scalar as we did in an example of the del operator:
$\frac{DR}{Dt}=\frac{\partial R}{\partial t}+\stackrel{\to }{U}·\stackrel{\to }{abla }R$
where the second term on the right hand side is called the advective derivative, which describes changes in rainfall that are solely due to the motion of the air parcel through a spatially variable
rainfall distribution.You should be able to show that equation [8.19] is the same as equation [8.18].
We can rearrange this equation to put the local derivative on the left.
$\frac{\partial R}{\partial t}=\frac{DR}{Dt}-\stackrel{\to }{U}·\stackrel{\to }{abla }R$
The term on the left is the local time derivative, which is the change in the variable R at a fixed observing station. The first term on the right is the total derivative, which is the change that is
occurring in the air parcel as it moves. The last term on the right, $-\stackrel{\to }{U}·\stackrel{\to }{abla }R$, is called the advection of R. Note that advection is simply the negative of the
advective derivative.
To go back to the analogy of the thunderstorm, the change in rainfall that you observed driving in your car was the total time derivative and it depended only on the change in the intensity of the
rain in the thunderstorm. However, for each observer in a house, the change in rainfall rate depended not only whether the rainfall within the thunderstorm was changing with time (which would depend,
for example, on the stage of the storm) but also on the movement of the thunderstorm across the landscape.
R can be any scalar. Rainfall rate is one example, but the most commonly used are pressure and temperature.
Equation [8.20] is called Euler’s relation and it relates the Eulerian framework to the Lagrangian framework. The two frameworks are related by this new concept called advection.
Let’s look at advection in more detail, focusing on temperature.
We generally think of advection being in the horizontal. So often we only consider the changes in the x and y directions and ignore the changes in the z direction:
$horizontal temperature advection=− U → H · ∇ → H T=−( u ∂T ∂x +v ∂T ∂y ) MathType@MTEF@5@5@+=
So what’s with the minus sign? Let’s see what makes physical sense. Suppose T increases only in the x-direction so that:
$\frac{\partial T}{\partial y}=0\text{and}\frac{\partial T}{\partial x}>0$
If u > 0 (westerlies, blowing eastward), then both u and $\frac{\partial T}{\partial x}$ are positive so that temperature advection is negative. What does this mean? It means that colder air blowing
from the west is replacing the warmer air, and the temperature at our location is decreasing from this advected air. Thus $\frac{\partial T}{\partial t}$ should be negative since time is increasing
and temperature is decreasing due to advection.
If the temperature advection is negative, then it is called cold-air advection, or simply cold advection. If the temperature advection is positive, then it is called warm-air advection, or simply
warm advection.
Some examples of simple cases of advection show these concepts (see figure below). When the wind blows along the isotherms, the temperature advection is zero (Case A). When the wind blows from the
direction of a lower temperature to a higher temperature (Case B), we have cold-air advection. When the wind blows as some non-normal direction to the isotherms, then we need to multiply the
magnitude of the wind and the temperature gradient by the cosine of the angle between them. We can estimate the temperature advection by doing what we did for the gradient, that is, replace all
derivatives and partial derivatives with finite $\Delta s$ .
When the isotherms with the same temperature difference are further apart on the map (see figure below), then the horizontal temperature advection will be less than when the isotherms are closer
together, if the wind velocity is the same in the two cases.
In summary, to calculate the temperature advection, first determine the magnitude and the direction of the temperature gradient. Second, determine the magnitude and direction of the wind. The
advection is simply the negative of the dot product of the velocity and the temperature gradient.
Watch this video (2:20) on calculating advection:
Quiz 8-4: The advection connection.
1. Find Practice Quiz 8-4 in Canvas. You may complete this practice quiz as many times as you want. It is not graded, but it allows you to check your level of preparedness before taking the graded
2. When you feel you are ready, take Quiz 8-4. You will be allowed to take this quiz only once. Good luck! | {"url":"https://www.e-education.psu.edu/meteo300/node/722","timestamp":"2024-11-06T12:24:59Z","content_type":"text/html","content_length":"54777","record_id":"<urn:uuid:c29696fb-c9c9-4954-a7fc-fd78b87d5a58>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00086.warc.gz"} |
How do you find the y-coordinate of a vertex?
Lesson Summary
1. Get the equation in the form y = ax2 + bx + c.
2. Calculate -b / 2a. This is the x-coordinate of the vertex.
3. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
What is the vertex point formula?
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. In this equation, the vertex of the parabola is the point (h,k) . You can see how this relates to the standard
equation by multiplying it out: y=a(x−h)(x−h)+ky=ax2−2ahx+ah2+k .
How do you find the coordinates of the vertex of a parabola?
To find the vertex of a parabola, you first need to find x (or y, if your parabola is sideways) through the formula for the axis of symmetry. Then, you’ll use that value to solve for y (or x if your
parabola opens to the side) by using the quadratic equation. Those two coordinates are your parabola’s vertex.
What is the vertex in Y?
(0, 0)
In the graph of y = x2, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward.
What is the y-coordinate of a root?
The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve
the equation, ax2 + bx + c = 0.
How do you find the Y coordinate?
The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value “5” is the Y Coordinate.
What is the Y coordinate?
Definition of y-coordinate : a coordinate whose value is determined by measuring parallel to a y-axis specifically : ordinate.
What’s the y-intercept formula?
The y-intercept formula says that the y-intercept of a function y = f(x) is obtained by substituting x = 0 in it. Using this, the y-intercept of a graph is the point on the graph whose x-coordinate
is 0. i.e., just look for the point where the graph intersects the y-axis and it is the y-intercept.
How do you find the coordinates on a graph?
To identify the x-coordinate of a point on a graph, read the number on the x-axis directly above or below the point. To identify the y-coordinate of a point, read the number on the y-axis directly to
the left or right of the point. Remember, to write the ordered pair using the correct order (x,y) .
How do you find the X and Y coordinates of a vertex?
This is the x- coordinate of the vertex. To find the y- coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y- coordinate of the vertex.
Click to see full answer.
What is the coordinates of the vertex (h k) vertex calculator?
The coordinates of the vertex (h, k) Vertex Calculator is a free online tool that displays the coordinates of the vertex point for the given parabola equation. BYJU’S online vertex calculator tool
makes the calculation faster, and it displays the vertex coordinates in a fraction of seconds. How to Use the Vertex Calculator?
How to find the vertex coordinates of a parabola?
The vertex formula helps to find the vertex coordinates of a parabola. The standard form of a parabola is y = ax 2 + bx + c. The vertex form of the parabola y = a (x – h) 2 + k. There are two ways in
which we can determine the vertex (h, k). They are: (h,k), where h = -b / 2a and evaluate y at h to find k.
What is the vertex formula?
Vertex Formula 1 D is the denominator 2 h,k are the coordinates of the vertex More | {"url":"https://tracks-movie.com/how-do-you-find-the-y-coordinate-of-a-vertex/","timestamp":"2024-11-04T22:00:39Z","content_type":"text/html","content_length":"51589","record_id":"<urn:uuid:0b47e5af-b54e-4a29-aa8b-91fa00f921a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00440.warc.gz"} |
In how many ways you can chose a committee of three students from a class of ten students?
My expected answer: ${10} choose {3}$ which is 120.
Alternative answer 1:(Lior) There are various ways: you can use majority vote, you can use dictatorship (e.g. the teacher choose); approval voting, Borda rule…
Alternative answer 2: There are precisely four ways: with repetitions where order does not matter; with repetitions where order matters; without repetitions where order matters; without repetitions
where order does not matter,
Alternative answer 3: The number is truly huge. First we need to understand in how many ways we can choose the class of ten students to start with. Should we consider the entire world population? or
just the set of all students in the world, or something more delicate? Once we choose the class of ten students we are left with the problem of chosing three among them.
Source: http://gilkalai.wordpress.com/ | {"url":"https://sak3lc.org/in-how-many-ways-you-can-chose-a-committee-of-three-students-from-a-class-of-ten-students/","timestamp":"2024-11-14T20:28:08Z","content_type":"text/html","content_length":"27155","record_id":"<urn:uuid:65ba4358-bbd5-4d38-953b-ff3ad539afac>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00261.warc.gz"} |
Aspects of non-relativistic quantum field theories
Non-relativistic quantum field theory is a framework that describes systems where the velocities are much smaller than the speed of light. A large class of those obey Schrödinger invariance, which is
the equivalent of the conformal symmetry in the relativistic world. In this review, we pedagogically introduce the main theoretical tools used to study non-relativistic physics: null reduction and
c→∞ limits, where c is the speed of light. We present a historical overview of non-relativistic wave equations, Jackiw–Pi vortices, the Aharonov–Bohm scattering, and the trace anomaly for a
Schrödinger scalar. We then review modern developments, including fermions at unitarity, the quantum Hall effect, off-shell actions, and a systematic classification of the trace anomaly. The last
part of this review is dedicated to current research topics. We define non-relativistic supersymmetry and a corresponding superspace to covariantly deal with quantum corrections. Finally, we define
the Spin Matrix Theory limit of the AdS/CFT correspondence, which is a non-relativistic sector of the duality obtained via a decoupling limit, where a precise matching of the two sides can be
ASJC Scopus subject areas
• Engineering (miscellaneous)
• Physics and Astronomy (miscellaneous)
Dive into the research topics of 'Aspects of non-relativistic quantum field theories'. Together they form a unique fingerprint. | {"url":"https://cris.bgu.ac.il/en/publications/aspects-of-non-relativistic-quantum-field-theories","timestamp":"2024-11-05T19:55:54Z","content_type":"text/html","content_length":"55273","record_id":"<urn:uuid:f30d441e-d872-457e-9c58-8a6827abe7d8>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00879.warc.gz"} |
Swapping Variables in python
How to swap variables in python
Quite often we will want to swap the values of two variables, a and b. It won't yield what we need if we try the following:
x = y
y = x
print('x=',x)#return 4
print('y=',y)#return 4
In the above code it might look a little suprise that we still can't get what we need even though it look like we have swapped the value they assigned. have you happened to have used the above and
felt shocked? Yes! i alse have done the same mistake. Now what is the logic? where is the error?
Assuming x is 3 and y is 4. The third line will set x to 4, which is good, but
then the fourth line will set y to 4 also because x is now 4. The trick is to use a third variable to
save the value of x like the following codes:
old_x = x
x = y # x is now 4
y = old_x # y is now the old_x i.e 3
In many programming languages, this is the usual way to swap variables. however,python provides a nice shortcut below
x,y = y,x # we have swapped here
The examples above swap the value that each of them stored.
x,y =y,x ==> these code is interpreted as
x=y, y=x
the most amazing part in this python shortcut is that it can accept as much as the number of variables we want to swap. try the following codes
print('a is ', a)
print('b is ', b)
print('c is ', c)
print('d is ', d)#we use "," to join the string with d
a is 3
b is 4
c is 1
d is 2
Run the code did you see their result? you can use it to swap 5,6 and as many as you want.
feel free to use whichever method you prefer.
The latter method, however, has the advantage of being shorter and easier to understand.
Before we stop there is one more advantage about this shortcut and that is destructuring! i mean with this method you can make your code short when you are assigning value to variables. consider the
following codes
a,b,c,d=1,2,3,4 # shortcut codes
print('a is ', a)
print('b is ', b)
The shortcut codes above is the same thing as:
So, if i were to assign value for 5 variables and swap them it is very easy for me with just two lines of code below
a,b,c,d,e = c,e,d,b,a
with that two lines of codes i have done swapping
first line : a=10,b=20,c=30,d=40,e=50
second line : a=30,b=50, c=40, d=20, e=10
so if you print before the second line you get first line values while second line value if the print is done after second line.
did you find these helpful? then don't forget to follow me here, instagram and on twitter.
Enjoy coding!
Top comments (0)
For further actions, you may consider blocking this person and/or reporting abuse | {"url":"https://dev.to/maxwizardth/find-substring-in-string-python-13dn","timestamp":"2024-11-14T17:59:59Z","content_type":"text/html","content_length":"78686","record_id":"<urn:uuid:ba42c56f-70ca-4f16-816b-1d3397a66e79>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00872.warc.gz"} |
Frieze Patterns Geometry
A frieze pattern or border pattern is a pattern that extends to the left and right in such a way that the pattern can be mapped onto itself by a horizontal translation. In addition to being mapped
onto itself by a horizontal translation, some frieze patterns can be mapped onto themselves by other transformations.
1. Translations T
2. 180° rotation R
3. Reflection in a horizontal line H
4. Reflection in a vertical line V
5. Horizontal glide reflection G
Describing Frieze Patterns
Example 1 :
Describe the transformations that will map each frieze pattern onto itself.
Solution :
a. This frieze pattern can be mapped onto itself by a horizontal translation (T).
b. This frieze pattern can be mapped onto itself by a horizontal translation (T) or by a 180° rotation (R).
c. This frieze pattern can be mapped onto itself by a horizontal translation (T) or by a horizontal glide reflection (G).
d. This frieze pattern can be mapped onto itself by a horizontal translation (T) or by a reflection in a vertical line (V).
Classifications of Frieze Patterns
T - Translation :
TR - Translation and 180° rotation :
TG - Translation and horizontal glide reflection :
TV - Translation and vertical glide reflection :
THG - Translation, horizontal line reflection and vertical glide reflection :
TRVG - Translation, 180° rotation, vertical line reflection and horizontal glide reflection :
TRHVG - Translation, 180° rotation, horizontal line reflection, vertical line reflection and horizontal glide reflection :
To classify a frieze pattern into one of the seven categories, first decide whether the pattern has 180° rotation. If it does, then there are three possible classifications: TR, TRVG, and TRHVG.
If the frieze pattern does not have 180° rotation, then there are four possible classifications: T, TV, TG, and THG. Decide whether the pattern has a line of reflection. By a process of elimination,
you will reach the correct classification.
Classifying a Frieze Pattern
Example 2 :
Categorize the snakeskin pattern of the mountain adder.
Solution :
This pattern is a TRHVG. The pattern can be mapped onto itself by a translation, a 180° rotation, a reflection in a horizontal line, a reflection in a vertical line, and a horizontal glide
Using Frieze Patterns in Real Life
Example (Identifying Frieze Patterns) :
The frieze patterns of ancient Doric buildings are located between the cornice and the architrave, as shown below.
The frieze patterns consist of alternating sections. Some sections contain a person or a symmetric design. Other sections have simple patterns of three or four vertical lines.
Portions of two frieze patterns are shown below. Classify the patterns.
Solution :
a. Following the diagrams on the previous page, you can see that this frieze pattern has rotational symmetry, line symmetry about a horizontal line and a vertical line, and that the pattern can be
mapped onto itself by a glide reflection. So, the pattern can be classified as TRHVG.
b. The only transformation that maps this pattern onto itself is a translation. So, the pattern can be classified as T.
Drawing a Frieze Pattern
Example 3 :
A border on a bathroom wall is created using the decorative tile at the right. The border pattern is classified as TR. Draw one such pattern.
Solution :
Begin by rotating the given tile 180°. Use this tile and the original tile to create a pattern that has rotational symmetry. Then translate the pattern several times to create the frieze pattern.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com | {"url":"https://www.onlinemath4all.com/frieze-patterns-geometry.html","timestamp":"2024-11-08T11:52:46Z","content_type":"text/html","content_length":"33450","record_id":"<urn:uuid:feb6b17a-69ea-44fd-8ffe-a4a3a767b8e6>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00202.warc.gz"} |
Q 15.33: Poster
Montag, 23. März 2015, 17:00–19:00, C/Foyer
Quasi-Condensation and Superfluidity in a Ring Trap — Hansjörg Polster and •Carsten Henkel — University of Potsdam, Germany
Low-dimensional Bose gases suffer from large phase fluctuations that prevent the formation of a proper condensate as defined by Penrose and Onsager. We study a one-dimensional, phase-fluctuating gas
in the cross-over region between the ideal gas and the quasi-condensate (weak interactions). Correlation functions of any order are found by mapping the quantum field theory to a random walk in the
complex plane, making a classical field approximation [1]. We discuss in particular full distribution functions for the atomic density, including the formation of pairs and clusters at the onset of
quasi-condensation. Currently we investigate the distribution function of the total particle current in a rotating ring trap [2] which provides insight into the superfluid behaviour of the gas.
[1] L. W. Gruenberg and L. Gunther, Phys. Lett. A 38 (1972) 463; D. J. Scalapino, M. Sears, and R. A. Ferrell, Phys. Rev. B 6 (1972) 3409
[2] I. Carusotto and Y. Castin, C. R. Physique 5 (2004) 107 | {"url":"https://www.dpg-verhandlungen.de/year/2015/conference/heidelberg/part/q/session/15/contribution/33","timestamp":"2024-11-02T15:47:16Z","content_type":"text/html","content_length":"7645","record_id":"<urn:uuid:82073fce-077e-482a-8562-454f5fb4eb2f>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00347.warc.gz"} |
An algorithmic framework for MINLP with separable non-convexity
Global optimization algorithms, e.g., spatial branch-and-bound approaches like those implemented in codes such as BARON and COUENNE, have had substantial success in tackling complicated, but
generally small scale, non-convex MINLPs (i.e., mixed-integer nonlinear programs having non-convex continuous relaxations). Because they are aimed at a rather general class of problems, the
possibility remains that larger instances from a simpler class may be amenable to a simpler approach. We focus on MINLPs for which the non-convexity in the objective and constraint functions is
manifested as the sum of non-convex univariate functions. There are many problems that are already in such a form, or can be brought into such a form via some simple substitutions. In fact, the first
step in spatial branch-and-bound is to bring problems into nearly such a form. For our purposes, we shift that burden back to the modeler. We have developed a simple algorithm, implemented at the
level of a modeling language (in our case AMPL), to attack such separable problems. First, we identify subintervals of convexity and concavity for the univariate functions using external calls to
MATLAB. With such an identification at hand, we develop a convex MINLP relaxation of the problem (i.e., as a mixed-integer nonlinear program having a convex continuous relaxation). Our convex MINLP
relaxation differs from those typically employed in spatial branch-and-bound; rather than relaxing the graph of a univariate function on an interval to an enclosing polygon, we work on each
subinterval of convexity and concavity separately, using linear relaxation on only the ``concave side'' of each function on the subintervals. The subintervals are glued together using binary
variables. Next, we employ ideas of spatial branch-and-bound, but rather than branching, we repeatedly refine our convex MINLP relaxation by modifying it at the modeling level. We attack our convex
MINLP relaxation, to get lower bounds on the global minimum, using the code BONMIN as a black-box convex MINLP solver. Next, by fixing the integer variables in the original non-convex MINLP, and then
locally solving the associated non-convex NLP restriction, we get an upper bound on the global minimum, using the code IPOPT. We use the solutions found by BONMIN and IPOPT to guide our choice of
further refinements in a way that overall guarantees convergence. Note that our proposed procedure is an exact algorithm, and not just a heuristic. We have had substantial success in our preliminary
computational experiments. In particular, we see very few major iterations occurring, so most of the time is spent in the solution of a small number of convex MINLPs. An advantage of our approach is
that it can be implemented easily using existing software components, and that further advances in technology for convex MINLP will immediately give our approach a benefit.
IBM Research Report RC24810, June 2009
View An algorithmic framework for MINLP with separable non-convexity | {"url":"https://optimization-online.org/2009/06/2331/","timestamp":"2024-11-12T15:30:09Z","content_type":"text/html","content_length":"86707","record_id":"<urn:uuid:0a9e46b7-df94-482f-81cb-f97490271919>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00385.warc.gz"} |
A study on the randomness of the digits of pi
Published in:
International Journal of Modern Physics C 16,2 (2005) 281-294;
We apply a newly-developed computational method, Geometric Random Inner Products (GRIP), to quantify the randomness of number sequences obtained from the decimal digits of pi. Several members from
the GRIP family of tests are used, and the results from pi are compared to those calculated from other random number generators. These include a recent hardware generator based on an actual physical
process, turbulent electroconvection. We find that the decimal digits of pi are in fact good candidates for random number generators and can be used for practical scientific and engineering
geometric probability;; geometric random inner products;; monte carlo methods;; random distance distribution;; random number generator;; randomness and pi;; random-number generators;;
elementary-functions;; simulations;; computation;; sequence;; tests
Date of this Version
January 2005 | {"url":"https://docs.lib.purdue.edu/physics_articles/245/","timestamp":"2024-11-09T09:36:06Z","content_type":"text/html","content_length":"30216","record_id":"<urn:uuid:08d67cbe-5fe0-4444-ad7c-53fb15badb9b>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00494.warc.gz"} |
KLA Corporation is a capital equipment company based in Milpitas, California. It supplies process control and yield management systems for the semiconductor industry and other related nanoelectronics
industries. The company's ...
All financial data is based on trailing twelve months (TTM) periods - updated quarterly, unless otherwise specified. Data from | {"url":"https://fullratio.com/stocks/nasdaq-klac/kla","timestamp":"2024-11-10T12:54:05Z","content_type":"text/html","content_length":"58214","record_id":"<urn:uuid:b67a0eea-b1f7-40c1-b392-373408fbf068>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00307.warc.gz"} |
Make Cell Blank if all Columns are "N"
Hi there,
Wondering how to amend this formula so that if all the cells are "N", it will return a blank in column "Report Status"
=IF(OR([PAR Items]16 = "Y", Proxies16 = "Y", Commissions16 = "Y", Constraints16 = "Y", [APX Reports]16 = "Y", [MRFP/SMA]16 = "Y", Commentary16 = "Y", Attachment16 = "Y", (COUNTIF([PAR Items]
16:Attachment16, "") > 0)), "Incomplete", "Complete")
• Try this. I combined with your other formula so it will check if all = N first and if not, it'll run through what you previously wrote. I also updated for @row to speed it up.
=IF(AND([PAR Items]@row= "N", Proxies@row = "N", Commissions@row = "N", Constraints@row = "N", [APX Reports]@row= "N", [MRFP/SMA]@row= "N", Commentary@row = "N", Attachment@row = "N"), " ", IF(OR
([PAR Items]@row= "Y", Proxies@row = "Y", Commissions@row = "Y", Constraints@row = "Y", [APX Reports]@row= "Y", [MRFP/SMA]@row= "Y", Commentary@row = "Y", Attachment@row = "Y", (COUNTIF([PAR
Items]@row:Attachment@row, "") > 0)), "Incomplete", "Complete")
• What are the possible entries? The way I am reading your formula, if at least one cell is blank or one cell contains a "Y", it will show as Incomplete. How would you generate a Complete other
than having all cells filled with an "N"? Having all cells filled with an "N" would currently generate a Complete result, so all you would have to do to generate a blank would be to change
"Complete" to "".
• Hi Paul,
I need it so that if any of the cells are "Y", it shows as incomplete and if any of them have initials (eg. TS), it shows complete. So right now, anything other than Y is causing the cell to say
complete but I need it so that if it is all N's in the cells, it will be blank.
• I think this works! Thank you
• Ok. That makes sense. The first thing to establish is how many possible entries there are. If there is the need for flexibility to allow for a differing number of columns whether you plan to add
or remove, we can use a simple COUNTIFS across the range.
=COUNTIFS([PAR Items]@row:Attachment@row, OR(ISBLANK(@cell), NOT(ISBLANK(@cell))))
As long as [PAR Items] is the leftmost column and Attachments is the rightmost column, you can add, remove, or rearrange everything in the middle.
For the sake of this example though, I will use a hard coded number. Your screenshot shows 8 columns within the range, so I will use the number 8. If you need the flexibility of the COUNTIFS,
just replace the number 8 with that formula within the overall formula.
So we will start with "Y". If any cell within the range contains a "Y", we want it to display "Incomplete".
=IF(CONTAINS("Y", [PAR Items]@row:Attachment@row), "Incomplete",
Next we will say that if they are ALL "N", display a blank.
=IF(CONTAINS("Y", [PAR Items]@row:Attachment@row), "Incomplete", IF(COUNTIFS([PAR Items]@row:Attachment@row, "N") = 8, "",
If there are zero cells with a "Y" in them making the first argument false, and not all cells contain an "N" making the second IF statement false, then the only other option would be to register
it as "Complete" and close out the formula.
=IF(CONTAINS("Y", [PAR Items]@row:Attachment@row), "Incomplete", IF(COUNTIFS([PAR Items]@row:Attachment@row, "N") = 8, "", "Complete"))
And there you have it. Short, sweet, and to the point.
Help Article Resources | {"url":"https://community.smartsheet.com/discussion/54651/make-cell-blank-if-all-columns-are-n","timestamp":"2024-11-04T16:41:00Z","content_type":"text/html","content_length":"436481","record_id":"<urn:uuid:697696c3-00e4-48c4-a9ef-ecd12e93861e>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00680.warc.gz"} |
Regression in Lavaan (Frequentist) - Rens van de Schoot
Regression in lavaan (Frequentist)
Last modified: 19 October 2019
This tutorial provides the reader with a basic tutorial how to perform a regression analysis in lavaan. Throughout this tutorial, the reader will be guided through importing datafiles, exploring
summary statistics and regression analyses. Here, we will exclusively focus on frequentist statistics.
We are continuously improving the tutorials so let me know if you discover mistakes, or if you have additional resources I can refer to. The source code is available via Github. If you want to be
the first to be informed about updates, follow me on Twitter.
This tutorial expects:
• Installation of R package lavaan. This tutorial was made using Lavaan version 0.6.5 in R version 3.6.1
• Basic knowledge of hypothesis testing
• Basic knowledge of correlation and regression
• Basic knowledge of coding in R
Example Data
The data we will be using for this exercise is based on a study about predicting PhD-delays (Van de Schoot, Yerkes, Mouw and Sonneveld 2013).The data can be downloaded here. Among many other
questions, the researchers asked the Ph.D. recipients how long it took them to finish their Ph.D. thesis (n=333). It appeared that Ph.D. recipients took an average of 59.8 months (five years and four
months) to complete their Ph.D. trajectory. The variable B3_difference_extra measures the difference between planned and actual project time in months (mean=9.97, minimum=-31, maximum=91, sd=14.43).
For more information on the sample, instruments, methodology and research context we refer the interested reader to the paper.
For the current exercise we are interested in the question whether age (M = 31.7, SD = 6.86) of the Ph.D. recipients is related to a delay in their project.
The relation between completion time and age is expected to be non-linear. This might be due to that at a certain point in your life (i.e., mid thirties), family life takes up more of your time than
when you are in your twenties or when you are older.
So, in our model the \(gap\) (B3_difference_extra) is the dependent variable and \(age\) (E22_Age) and \(age^2\)(E22_Age_Squared ) are the predictors. The data can be found in the file phd-delays.csv
Question: Write down the null and alternative hypotheses that represent this question. Which hypothesis do you deem more likely?
< class="collapseomatic " id="id67283ec517736" tabindex="0" title="" >>
\(H_0:\) \(age\) is not related to a delay in the PhD projects.
\(H_1:\) \(age\) is related to a delay in the PhD projects.
\(H_0:\) \(age^2\) is not related to a delay in the PhD projects.
\(H_1:\) \(age^2\)is related to a delay in the PhD projects.
Preparation – Importing and Exploring Data
Install the following packages in R:
library(psych) #to get some extended summary statistics
library(tidyverse) # needed for data manipulation and plotting
You can find the data in the file phd-delays.csv , which contains all variables that you need for this analysis. Although it is a .csv-file, you can directly load it into R using the following
#read in data
dataPHD <- read.csv2(file="phd-delays.csv")
colnames(dataPHD) <- c("diff", "child", "sex","age","age2")
Alternatively, you can directly download them from GitHub into your R work space using the following command:
dataPHD <- read.csv2(file="https://raw.githubusercontent.com/LaurentSmeets/Tutorials/master/Blavaan/phd-delays.csv")
colnames(dataPHD) <- c("diff", "child", "sex","age","age2")
GitHub is a platform that allows researchers and developers to share code, software and research and to collaborate on projects (see https://github.com/)
Once you loaded in your data, it is advisable to check whether your data import worked well. Therefore, first have a look at the summary statistics of your data. you can do this by using the describe
() function.
Question: Have all your data been loaded in correctly? That is, do all data points substantively make sense? If you are unsure, go back to the .csv-file to inspect the raw data.
## vars n mean sd median trimmed mad min max range skew
## diff 1 333 9.97 14.43 5 6.91 7.41 -31 91 122 2.21
## child 2 333 0.18 0.38 0 0.10 0.00 0 1 1 1.66
## sex 3 333 0.52 0.50 1 0.52 0.00 0 1 1 -0.08
## age 4 333 31.68 6.86 30 30.39 2.97 26 80 54 4.45
## age2 5 333 1050.22 656.39 900 928.29 171.98 676 6400 5724 6.03
## kurtosis se
## diff 5.92 0.79
## child 0.75 0.02
## sex -2.00 0.03
## age 24.99 0.38
## age2 42.21 35.97
The descriptive statistics make sense:
diff: Mean (9.97), SE (0.79)
\(Age\): Mean (31.68), SE (0.38)
\(Age^2\): Mean (1050.22), SE (35.97)
Before we continue with analyzing the data we can also plot the expected relationship.
dataPHD %>%
ggplot(aes(x = age,
y = diff)) +
geom_point(position = "jitter",
alpha = .6)+ #to add some random noise for plotting purposes
geom_smooth(method = "lm", # to add the linear relationship
aes(color = "linear"),
se = FALSE) +
geom_smooth(method = "lm",
formula = y ~ x + I(x^2),# to add the quadratic relationship
aes(color = "quadratic"),
se = FALSE) +
labs(title = "Delay vs. age",
subtitle = "There seems to be some quadratic relationship",
x = "Age",
y = "Delay",
color = "Type of relationship" ) +
theme(legend.position = "bottom")
Regression Analysis
Now, let’s run a multiple regression model predicting the difference between Ph.D. students’ planned and actual project time by their age (note that we ignore assumption checking, if you want a quick
introduction to the assumptions underlying a regression, please have look at https://statistics.laerd.com/spss-tutorials/linear-regression-using-spss-statistics.php).
To run a multiple regression with lavaan, you first specify the model, then fit the model and finally acquire the summary. The model is specified as follows:
1. A depedent variable we want to predict.
2. A “~”, that we use to indicate that we now give the other variables of interest. (comparable to the ‘=’ of the regression equation).
3. The different indepedent variables separated by the summation symbol ‘+’.
4. Finally, we specify that the dependent variable has a variance and that we want an intercept.
5. To fit the model we use the lavaan() function, which needs a model= and a data= input.
For more information on the basics of lavaan, see their website
The following code is how to specify the regression model:
model.regression <- '#the regression model
diff ~ age + age2
#show that dependent variable has variance
diff ~~ diff
#we want to have an intercept
diff ~ 1'
Now, perform a multiple linear regression and answer the following question:
Question: Using a significance criterion of 0.05, is there a significant effect of \(age\) and \(age^2\)?
fit <- lavaan(model = model.regression, data = dataPHD)
summary(fit, fit.measures = TRUE, ci = TRUE, rsquare = TRUE)
## lavaan 0.6-5 ended normally after 24 iterations
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 4
## Number of observations 333
## Model Test User Model:
## Test statistic 0.000
## Degrees of freedom 0
## Model Test Baseline Model:
## Test statistic 21.521
## Degrees of freedom 2
## P-value 0.000
## User Model versus Baseline Model:
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
## Loglikelihood and Information Criteria:
## Loglikelihood user model (H0) -1350.154
## Loglikelihood unrestricted model (H1) -1350.154
## Akaike (AIC) 2708.308
## Bayesian (BIC) 2723.541
## Sample-size adjusted Bayesian (BIC) 2710.852
## Root Mean Square Error of Approximation:
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 NA
## Standardized Root Mean Square Residual:
## SRMR 0.000
## Parameter Estimates:
## Information Expected
## Information saturated (h1) model Structured
## Standard errors Standard
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## diff ~
## age 2.657 0.583 4.554 0.000 1.514
## age2 -0.026 0.006 -4.236 0.000 -0.038
## ci.upper
## 3.801
## -0.014
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .diff -47.088 12.285 -3.833 0.000 -71.166
## ci.upper
## -23.010
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .diff 194.641 15.084 12.903 0.000 165.076
## ci.upper
## 224.206
## R-Square:
## Estimate
## diff 0.063
There is a significant effect of \(age\) and \(age^2\), with b=2.657, p <.001 for \(age\), and b=-0.026, p<.001 for \(age^2\).
Surveys in academia have shown that a large number of researchers interpret the p-value wrong and misinterpretations are way more widespread than thought. Have a look at the article by Greenland et
al. (2016) that provides a guide to clear and concise interpretations of p.
Question: What can you conclude about the hypothesis being tested using the correct interpretation of the p-value?
Assuming that the null hypothesis is true in the population, the probability of obtaining a test statistic that is as extreme or more extreme as the one we observe is <0.1%. Because the effect of \
(age^2\) is below our pre-determined alpha level, we reject the null hypothesis.
Recently, a group of 72 notable statisticians proposed to shift the significance threshold to 0.005 (Benjamin et al. 2017, but see also a critique byTrafimow, …, Van de Schoot, et al., 2018). They
argue that a p-value just below 0.05 does not provide sufficient evidence for statistical inference.
Question: How does your conclusion change if you follow this advice?
Because the p-values for both regression coefficients were really small <.001, the conclusion doesn’t change in this case.
Of course, we should never base our decisions on single criterions only. Luckily, there are several additional measures that we can take into account. A very popular measure is the confidence
interval. In the summary() function, these intervals can be demanded, which has already been done in the previous step.
Question: What can you conclude about the hypothesis being tested using the correct interpretation of the confidence interval?
\(Age\): 95% CI [1.514, 3.801]
\(Age^2\): 95% CI [-0.038, -0.014]
In both cases the 95% CI’s don’t contain 0, which means, the null hypotheses should be rejected. A 95% CI means, that, if infinitely samples were taken from the population, then 95% of the samples
contain the true population value. But we do not know whether our current sample is part of this collection, so we only have an aggregated assurance that in the long run if our analysis would be
repeated our sample CI contains the true population parameter.
Additionally, to make statements about the actual relevance of your results, focusing on effect size measures is inevitable.
Question: What can you say about the relevance of your results? Focus on the explained variance and the standardized regression coefficients.
R\(^2\)= 0.063 in the regression model. This means that 6.3% of the variance in the PhD delays, can be explained by \(age\) and \(age^2\).
We can also run the analysis again, but now with standardized coefficients.Lavaan has the inbuilt-function standardizedsolution() to obtain standardized coefficients.
## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 diff ~ age 1.262 0.265 4.763 0 0.743 1.782
## 2 diff ~ age2 -1.174 0.267 -4.402 0 -1.697 -0.651
## 3 diff ~~ diff 0.937 0.025 37.057 0 0.888 0.987
## 4 diff ~1 -3.268 0.819 -3.992 0 -4.872 -1.664
## 5 age ~~ age 1.000 0.000 NA NA 1.000 1.000
## 6 age ~~ age2 0.982 0.000 NA NA 0.982 0.982
## 7 age2 ~~ age2 1.000 0.000 NA NA 1.000 1.000
## 8 age ~1 4.627 0.000 NA NA 4.627 4.627
## 9 age2 ~1 1.602 0.000 NA NA 1.602 1.602
The standardized coefficients, \(age\) (1.262) and \(age^2\) (-1.174), show that the effects of both regression coefficients are comparable, but the effect of \(age\) is somewhat higher.This means
that the linear effect of age on PhD delay (age) is a bit larger than the quadratic effect of age on PhD delay (age2)
Only a combination of different measures assessing different aspects of your results can provide a comprehensive answer to your research question.
Question: Drawing on all the measures we discussed above, formulate an answer to your research question.
The variables \(age\) and \(age^2\) are significantly related to PhD delays. However, the total explained variance by those two predictors is only 6.3%. Therefore, a large part of the variance is
still unexplained.
Benjamin, D. J., Berger, J., Johannesson, M., Nosek, B. A., Wagenmakers, E.,… Johnson, V. (2017, July 22). Redefine statistical significance. Retrieved from psyarxiv.com/mky9j
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N. Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations.
European Journal of Epidemiology 31 (4). https://doi.org/10.1007/s10654-016-0149-3 _ _
_ Rosseel, Y. (2012)._ lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36.
van de Schoot R, Yerkes MA, Mouw JM, Sonneveld H (2013) What Took Them So Long? Explaining PhD Delays among Doctoral Candidates. PLoS ONE 8(7): e68839. https://doi.org/10.1371/journal.pone.0068839
Trafimow D, Amrhein V, Areshenkoff CN, Barrera-Causil C, Beh EJ, Bilgi? Y, Bono R, Bradley MT, Briggs WM, Cepeda-Freyre HA, Chaigneau SE, Ciocca DR, Carlos Correa J, Cousineau D, de Boer MR, Dhar SS,
Dolgov I, G?mez-Benito J, Grendar M, Grice J, Guerrero-Gimenez ME, Guti?rrez A, Huedo-Medina TB, Jaffe K, Janyan A, Karimnezhad A, Korner-Nievergelt F, Kosugi K, Lachmair M, Ledesma R, Limongi R,
Liuzza MT, Lombardo R, Marks M, Meinlschmidt G, Nalborczyk L, Nguyen HT, Ospina R, Perezgonzalez JD, Pfister R, Rahona JJ, Rodr?guez-Medina DA, Rom?o X, Ruiz-Fern?ndez S, Suarez I, Tegethoff M, Tejo
M, ** van de Schoot R** , Vankov I, Velasco-Forero S, Wang T, Yamada Y, Zoppino FC, Marmolejo-Ramos F. (2017) Manipulating the alpha level cannot cure significance testing – comments on “Redefine
statistical significance”_ _PeerJ reprints 5:e3411v1 https://doi.org/10.7287/peerj.preprints.3411v1 | {"url":"https://www.rensvandeschoot.com/tutorials/regression-in-lavaan-frequentist/","timestamp":"2024-11-05T11:57:18Z","content_type":"text/html","content_length":"106081","record_id":"<urn:uuid:1047d6c7-fb4a-40be-a6dc-334aaded0d47>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00602.warc.gz"} |
Base Bootstrap
Base Bootstrap
class tsbootstrap.base_bootstrap.BaseDistributionBootstrap(n_bootstraps: Integral = 10, distribution: str = 'normal', refit: bool = False, model_type: Literal['ar', 'arima', 'sarima', 'var'] = 'ar',
model_params=None, order: Integral | List[Integral] | tuple[Integral, Integral, Integral] | tuple[Integral, Integral, Integral, Integral] | None = None, save_models: bool = False, rng=None, **
Implementation of the Distribution Bootstrap (DB) method for time series data.
The DB method is a non-parametric method that generates bootstrapped samples by fitting a distribution to the residuals and then generating new residuals from the fitted distribution. The new
residuals are then added to the fitted values to create the bootstrapped samples.
☆ n_bootstraps (Integral, default=10) – The number of bootstrap samples to create.
☆ distribution (str, default='normal') – The distribution to use for generating the bootstrapped samples. Must be one of ‘poisson’, ‘exponential’, ‘normal’, ‘gamma’, ‘beta’, ‘lognormal’,
‘weibull’, ‘pareto’, ‘geometric’, or ‘uniform’.
☆ refit (bool, default=False) – Whether to refit the distribution to the resampled residuals for each bootstrap. If False, the distribution is fit once to the residuals and the same
distribution is used for all bootstraps.
☆ model_type (str, default="ar") – The model type to use. Must be one of “ar”, “arima”, “sarima”, “var”, or “arch”.
☆ model_params (dict, default=None) – Additional keyword arguments to pass to the TSFit model.
☆ order (Integral or list or tuple, default=None) – The order of the model. If None, the best order is chosen via TSFitBestLag. If Integral, it is the lag order for AR, ARIMA, and SARIMA,
and the lag order for ARCH. If list or tuple, the order is a tuple of (p, o, q) for ARIMA and (p, d, q, s) for SARIMAX. It is either a single Integral or a list of non-consecutive ints
for AR, and an Integral for VAR and ARCH. If None, the best order is chosen via TSFitBestLag. Do note that TSFitBestLag only chooses the best lag, not the best order, so for the tuple
values, it only chooses the best p, not the best (p, o, q) or (p, d, q, s). The rest of the values are set to 0.
☆ save_models (bool, default=False) – Whether to save the fitted models.
☆ rng (Integral or np.random.Generator, default=np.random.default_rng()) – The random number generator or seed used to generate the bootstrap samples.
The distribution object used to generate the bootstrapped samples. If None, the distribution has not been fit yet.
scipy.stats.rv_continuous or None
The parameters of the distribution used to generate the bootstrapped samples. If None, the distribution has not been fit yet.
tuple or None
__init__ : Initialize the BaseDistributionBootstrap class.
fit_distribution(resids: np.ndarray) tuple[rv_continuous, tuple]
Fit the specified distribution to the residuals and return the distribution object and the parameters of the distribution.
The DB method is defined as:
\[\begin{split}\\hat{X}_t = \\hat{\\mu} + \\epsilon_t\end{split}\]
where \(\\epsilon_t \\sim F_{\\hat{\\epsilon}}\) is a random variable sampled from the distribution \(F_{\\hat{\\epsilon}}\) fitted to the residuals \(\\hat{\\epsilon}\).
class tsbootstrap.base_bootstrap.BaseMarkovBootstrap(n_bootstraps: Integral = 10, method: Literal['first', 'middle', 'last', 'mean', 'mode', 'median', 'kmeans', 'kmedians', 'kmedoids'] = 'middle',
apply_pca_flag: bool = False, pca=None, n_iter_hmm: Integral = 10, n_fits_hmm: Integral = 1, blocks_as_hidden_states_flag: bool = False, n_states: Integral = 2, model_type: Literal['ar', 'arima',
'sarima', 'var'] = 'ar', model_params=None, order: Integral | List[Integral] | tuple[Integral, Integral, Integral] | tuple[Integral, Integral, Integral, Integral] | None = None, save_models: bool
= False, rng=None, **kwargs)[source]
Base class for Markov bootstrap.
☆ n_bootstraps (Integral, default=10) – The number of bootstrap samples to create.
☆ method (str, default="middle") – The method to use for compressing the blocks. Must be one of “first”, “middle”, “last”, “mean”, “mode”, “median”, “kmeans”, “kmedians”, “kmedoids”.
☆ apply_pca_flag (bool, default=False) – Whether to apply PCA to the residuals before fitting the HMM.
☆ pca (PCA, default=None) – The PCA object to use for applying PCA to the residuals.
☆ n_iter_hmm (Integral, default=10) – Number of iterations for fitting the HMM.
☆ n_fits_hmm (Integral, default=1) – Number of times to fit the HMM.
☆ blocks_as_hidden_states_flag (bool, default=False) – Whether to use blocks as hidden states.
☆ n_states (Integral, default=2) – Number of states for the HMM.
☆ model_type (str, default="ar") – The model type to use. Must be one of “ar”, “arima”, “sarima”, “var”, or “arch”.
☆ model_params (dict, default=None) – Additional keyword arguments to pass to the TSFit model.
☆ order (Integral or list or tuple, default=None) – The order of the model. If None, the best order is chosen via TSFitBestLag. If Integral, it is the lag order for AR, ARIMA, and SARIMA,
and the lag order for ARCH. If list or tuple, the order is a tuple of (p, o, q) for ARIMA and (p, d, q, s) for SARIMAX. It is either a single Integral or a list of non-consecutive ints
for AR, and an Integral for VAR and ARCH. If None, the best order is chosen via TSFitBestLag. Do note that TSFitBestLag only chooses the best lag, not the best order, so for the tuple
values, it only chooses the best p, not the best (p, o, q) or (p, d, q, s). The rest of the values are set to 0.
☆ save_models (bool, default=False) – Whether to save the fitted models.
☆ rng (Integral or np.random.Generator, default=np.random.default_rng()) – The random number generator or seed used to generate the bootstrap samples.
The MarkovSampler object used for sampling.
MarkovSampler or None
__init__ : Initialize the Markov bootstrap.
Fitting Markov models is expensive, hence we do not allow re-fititng. We instead fit once to the residuals and generate new samples by changing the random_seed.
class tsbootstrap.base_bootstrap.BaseResidualBootstrap(n_bootstraps: Integral = 10, rng=None, model_type: Literal['ar', 'arima', 'sarima', 'var'] = 'ar', model_params=None, order: Integral | List[
Integral] | tuple[Integral, Integral, Integral] | tuple[Integral, Integral, Integral, Integral] | None = None, save_models: bool = False)[source]
Base class for residual bootstrap.
☆ n_bootstraps (Integral, default=10) – The number of bootstrap samples to create.
☆ model_type (str, default="ar") – The model type to use. Must be one of “ar”, “arima”, “sarima”, “var”, or “arch”.
☆ model_params (dict, default=None) – Additional keyword arguments to pass to the TSFit model.
☆ order (Integral or list or tuple, default=None) – The order of the model. If None, the best order is chosen via TSFitBestLag. If Integral, it is the lag order for AR, ARIMA, and SARIMA,
and the lag order for ARCH. If list or tuple, the order is a tuple of (p, o, q) for ARIMA and (p, d, q, s) for SARIMAX. It is either a single Integral or a list of non-consecutive ints
for AR, and an Integral for VAR and ARCH. If None, the best order is chosen via TSFitBestLag. Do note that TSFitBestLag only chooses the best lag, not the best order, so for the tuple
values, it only chooses the best p, not the best (p, o, q) or (p, d, q, s). The rest of the values are set to 0.
☆ save_models (bool, default=False) – Whether to save the fitted models.
☆ rng (Integral or np.random.Generator, default=np.random.default_rng()) – The random number generator or seed used to generate the bootstrap samples.
The fitted model.
The residuals of the fitted model.
The fitted values of the fitted model.
The coefficients of the fitted model.
__init__ : Initialize self.
_fit_model : Fits the model to the data and stores the residuals.
class tsbootstrap.base_bootstrap.BaseSieveBootstrap(n_bootstraps: Integral = 10, rng=None, resids_model_type: Literal['ar', 'arima', 'sarima', 'var', 'arch'] = 'ar', resids_order=None,
save_resids_models: bool = False, kwargs_base_sieve=None, model_type: Literal['ar', 'arima', 'sarima', 'var'] = 'ar', model_params=None, order: Integral | List[Integral] | tuple[Integral,
Integral, Integral] | tuple[Integral, Integral, Integral, Integral] | None = None, **kwargs_base_residual)[source]
Base class for Sieve bootstrap.
This class provides the core functionalities for implementing the Sieve bootstrap method, allowing for the fitting of various models to the residuals and generation of bootstrapped samples. The
Sieve bootstrap is a parametric method that generates bootstrapped samples by fitting a model to the residuals and then generating new residuals from the fitted model. The new residuals are then
added to the fitted values to create the bootstrapped samples.
☆ resids_model_type (str, default="ar") – The model type to use for fitting the residuals. Must be one of “ar”, “arima”, “sarima”, “var”, or “arch”.
☆ resids_order (Integral or list or tuple, default=None) – The order of the model to use for fitting the residuals. If None, the order is automatically determined.
☆ save_resids_models (bool, default=False) – Whether to save the fitted models for the residuals.
☆ kwargs_base_sieve (dict, default=None) – Keyword arguments to pass to the SieveBootstrap class.
☆ model_type (str, default="ar") – The model type to use. Must be one of “ar”, “arima”, “sarima”, “var”, or “arch”.
☆ model_params (dict, default=None) – Additional keyword arguments to pass to the TSFit model.
☆ order (Integral or list or tuple, default=None) – The order of the model. If None, the best order is chosen via TSFitBestLag. If Integral, it is the lag order for AR, ARIMA, and SARIMA,
and the lag order for ARCH. If list or tuple, the order is a tuple of (p, o, q) for ARIMA and (p, d, q, s) for SARIMAX. It is either a single Integral or a list of non-consecutive ints
for AR, and an Integral for VAR and ARCH. If None, the best order is chosen via TSFitBestLag. Do note that TSFitBestLag only chooses the best lag, not the best order, so for the tuple
values, it only chooses the best p, not the best (p, o, q) or (p, d, q, s). The rest of the values are set to 0.
Coefficients of the fitted residual model. Replace “type” with the specific type if known.
type or None
Fitted residual model object. Replace “type” with the specific type if known.
type or None
__init__ : Initialize the BaseSieveBootstrap class.
_fit_resids_model : Fit the residual model to the residuals.
class tsbootstrap.base_bootstrap.BaseStatisticPreservingBootstrap(n_bootstraps: Integral = 10, statistic: Callable | None = None, statistic_axis: Integral = 0, statistic_keepdims: bool = False, rng=
Bootstrap class that generates bootstrapped samples preserving a specific statistic.
This class generates bootstrapped time series data, preserving a given statistic (such as mean, median, etc.) The statistic is calculated from the original data and then used as a parameter for
generating the bootstrapped samples. For example, if the statistic is np.mean, then the mean of the original data is calculated and then used as a parameter for generating the bootstrapped
☆ n_bootstraps (Integral, default=10) – The number of bootstrap samples to create.
☆ statistic (Callable, default=np.mean) – A callable function to compute the statistic that should be preserved.
☆ statistic_axis (Integral, default=0) – The axis along which the statistic should be computed.
☆ statistic_keepdims (bool, default=False) – Whether to keep the dimensions of the statistic or not.
☆ rng (Integral or np.random.Generator, default=np.random.default_rng()) – The random number generator or seed used to generate the bootstrap samples.
The statistic calculated from the original data. This is used as a parameter for generating the bootstrapped samples.
np.ndarray, default=None
__init__ : Initialize the BaseStatisticPreservingBootstrap class.
_calculate_statistic(X: np.ndarray) np.ndarray : Calculate the statistic from the input data.[source]
class tsbootstrap.base_bootstrap.BaseTimeSeriesBootstrap(n_bootstraps: Integral = 10, rng=None)[source]
Base class for time series bootstrapping.
ValueError – If n_bootstraps is not greater than 0.
bootstrap(X: ndarray, return_indices: bool = False, y=None, test_ratio: float | None = None)[source]
Generate indices to split data into training and test set.
○ X (2D array-like of shape (n_timepoints, n_features)) – The endogenous time series to bootstrap. Dimension 0 is assumed to be the time dimension, ordered
○ return_indices (bool, default=False) – If True, a second output is retured, integer locations of index references for the bootstrap sample, in reference to original indices. Indexed
values do are not necessarily identical with bootstrapped values.
○ y (array-like of shape (n_timepoints, n_features_exog), default=None) – Exogenous time series to use in bootstrapping.
○ test_ratio (float, default=0.0) – The ratio of test samples to total samples. If provided, test_ratio fraction the data (rounded up) is removed from the end before applying the
bootstrap logic.
○ X_boot_i (2D np.ndarray-like of shape (n_timepoints_boot_i, n_features)) – i-th bootstrapped sample of X.
○ indices_i (1D np.nparray of shape (n_timepoints_boot_i,) integer values,) – only returned if return_indices=True. Index references for the i-th bootstrapped sample of X. Indexed
values do are not necessarily identical with bootstrapped values.
get_n_bootstraps(X=None, y=None) int[source]
Returns the number of bootstrap instances produced by the bootstrap.
○ X (2D array-like of shape (n_timepoints, n_features)) – The endogenous time series to bootstrap. Dimension 0 is assumed to be the time dimension, ordered
○ y (array-like of shape (n_timepoints, n_features_exog), default=None) – Exogenous time series to use in bootstrapping.
Return type:
The number of bootstrap instances produced by the bootstrap. | {"url":"https://tsbootstrap.readthedocs.io/en/latest/base_bootstrap.html","timestamp":"2024-11-05T01:04:50Z","content_type":"text/html","content_length":"61899","record_id":"<urn:uuid:ba5350bd-dd85-49bd-b785-55804f7fdb2e>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00561.warc.gz"} |
tree of life superstring theory part 27
numbers up to 64 and the numbers related to 3,6 and 9 on the tree of life and 6 the universe and 5 the atoms and strings on the tree of life and 8 tree of life's make the 64 tetrahedron grid(E8 lie
group) the tetragrammaton is the leters of god and is the isotropic vector matrix which is 1,2,3 and 4 each leter has a mathematical number atached to it the numbers are 10,15,21 and 26 they all add
up to 72 and 2(tetragrammaton)=144=(64 tetrahedron grid(E8 lie group)) 10 yods (spheres) that are joined by pathways of creation which is the tree of life the yods are connected to a crown yod by a
root and in the crown yod god goes to infinity(9xen) so (tree of life)=9 yods and (8 tree of life's)=(64 tetrahedron grid) 72=9 144=9 | {"url":"https://www.64tge8st.com/post/2017/01/28/tree-of-life-superstring-theory-6","timestamp":"2024-11-01T19:12:38Z","content_type":"text/html","content_length":"1050486","record_id":"<urn:uuid:dbe61163-6d01-4002-a6f5-919379b15f39>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00342.warc.gz"} |
The Magic Cafe Forums - Tuc quarter and expanded [ So many possibilities
chasesummers20 I just received my expanded[ from todds commercial site. It fits perfectly over my tuc. This nest is pretty fun to play with. I wonder who can come up with the coolest routines.
Here is a little trick.
New user
Kansas City Effect:He Shows three coins in his left palm. The magician openly takes one coin out and visually places in his pocket and shows right hand empty. He then waves his right hand
57 Posts over the coins and there are 3 again. He then openly takes another quarter out without closing his left fist and openly places it in his pocket. He then shows his right hand
empty again. He takes the remaining coins in his left hand and transfers now 3 to his right palm. Again there are 3 coins remaining. He takes one quarter out one last time, this
time closing his fist and asks the spectator "how many coins do I have in my hand. They reply. He says no there are none. All the coins are gone now and you end clean.
If you feel comfortable posting any simple ideas for this nested set then do so below. This will be fun.
Since the TUC is magnetic I can be Idled like a Hooker.
The combination of a Exp [ and Idled coin is called Birch Stack with dozens of effects published including an incredible Close-up Misers.
The additional features of the TUC allow for easy additions to these effects. The effect can also allow for a TUC to be Switched In for a borrowed quarter.
Eternal Order
old things in new example right off the top ...
ways - new things
in old ways Borrow a quarter. Toss it back and forth between your hands to "heat it up" and show empty. Split the coin in two, one tossed to the left hand.
10020 Posts Show both hands with coin on palm and close fists. Wiggle little fingers and open hands - both now in right hand.
Toss one back to spectator. Split that one in two and repeat - now both in left hand. Take one and visibly drop in pocket.
Split again and repeat. Spectator guesses which hand they will be in. Hussah! Take one and toss in the air to vanish.
Take the other one in the fingertips and rub. Both hand now empty.
New user
Kansas City Funsway I knew you would be the first to reply to this. I know you are really clever with the TUC.
57 Posts
The Magic Cafe Forum Index » » Trick coin trickery » » Tuc quarter and expanded [ So many possibilities (0 Likes) | {"url":"https://www.themagiccafe.com/forums/viewtopic.php?topic=576466#2","timestamp":"2024-11-06T09:34:38Z","content_type":"application/xhtml+xml","content_length":"12135","record_id":"<urn:uuid:5c7f4f32-710a-4c64-bf87-a9b93cd3ef2e>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00597.warc.gz"} |
free online calculator and trigonometry
free online calculator and trigonometry Related topics: calculus 102 - lecture 12
prentice-hall pre algebra.com
change this radical to an algebraic expression with fractional exponents.
rational expressions for idiots
kids math free tutorial
quadratic factoring system
simplifying radicals using the ti-89 titanium
quick tips algebra
free exponents games for kids
simplyfing integers
Author Message
Danen Flad Posted: Sunday 13th of Aug 09:39
Does anyone here know anything concerning free online calculator and trigonometry? I’m a little puzzled and I don’t know how to finish my algebra homework about this topic. I tried
reading all tutorials about it that could help me figure things out but I still don’t get . I’m having a hard time understanding it especially the topics absolute values, leading
coefficient and distance of points. It will take me days to answer my math homework if I can’t get any assistance. It would really help me if someone would recommend anything that can
help me with my algebra homework.
From: Digital
Back to top
ameich Posted: Monday 14th of Aug 13:56
Hi! I guess I can give you ideas on how to solve your homework. But for that I need more details. Can you give details about what exactly is the free online calculator and trigonometry
homework that you have to solve. I am quite good at solving these kind of things. Plus I have this great software Algebrator that I downloaded from the internet which is soooo good at
solving algebra assignment. Give me the details and perhaps we can work something out...
From: Prague,
Back to top
Admilal`Leker Posted: Tuesday 15th of Aug 09:10
Thanks for the pointer. Algebrator is actually a life-saving math software. I was able to get answers to problems I had about algebraic signs, graphing inequalities and graphing lines.
You only need to type in a problem, click on Solve and you get the all the results you need. You can use it for any number of algebra things, like Pre Algebra, Intermediate algebra and
Basic Math. I think everyone should use Algebrator.
From: NW AR,
Back to top
NrNevets Posted: Tuesday 15th of Aug 16:28
Thank you, I will try the suggested software. I have never worked with any software before , I didn't even know that they exist. But it sure sounds amazing ! Where did you find the
software ? I want to get it as soon as possible , so I have time to get ready for the test .
From: NJ
Back to top
caxee Posted: Wednesday 16th of Aug 18:05
Sure, here it is: https://softmath.com/links-to-algebra.html. Good Luck with your exams. Oh, and before I forget , this company is also offering unrestricted money back guarantee, that
just goes to show how sure they are about their product. I’m sure that you’ll love it . Cheers.
From: Boston,
MA, US
Back to top | {"url":"https://www.softmath.com/algebra-software-4/free-online-calculator-and.html","timestamp":"2024-11-09T23:40:38Z","content_type":"text/html","content_length":"41451","record_id":"<urn:uuid:d7685a2c-cb17-49d7-a8ea-5cc964696460>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00239.warc.gz"} |
Random variable
In probability theory, a branch of mathematics, a random variable is, as its name suggests, a "variable" that can take on random values. More formally, it is not actually a variable, but a function
whose argument takes on a particular value according to some probability measure (a measure that takes on the value 1 over the largest set on which it is defined).
Formal definition
Let ${\displaystyle (\Omega ,{\mathcal {F}},P)}$ be an arbitrary probability space and ${\displaystyle (\Omega ',{\mathcal {F}}')}$ an arbitrary measurable space. Then a random variable is any
measurable function X mapping ${\displaystyle (\Omega ,{\mathcal {F}})}$ to ${\displaystyle (\Omega ',{\mathcal {F}}')}$.
The reason a random variable has been defined in this way is that it captures the idea that events corresponding to the random variable taking on certain values can always be assigned probabilities.
For example, suppose that the event E of interest is the a random variable X taking on a value in the set ${\displaystyle A\in {\mathcal {F}}'}$. This event can be expressed as ${\displaystyle E=\{\
omega \in \Omega \mid X(\omega )\in A\}}$. By the measurability of X as a random variable it follows that ${\displaystyle E\in {\mathcal {F}}}$, hence E can be assigned a probability (i.e., ${\
displaystyle P(E)}$). If X is not measurable then it cannot be ascertained that E will belong to ${\displaystyle {\mathcal {F}}}$, hence it may not be assignable a probability via P.
An easy example
Consider the probability space ${\displaystyle (\mathbb {R} ,{\mathcal {B}}(\mathbb {R} ),P)}$ where ${\displaystyle {\mathcal {B}}(\mathbb {R} )}$ is the sigma algebra of Borel subsets of ${\
displaystyle \mathbb {R} }$ and P is a probability measure on ${\displaystyle \mathbb {R} }$ (hence P is a measure with ${\displaystyle P(\mathbb {R} )=1}$). Then the identity map ${\displaystyle I:
(\mathbb {R} ,{\mathcal {B}}(\mathbb {R} ))\rightarrow (\mathbb {R} ,{\mathcal {B}}(\mathbb {R} ))}$ defined by ${\displaystyle I(x)=x}$ is trivially a measurable function, hence is a random
1. P. Billingsley, Probability and Measure (2 ed.), ser. Wiley Series in Probability and Mathematical Statistics, Wiley, 1986.
2. D. Williams, Probability with Martingales, Cambridge : Cambridge University Press, 1991.
External links | {"url":"https://en.citizendium.org/wiki/Random_variable","timestamp":"2024-11-07T14:04:33Z","content_type":"text/html","content_length":"49622","record_id":"<urn:uuid:26b9735d-f3be-41c1-9168-7eb7b38c846b>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00666.warc.gz"} |
100NM MANUAL MOTOR
$159.50 $199.90
Item # 9071100 100 NM Manual/Motor Rated Torque : 100 Newton Meters Rated Speed (RPM) : 11 Maximum No. of Turns : 22 Length : 638mm Rated Current : 2.94 Amp In summary, Newton law of motion states
that Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity reduced by several factors, such as material dimensions (height and thickness of slats),
friction of material in the track, length and height of curtain, installation techniques and accessories (end retention slat locks). The lifting capacity chart below is based on the Newton’s Law of
motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above. This chart is provided as an indicator of the amount of weight each motor can lift. The
actual capacity depends on the amount of external factors deviate from the theoretical environment. Also included below is a lifting capacity charts which includes a 30% safety factor. This shows the
effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current : 2.20 Amp
100Nm RADIO + MANUAL O/R MOTOR
$198.00 $247.50
Item # 9073100 100Nm Radio Manual Override In summary, Newton law of motion states that Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity
reduced by several factors, such as material dimensions (height and thickness of slats), friction of material in the track, length and height of curtain, installation techniques and accessories (end
retention slat locks). The lifting capacity chart below is based on the Newton’s Law of motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above.
This chart is provided as an indicator of the amount of weight each motor can lift. The actual capacity depends on the amount of external factors deviate from the theoretical environment. Also
included below is a lifting capacity charts which includes a 30% safety factor. This shows the effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current :
2.20 Amp
100Nm RADIO MOTOR
$154.00 $192.50
Item # 9072100100Nm Radio Motor Rated Torque : 100 Newton Meters Rated Speed (RPM) : 11 Maximum No. of Turns : 22 Length : 768mm Rated Current : 2.94 Amp In summary, Newton law of motion states that
Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity reduced by several factors, such as material dimensions (height and thickness of slats),
friction of material in the track, length and height of curtain, installation techniques and accessories (end retention slat locks). The lifting capacity chart below is based on the Newton’s Law of
motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above. This chart is provided as an indicator of the amount of weight each motor can lift. The
actual capacity depends on the amount of external factors deviate from the theoretical environment. Also included below is a lifting capacity charts which includes a 30% safety factor. This shows the
effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current : 2.20 Amp
100Nm STANDARD MOTOR
$139.70 $175.50
Item # 9070100100Nm straight Motor 4 wires In summary, Newton law of motion states that Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity
reduced by several factors, such as material dimensions (height and thickness of slats), friction of material in the track, length and height of curtain, installation techniques and accessories (end
retention slat locks). The lifting capacity chart below is based on the Newton’s Law of motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above.
This chart is provided as an indicator of the amount of weight each motor can lift. The actual capacity depends on the amount of external factors deviate from the theoretical environment. Also
included below is a lifting capacity charts which includes a 30% safety factor. This shows the effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current :
2.20 Amp
300Nm MANUAL MOTOR
$369.60 $462.00
Item # 9071300300Nm Manual Motor Rated Torque : 300 Newton Meters Rated Speed (RPM) : 11 Maximum No. of Turns : 30 Length : 593mm Rated Current : 8.17 Amp In summary, Newton law of motion states that
Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity reduced by several factors, such as material dimensions (height and thickness of slats),
friction of material in the track, length and height of curtain, installation techniques and accessories (end retention slat locks). The lifting capacity chart below is based on the Newton’s Law of
motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above. This chart is provided as an indicator of the amount of weight each motor can lift. The
actual capacity depends on the amount of external factors deviate from the theoretical environment. Also included below is a lifting capacity charts which includes a 30% safety factor. This shows the
effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current : 2.20 Amp
300Nm STANDARD MOTOR
$363.00 $453.75
Item # 9070300300Nm Standard Motor Rated Torque : 300 Newton Meters Rated Speed (RPM) : 11 Maximum No. of Turns : 30 Length : 593mm Rated Current : 8.17 Amp In summary, Newton law of motion states
that Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity reduced by several factors, such as material dimensions (height and thickness of slats),
friction of material in the track, length and height of curtain, installation techniques and accessories (end retention slat locks). The lifting capacity chart below is based on the Newton’s Law of
motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above. This chart is provided as an indicator of the amount of weight each motor can lift. The
actual capacity depends on the amount of external factors deviate from the theoretical environment. Also included below is a lifting capacity charts which includes a 30% safety factor. This shows the
effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current : 2.20 Amp
50Nm MANUAL O/R MOTOR
$110.00 $137.50
50 Nm Manual/Motor Rated Torque : 50 Newton Meters Rated Speed (RPM) : 13 Maximum No. of Turns : 22 Length : 618mm Rated Current : 2.20 Amp In summary, Newton law of motion states that Torque equal
to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity reduced by several factors, such as material dimensions (height and thickness of slats), friction of
material in the track, length and height of curtain, installation techniques and accessories (end retention slat locks). The lifting capacity chart below is based on the Newton’s Law of motions and
includes as 25% reduction of the theoretical capacity to compensate for the factor described above. This chart is provided as an indicator of the amount of weight each motor can lift. The actual
capacity depends on the amount of external factors deviate from the theoretical environment. Also included below is a lifting capacity charts which includes a 30% safety factor. This shows the
effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current : 2.20 Amp
50Nm RADIO MOTOR
$132.00 $165.00
Item # 907025050Nm Radio Motor Rated Torque : 50 Newton Meters Rated Speed (RPM) : 13 Maximum No. of Turns : 22 Length : 697mm Rated Current : 2.20 Amp Recommended Lifting Weight Capacity Chart The
lifting capacity of all motors is based on Newton’s Law of Motion. In summary, Newton law of motion states that Torque equal to the radius of Motors Tube times the weight being lifted. The
theoretical lifting capacity reduced by several factors, such as material dimensions (height and thickness of slats), friction of material in the track, length and height of curtain, installation
techniques and accessories (end retention slat locks). The lifting capacity chart below is based on the Newton’s Law of motions and includes as 25% reduction of the theoretical capacity to compensate
for the factor described above. This chart is provided as an indicator of the amount of weight each motor can lift. The actual capacity depends on the amount of external factors deviate from the
theoretical environment. Also included below is a lifting capacity charts which includes a 30% safety factor. This shows the effects when externals factors are greater than the assumption of 25%.
50Nm STANDARD MOTOR
$95.70 $119.00
Item # 9070050 50Nm Standard/ Straight Rated Torque : 50 Newton Meters Rated Speed (RPM) : 13 Maximum No. of Turns : 22 The lifting capacity of all motors is based on Newton’s Law of Motion. In
summary, Newton law of motion states that Torque equal to the radius of Motors Tube times the weight being lifted. The theoretical lifting capacity reduced by several factors, such as material
dimensions (height and thickness of slats), friction of material in the track, length and height of curtain, installation techniques and accessories (end retention slat locks). The lifting capacity
chart below is based on the Newton’s Law of motions and includes as 25% reduction of the theoretical capacity to compensate for the factor described above. This chart is provided as an indicator of
the amount of weight each motor can lift. The actual capacity depends on the amount of external factors deviate from the theoretical environment. Also included below is a lifting capacity charts
which includes a 30% safety factor. This shows the effects when externals factors are greater than the assumption of 25%. Length : 557mm Rated Current : 2.20 Amp | {"url":"https://fittingsplus.com/collections/motors","timestamp":"2024-11-05T03:14:20Z","content_type":"text/html","content_length":"611597","record_id":"<urn:uuid:422b5952-18ff-4f19-a9f4-65a918bb0936>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00402.warc.gz"} |
No power: exponential expressions are not processed automatically as such
Little is known about the mental representation of exponential expressions. The present study examined the automatic processing of exponential expressions under the framework of multi-digit numbers,
specifically asking which component of the expression (i.e., the base/power) is more salient during this type of processing. In a series of three experiments, participants performed a physical size
comparison task. They were presented with pairs of exponential expressions that appeared in frames that differed in their physical sizes. Participants were instructed to ignore the stimuli within the
frames and choose the larger frame. In all experiments, the pairs of exponential expressions varied in the numerical values of their base and/or power component. We manipulated the compatibility
between the base and the power components, as well as their physical sizes to create a standard versus nonstandard syntax of exponential expressions. Experiments 1 and 3 demonstrate that the
physically larger component drives the size congruity effect, which is typically the base but was manipulated here in some cases to be the power. Moreover, Experiments 2 and 3 revealed similar
patterns, even when manipulating the compatibility between base and power components. Our findings support componential processing of exponents by demonstrating that participants were drawn to the
physically larger component, even though in exponential expressions, the power, which is physically smaller, has the greater mathematical contribution. Thus, revealing that the syntactic structure of
an exponential expression is not processed automatically. We discuss these results with regard to multi-digit numbers research.
أدرس بدقة موضوعات البحث “No power: exponential expressions are not processed automatically as such'. فهما يشكلان معًا بصمة فريدة. | {"url":"https://cris.ariel.ac.il/ar/publications/no-power-exponential-expressions-are-not-processed-automatically--3","timestamp":"2024-11-14T14:59:50Z","content_type":"text/html","content_length":"59444","record_id":"<urn:uuid:36de7f8a-705e-46e9-b385-1bc36d932e11>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00310.warc.gz"} |
OpenFst Examples
Reading the
quick tour
first is recommended. That includes a simple
of FST application using either the C++ template level or the shell-level operations. The
advanced usage
topic contains an
using the template-free intermediate
scripting level
as well. The following data files are used in the examples below:
│ File │ Description │ Source │
│wotw.txt │(normalized) text of H.G. Well's War of the Worlds │public domain │
│wotw.lm.gz │5-gram language model for wotw.txt in OpenFst text format│www.opengrm.org │
│wotw.syms │FST symbol table file for wotw.lm │www.opengrm.org │
│ascii.syms │FST symbol table file for ASCII letters │Python: for i in range(33,127): print "%c %d\n" % (i,i) │
│lexicon.txt.gz │letter-to-token FST for wotw.syms │see first example below │
│lexicon_opt.txt.gz│optimized letter-to-token FST for wotw.syms │see first example below │
│downcase.txt │ASCII letter-to-downcased letter FST │awk 'NR>1 { print 0,0,$1,tolower($1) } ; END { print 0 }' <ascii.syms >downcase.txt│
With these files and the descriptions below, the reader should be able to repeat the examples. With about 340,000 words in
The War of the Worlds
, it is a small corpus that allows non-trivial examples. A few general comments about the examples:
1. For the most part, we illustrate with the shell-level commands for convenience.
2. The fstcompose operation is used often here. Typically, one or both of the input FSTs should be appropriately sorted before composition. In the examples below, however, we have only illustrated
sorting where it is necessary, to keep the presentation shorter. The provided data files are pre-sorted for their intended use. (See Exercise 4 for more details.)
3. Files with a .fst extension should be produced from their text description by a call to fstcompile. This is illustrated at the beginning, but is often implicit throughout the rest of this
The first example converts a sequence of ASCII characters into a sequence of word tokens with punctuation and whitespace stripped. To do so we will need a
transducer that maps from letters to their corresponding word tokens. A simple way to generate this is using the
OpenFst text format
. For example, the word
would have the form:
$ fstcompile --isymbols=ascii.syms --osymbols=wotw.syms >Mars.fst <<EOF
0 1 M Mars
1 2 a <epsilon>
2 3 r <epsilon>
3 4 s <epsilon>
This can be drawn with:
$ fstdraw --isymbols=ascii.syms --osymbols=wotw.syms -portrait Mars.fst | dot -Tjpg >Mars.jpg
which produces: Suppose that
have similarly been created, then:
$ fstunion man.fst Mars.fst | fstunion - Martian.fst | fstclosure >lexicon.fst
produces a finite-state lexicon that transduces zero or more spelled-out word sequences into their word tokens: The non-determinism and non-minimality introduced by the construction can be removed
$ fstrmepsilon lexicon.fst | fstdeterminize | fstminimize >lexicon_opt.fst
resulting in the equvialent, deterministic and minimal: In order to handle punctuation symbols, we change the lexicon construction to:
$ fstunion man.fst Mars.fst | fstunion - Martian.fst | fstconcat - punct.fst | fstclosure >lexicon.fst
$ fstcompile --isymbols=ascii.syms --osymbols=wotw.syms >punct.fst <<EOF
0 1 <space> <epsilon>
0 1 . <epsilon>
0 1 , <epsilon>
0 1 ? <epsilon>
0 1 ! <epsilon>
is a transducer that deletes common punctuation symbols. The full punctuation transducer is
. Now, the tokenizaton of the example string
Mars man
encoded as an FST: can be done with:
$ fstcompose Marsman.fst lexicon_opt.fst | fstproject --project_output | fstrmepsilon >tokens.fst
giving: Note that our construction of
requires that all tokens be separated by
one whitespace character, including at the end of the string (hence the '!' in the previous example). To generate a full lexicon of all 7102 distinct words in the
War of Worlds
, it is convenient to dispense with the union of individual word FSTs above and instead generate a single text FST from the word symbols in
is a python script that does that and was used, along with the above steps, to generate the
full optimized lexicon
(which you should compile to
Exercise 1
The above tokenization does not handle numeric character input. (a) Create a transducer that maps numbers in the range 0 - 999999 represented as digit strings to their English read form, e.g.:
1 -> one
11 -> eleven
111 -> one hundred eleven
1111 -> one thousand one hundred eleven
11111 -> eleven thousand one hundred eleven
(b) Incorporate this transduction into the letter-to-token transduction above and apply to the input
Mars is 4225 miles across.
represented as letters.
Downcasing Text
The next example converts case-sensitive input to all lowercase output. To do the conversion, we create a
transducer of the form:
$ fstcompile --isymbols=ascii.syms --osymbols=ascii.syms >downcase.fst <<EOF
0 0 ! !
0 0 A a
0 0 B b
0 0 a a
0 0 b b
which produces: A downcasing flower transducer for the full character set is
. This transducer can be applied to the
Mars men
automaton from the previous example with:
$ fstproject Marsman.fst | fstcompose - full_downcase.fst | fstproject --project_output >marsman.fst
giving: Why use transducers for this when UNIX commands like
and C library routines like
are some of the many easy ways to downcase text? Transducers have several advantages over these approaches. First, more complex transformations are almost as easy to write (see Example 2). Second,
trying to invert this transduction is less trivial and can be quite useful (see the next section). Finally, this transducer operates on any finite-state input not just a string. For example,
$ fstinvert lexicon_opt.fst | fstcompose - full_downcase.fst | fstinvert >lexicon_opt_downcase.fst
downcases the letters in the lexicon from the previous example. A transducer that downcases at the token level (but see Exercise 3a) can be created with:
$ fstinvert lexicon_opt.fst | fstcompose - full_downcase.fst | fstcompose - lexicon_opt.fst |
fstrmepsilon | fstdeterminize | fstminimize >downcase_token.fst
Exercise 2
Create a transducer that: (a) upcases letters that are string-initial or after a punctuation symbol/space (
capitalization transducer
). (b) converts lowercase underscore-separated identifiers such as
to the form
CamelCase transducer
Exercise 3
(a) The letter-level downcasing transducer downcases any ASCII input. For which inputs does the token-level downcasing transducer work? What changes would be necessary to cover all inputs from
? (b) If a token
were applied to
, what would the output look like? What would it look like if the optimizations (epsilon-removal, determinization and minimization) were omitted from the construction of
Exercise 4
Create a 1,000,000 ASCII character string represented as an FST. Compose it on the left with
and time the computation. Compose it on the right and time the computation. The labels in
were pre-sorted on one side; use
to determine which side. Use
to sort
on the opposite side and repeat the experiments above. Given that
matching uses binary search on the sorted side (with the higher out-degree, if both sides are sorted), explain the differences in computation time that you observe.
Case Restoration in Text
This example creates a transducer that attempts to restore the case of downcased input. This is the first non-trivial example and, in general, there is no error-free way to do this. The approach
taken here will be to use case statistics gathered from the
The War of the Worlds
source text to help solve this. In particular, we will use an
n-gram language model
created on this text that is represented as a finite-state automaton in
format, which you should compile to the file
. Here is a typical path in this 5-gram automaton:
$ fstrandgen --select=log_prob wotw.lm.fst | fstprint --isymbols=wotw.syms --osymbols=wotw.syms
0 1 The The
1 2 desolating desolating
2 3 cry cry
3 4 <epsilon> <epsilon>
4 5 worked worked
5 6 <epsilon> <epsilon>
6 7 upon upon
7 8 my my
8 9 mind mind
9 10 <epsilon> <epsilon>
10 11 once once
11 12 <epsilon> <epsilon>
12 13 <epsilon> <epsilon>
13 14 I I
14 15 <epsilon> <epsilon>
15 16 <epsilon> <epsilon>
16 17 slept slept
17 18 <epsilon> <epsilon>
18 19 little little
This model is constructed to have a transition for every 1-gram to 5-gram seen in 'War of the Worlds' with its weight related to the (negative log) probability of that n-gram occurring in the text
corpus. The epsilon transitions correspond to backoff transitions in the smoothing of the model that was performed to allow accepting input sequences not seen in training. Given this language model
and using the lexicon and downcasing transducers from the previous examples, a solution is:
# Before trying this, read the whole section.
$ fstcompose lexicon_opt.fst wotw.lm.fst | fstarcsort --sort_type=ilabel >wotw.fst
$ fstinvert full_downcase.fst | fstcompose - wotw.fst >case_restore.fst
The first FST,
, maps from letters to tokens following the probability distribution of the language model. The second FST,
is similar but uses only downcased letters. Case prediction can then be performed with:
$ fstcompose marsman.fst case_restore.fst | fstshortestpath |
fstproject --project_output | fstrmepsilon | fsttopsort >prediction.fst
which gives: In other words, the most likely case of the input is determinized with respect to the n-gram model. There is a serious problem, however, with the above solution. For all but tiny
corpora, the first composition is extremely expensive with the classical
algorithm since the output labels in
have been pushed back when it was determinized and this greatly delays matching with the labels in
. There are three possible solutions: First, we can use the input to restrict the composition chain as:
$ fstcompose full_downcase.fst marsman.fst | fstinvert | fstcompose - lexicon_opt.fst |
fstcompose - wotw.lm.fst | fstshortestpath | fstproject -project_output | fstrmepsilon | fsttopsort >prediction.fst
This works fine but has the disadvantage that we don't have a single transducer to apply and we are depending on the input being a string or otherwise small. A second solution, which gives a single
optimized transducer, is to replace transducer determinization and minimization of
with automata determinization and minimization (via
the input and output label pairs into a single new label) followed by the transducer determinization and minimization of the result of the composition with
$ fstencode --encode_labels lexicon.fst enc.dat | fstdeterminize | fstminimize |
fstencode --decode - enc.dat >lexicon_compact.fst
$ fstcompose lexicon_compact.fst wotw.lm.fst | fstdeterminize | fstminimize | fstarcsort --sort_type=ilabel >wotw.fst
$ fstinvert full_downcase.fst | fstcompose - wotw.fst >case_restore.fst
This solution is a natural and simple one but has the disadvantage that the transducer determinization and minimization steps are quite expensive. A final solution is to use an FST representation
that allows
lookahead matching
, which composition can exploit to avoid the matching delays:
# Converts to a lookahead lexicon
$ fstconvert --fst_type=olabel_lookahead --save_relabel_opairs=relabel.pairs lexicon_opt.fst >lexicon_lookahead.fst
$ fstrelabel --relabel_ipairs=relabel.pairs wotw.lm.fst | fstarcsort --sort_type=ilabel >wotw_relabel.lm
# Relabels the language model input (required by lookahead implementation)
$ fstcompose lexicon_lookahead.fst wotw_relabel.lm >wotw.fst
$ fstinvert full_downcase.fst | fstcompose - wotw.fst >case_restore.fst
The relabeling of the input labels of the language model is a by-product of how the lookahead matching works. Note in order to use the lookahead FST formats you must use
in the library configuration and you must set your
(or equivalent)
Exercise 5
(a) Find the weight of the
token sequence in the prediction example above. (b) Find the weight of the
token sequence in the prediction example above
using the
flag (hint: use
). (c) Find all paths within weight 10 of the shortest path in prediction example.
Exercise 6
(a) The case restoration above can only work for words that are found in the
text corpus
. Describe an alternative that gives a plausible result on any letter sequence. (b) Punctuation can give clues to the case of nearby words (e.g.
i was in cambridge, ma. before. it was nice.
). Describe a method to exploit this information in case restoration.
Exercise 7
Create a transducer that converts the digits 0-9 into their possible telephone keypad alphabetic equivalents (e.g., 2: a,b,c; 3: d,e,f) and allows for spaces as well. Use this transducer to convert
the sentence
no one would have believed in the last years of the nineteenth century that this world was being watched keenly and closely
into digits and spaces. Use the lexicon alone to disambiguate this digit and space sequence (cf.
phone input). Now use both the lexicon and the language model to disambiguate it.
Edit Distance
Since the predictions made in the previous example might not always be correct, we may want to measure the error when we have the correct
answers as well. One common error measure is computed by aligning the hypothesis and reference, defining:
edit distance = # of substitutions + # of deletions + # of insertions
and then defining
error rate = edit distance / # of reference symbols
If this is computed on letters, it is called the
letter error rate
; on words, it is called the
word error rate
. Suppose the reference and (unweighted) hypothesis are represented as finite-state automata
respectively. Then:
$ fstcompose ref.fst edit.fst | fstcompose - hyp.fst |
# Returns shortest distance from final states to the initial (first) state
$ fstshortestdistance --reverse | head -1
computes the edit distance between the reference and hypothesis according to the edit transducer
. The edit transducer for two letters
is the flower automaton: This counts any substitution (
a:b, b:a
), insertion (
<epsilon>:a, <epsilon>:b
), or deletion as (
a:<epsilon>:a, b:<epsilon>
) as 1 edit and matches (
a:a, b:b
) as zero edits. For word error rate, we use the
edit distance, i.e. where the cost of substitutions, insertions, and deletions are all the same. However, each pairing of a symbol (or epsilon) with another symbol can be given a separate cost in a
more general edit distance. This can obviously be implemented by choosing different weights for the corresponding edit transducer transitions. Even more general edit distances can be defined (see
Exercise 8). Note that if the hypothesis is not a string but a more general automaton representing a set of hypotheses (e.g. the result from Exercise 5c) then this procedure returns the
oracle edit distance
, i.e., the edit distance of the best-matching ('oracle-provided') hypothesis compared to the reference. The corresponding
oracle error rate
is a measure of the quality of the hypothesis set (often called a 'lattice'). There is one serious problem with this approach and that is when the symbol set is large. For the 95 letter
, the Levenstein edit transducer will have 9215 transitions. For the 7101 word
, there would need to be 50,438,403 transitions. While this is still manageable, larger vocabularies of 100,000 and more words are unwieldy. For the Levenstein distance, there is a simple solution:
factor the edit transducer into two components. Using the example above, the left factor,
, is: and the right factor,
, is: These transducers include new symbols
, and
that are used for the substitution, deletion and insertion of other symbols respectively. In fact, the composition of these two transducers is equivalent to the original edit transducer
. However, each of these transducers has
4 |V|
transitions where
is the number of distinct symbols, whereas the original edit transducer has
transitions. Given these factors, compute:
$ fstcompose ref.fst edit1.fst | fstarcsort >ref_edit.fst
$ fstcompose edit2.fst hyp.fst | fstarcsort >hyp_edit.fst
$ fstcompose ref_edit.fst hyp_edit.fst | fstshortestdistance --reverse | head -1
With large inputs, the shortest distance algorithm may need to use inadmissable
. This is because the edit transducer allows arbitrary insertions and deletions, so the search space is quadratic in the length of the input. Alternatively the edit transducer could be changed (see
Exercise 8b). With more general edit transducers, this factoring may not be possible. In that case, representing the edit transducer in some specialized compact FST representation would be possible
but pairwise compositions might be very expensive. A three-way composition algorithm or specialized composition
are approaches that could implement this more efficiently. As an example, we can see to what extent the case restoration transducer errs on a given input by computing the edit distance between the
output it yields and the reference answer. We will use the Levenshtein distance. First, generate
. These should be structured like the example above, but should provide transitions for each symbol of
not just 'a' and 'b'. You will need to create
which contains the definitions of
plus new definitions for "<ins>", "<del>" and "<sub>". Then, prepare the transducers
as above from
, and compile them (
would have
as input symbols and
as output symbols, and vice versa for
). Create a transducer
representing a correctly capitalized English sentence using words from the corpus and with adequate whitespace. You might want to use words which appear both capitalized and uncapitalized in the
source text to have a chance to observe a non-zero edit distance. A suitable (nonsensical) example is the following: "The nice chief astronomer says that both the terraces of the south tower and the
western mills in the East use the English Channel as a supply pool " You can now downcase
(with the
transducer presented above), apply
to it and get the hypothesis output for this input (as was explained in the section about case restoration). Compose that with the reversed tokenizer to get the hypothesis represented as a sequence
of characters not tokens. This is
, which should be a FST representing a string along the lines of "The Nice chief Astronomer says that both the terraces of the south Tower and the western Mills in the east use the English channel as
a Supply Pool ". Now, you can compute the edit distance as in the example above. For the given
, the edit distance should be 8. You can also show the alignment (which, in the present case, will only include substitutions):
$ fstcompose ref.fst edit1.fst | fstarcsort >ref_edit.fst
$ fstcompose edit2.fst hyp.fst | fstarcsort >hyp_edit.fst
$ fstcompose ref_edit.fst hyp_edit.fst | fstshortestpath | fstrmepsilon | fsttopsort |
fstprint --isymbols=levenshtein.syms --osymbols=levenshtein.syms
Here is the output (with some added color to make it easier to read):
0 1 T T
1 2 h h
2 3 e e
3 4 <space> <space>
4 5 n N 1
5 6 i i
6 7 c c
7 8 e e
8 9 <space> <space>
9 10 c c
10 11 h h
11 12 i i
12 13 e e
13 14 f f
14 15 <space> <space>
15 16 a A 1
16 17 s s
17 18 t t
18 19 r r
19 20 o o
20 21 n n
21 22 o o
22 23 m m
23 24 e e
24 25 r r
25 26 <space> <space>
26 27 s s
27 28 a a
28 29 y y
29 30 s s
30 31 <space> <space>
31 32 t t
32 33 h h
33 34 a a
34 35 t t
35 36 <space> <space>
36 37 b b
37 38 o o
38 39 t t
39 40 h h
40 41 <space> <space>
41 42 t t
42 43 h h
43 44 e e
44 45 <space> <space>
45 46 t t
46 47 e e
47 48 r r
48 49 r r
49 50 a a
50 51 c c
51 52 e e
52 53 s s
53 54 <space> <space>
54 55 o o
55 56 f f
56 57 <space> <space>
57 58 t t
58 59 h h
59 60 e e
60 61 <space> <space>
61 62 s s
62 63 o o
63 64 u u
64 65 t t
65 66 h h
66 67 <space> <space>
67 68 t T 1
68 69 o o
69 70 w w
70 71 e e
71 72 r r
72 73 <space> <space>
73 74 a a
74 75 n n
75 76 d d
76 77 <space> <space>
77 78 t t
78 79 h h
79 80 e e
80 81 <space> <space>
81 82 w w
82 83 e e
83 84 s s
84 85 t t
85 86 e e
86 87 r r
87 88 n n
88 89 <space> <space>
89 90 m M 1
90 91 i i
91 92 l l
92 93 l l
93 94 s s
94 95 <space> <space>
95 96 i i
96 97 n n
97 98 <space> <space>
98 99 t t
99 100 h h
100 101 e e
101 102 <space> <space>
102 103 E e 1
103 104 a a
104 105 s s
105 106 t t
106 107 <space> <space>
107 108 u u
108 109 s s
109 110 e e
110 111 <space> <space>
111 112 t t
112 113 h h
113 114 e e
114 115 <space> <space>
115 116 E E
116 117 n n
117 118 g g
118 119 l l
119 120 i i
120 121 s s
121 122 h h
122 123 <space> <space>
123 124 C c 1
124 125 h h
125 126 a a
126 127 n n
127 128 n n
128 129 e e
129 130 l l
130 131 <space> <space>
131 132 a a
132 133 s s
133 134 <space> <space>
134 135 a a
135 136 <space> <space>
136 137 s S 1
137 138 u u
138 139 p p
139 140 p p
140 141 l l
141 142 y y
142 143 <space> <space>
143 144 p P 1
144 145 o o
145 146 o o
146 147 l l
147 148 <space> <space>
Exercise 8
Create an edit transducer that: (a) allows only a fixed number N of contiguous insertions or deletions. (b) computes the Levenshtein distance between American and English spellings of words except
common spelling variants
are given lower cost.
Exercise 9
Provide a way to: (a) compute the error rate rather than the edit distance using transducers. (b) compute the oracle error path as well as the oracle rate for a lattice. | {"url":"https://www.openfst.org/twiki/bin/view/FST/FstExamples","timestamp":"2024-11-08T09:39:25Z","content_type":"application/xhtml+xml","content_length":"88951","record_id":"<urn:uuid:fc283ec8-aadc-4c7c-b8fb-09bb6abed979>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00428.warc.gz"} |
Download Continuum and solid mechanics : concepts and applications by Victor Quinn, Andrew Stubblefield PDF
By Victor Quinn, Andrew Stubblefield
This publication bargains with options and functions of Continuum and stable Mechanics
Read or Download Continuum and solid mechanics : concepts and applications PDF
Best mechanics books
Mechanics of Hydraulic Fracturing (2nd Edition)
Revised to incorporate present elements thought of for today’s unconventional and multi-fracture grids, Mechanics of Hydraulic Fracturing, moment version explains essentially the most vital positive
factors for fracture layout — the facility to foretell the geometry and features of the hydraulically brought about fracture.
Partial differential equations of mathematical physics
Harry Bateman (1882-1946) was once an esteemed mathematician quite recognized for his paintings on distinct features and partial differential equations. This booklet, first released in 1932, has been
reprinted repeatedly and is a vintage instance of Bateman's paintings. Partial Differential Equations of Mathematical Physics used to be constructed mainly with the purpose of acquiring designated
analytical expressions for the answer of the boundary difficulties of mathematical physics.
Relocating so much on Ice Plates is a special research into the influence of automobiles and airplane traveling throughout floating ice sheets. It synthesizes in one quantity, with a coherent subject
and nomenclature, the various literature at the subject, hitherto on hand basically as examine magazine articles. Chapters at the nature of unpolluted water ice and sea ice, and on utilized continuum
mechanics are incorporated, as is a bankruptcy at the subject's venerable background in similar components of engineering and technology.
This quantity constitutes the court cases of a satellite tv for pc symposium of the XXXth congress of the foreign Union of Physiological Sciences. The symposium has been held In Banff, Alberta Canada
July Sept. 11 1986. this system used to be prepared to supply a selective review of present advancements in cardiac biophysics, biochemistry, and body structure.
Additional resources for Continuum and solid mechanics : concepts and applications
Sample text
4): where A is a rotation matrix with components aij. 4 Transformation of the stress tensor Expanding the matrix operation, and simplifying some terms by taking advantage of the symmetry of the
stress tensor, gives The Mohr circle for stress is a graphical representation of this transformation of stresses. Normal and shear stresses The magnitude of the normal stress component σn of any
stress vector T(n) acting on an arbitrary plane with normal vector n at a given point, in terms of the components σij of the stress tensor σ, is the dot product of the stress vector and the normal
vector: The magnitude of the shear stress component τn, acting in the plane spanned by the two vectors T(n) and n, can then be found using the Pythagorean theorem: where Equilibrium equations and
symmetry of the stress tensor Figure 4.
The 11-component of stress on that interface is the sum of all pairwise forces between atoms on the two sides.... Stress modeling (Cauchy) In general, stress is not uniformly distributed over the
cross-section of a material body, and consequently the stress at a point in a given region is different from the average stress over the entire area. 1). According to Cauchy, the stress at any point
in an object, assumed to behave as a continuum, is completely defined by the nine components of a second-order tensor of type (0,2) known as the Cauchy stress tensor, : The Cauchy stress tensor obeys
the tensor transformation law under a change in the system of coordinates.
Not imaginary due to the symmetry of the stress tensor. The three roots , , and are the eigenvalues or principal stresses, and they are the roots of the Cayley–Hamilton theorem. The principal
stresses are unique for a given stress tensor. Therefore, from the characteristic equation it is seen that the coefficients , and , called the first, second, and third stress invariants,
respectively, have always the same value regardless of the orientation of the coordinate system chosen. For each eigenvalue, there is a non-trivial solution for in the equation .
Rated of 5 – based on votes | {"url":"http://blog.reino.co.jp/index.php/ebooks/continuum-and-solid-mechanics-concepts-and-applications","timestamp":"2024-11-05T07:40:24Z","content_type":"text/html","content_length":"38606","record_id":"<urn:uuid:a6ac6bc2-e72b-4533-8125-57a9346656f3>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00364.warc.gz"} |
30 Top SAS STAT Interview Questions - Prepare Yourself - DataFlair
30 Top SAS STAT Interview Questions – Prepare Yourself
Job-ready Online Courses: Click for Success - Start Now!
SAS-STAT Interview Questions
We saw a comprehensive understanding of what is SAS STAT, it’s procedures, how to create programs and different operations associated with it. Now we will cover some of the important and most
frequently asked “SAS-STAT Interview Questions”. These SAS-STAT Interview Questions and Answers help both fresher/beginners and experienced/professionals.
So, let’s begin Best SAS-STAT Interview Questions and Answers.
Mostly Asked SAS-STAT Interview Questions
Here, we will help freshers & experience professionals to face SAS interview with these simple SAS-STAT interview questions with answers.
Q1. What is SAS STAT?
SAS/STAT is one of the many products presented by using the SAS gadget that’s fully incorporated and that gives large statistical competencies that meet the desires of a whole corporation.
SAS/STAT software affords tools and processes for statistical modeling of records, as an example, analysis of variance, linear regression, predictive modeling, statistical visualization strategies
and lots greater. The software program meets the analytical needs of both specialized and organization-huge issues.
Q2. What are the features of SAS STAT?
SAS STAT is the quality platform that you can choose. for the reason that it is loaded with many benefits, you may enjoy capabilities along with:
Let’s explore more SAS/STAT Features in detail
Q3. What are the advantages of using SAS STAT?
• You may observe the modern-day statistical strategies. With every new update, SAS STAT brings its users a ramification of recent manner to fulfill marketplace requirements.
• The dimensions and type of facts isn’t always a barrier.
• SAS/ STAT software has graphs like field plots, scatter plots, bar charts and all are customizable to assist users in the better analysis.
• You can take advantage of SAS technical aid and internet consumer groups.
• Use tested and verified methods in statistics.
• Expansive library of equipped-to-use statistical procedures.
• Fantastically interpretable statistical output.
• Comprehensive documentation and training.
• Go-platform guide and scalability.
• Simplify with a single surrounding.
Q4. What are the uses of SAS\STAT?
SAS\STAT software affords tools for an extensive kind of packages in commercial enterprise, authorities, and academia. foremost uses of SAS are a financial evaluation, forecasting, economic and
financial modeling, time series analysis, economic reporting, and manipulation of time collection facts.
Q5. What is ANOVA?
Analysis of Variance (ANOVA) in SAS Programming Language is used for evaluating way of various organizations. However, it based on a concept of “resources of Variance”. It has three variances –
standard variance, variance because of organizations, and variance inside agencies.
Q6. What are the procedures offered in SAS STAT for performing ANOVA?
• PROC ANOVA
• PROC CATMOD
• PROC GLM
• PROC INBREED
• PROC LATTICE
• PROC NESTED
• PROC PLAN
• PROC TTEST
Read more about SAS/STAT ANOVA in detail
Q7. What are the two required statements while using PROC CATMOD?
The PROC CATMOD and MODEL statements are required.
Q8. What is the PROC GLM procedure in SAS/STAT and what is its syntax?
The PROC GLM suits linear models the usage of the approach of least squares. SAS PROC GLM handles models through touching on one or numerous continuous established variables to one or numerous
independent variables. It has statistical methods like regression, evaluation of variance, evaluation of covariance, multivariate evaluation of variance, and partial correlation.
PROC GLM dataset;
CLASS variables;
MODEL ;
Q9. Which procedure in SAS STAT can be used for analysis of variance on random effects for data?
PROC NESTED can be used for this type of data. The PROC NESTED procedure in SAS/STAT performs analysis of variance on random outcomes for data from an experiment that has a nested (hierarchical)
shape. SAS PROC NESTED is suitable for models with only class effects, it does no longer deal with fashions that include continuous covariates.
Q10. What is Bayesian analysis?
SAS/ STAT Bayesian Evaluation is a statistical technique that helps us in answering research questions on unknown parameters the usage of chance statements.
SAS-STAT Interview Questions For Beginners. Q- 1,2,3,4,5,9,10
SAS-STAT Interview Questions For Professional. Q- 6,7,8
Q11. What are the procedures offered in SAS STAT for performing the Bayesian analysis?
• PROC BCHOICE
• PROC FMM
• PROC GENMOD
• PROC MCMC
• PROC PHREG
• PROC LIFEREG
Let’s discuss the concept of SAS/STAT Bayesian Analysis Procedures in detail
Q12. How can we fit statistical models in SAS STAT?
The PROC FMM system in SAS/STAT software suits statistical models to statistics for which the distribution of the response is a finite combination of distributions—that is, each reaction is drawn
with an unknown opportunity from certainly one of several distributions.
Q13. What does the OUTPOST= option in the GENMOD procedure do?
The outpost = option saves samples (posterior) to the POST dataset for post-processing.
Q14. What is the syntax for the PROC MCMC procedure?
PROC MCMC dataset;
PARMS <list of parameters>;
PRIOR <type of distribution of each parameter>;
MODEL <variable used as likelihood>;
Q15. What is the PROC LOGISTIC procedure used for in SAS STAT and what are the required statements in it?
The PROC LOGISTIC process in SAS/STAT plays a logistic regression of statistics. The LOGISTIC technique suits linear logistic regression models by way of the method of maximum probability.
The PROC LOGISTIC and model statements are required statements.
Q16. Explain the use of each statement in the below syntax.
PROC PROBIT dataset;
CLASS <dependent variables>;
Model< dependent variables>= <independent VARIABLES>;
The DATA= option specifies the dataset that will be studied.
The PLOTS= choice within the PROC PROBIT statement, collectively with the ODS graphics announcement, requests all plots (due to the fact all has been specified in brackets, we will pick out a
selected plot also) for the anticipated opportunity values and peak ranges.
The model statement prepares a response between a structured variable and impartial variables. The variables top and weight are the stimuli or explanatory variables.
The new dataset is created by OUTPUT statement. For example, ABC, that contains all the variables of the original data set, and a new variable, PROB that represents possibilities.
Q17. What are the different plot options that can be specified with the PLOT= option in the PROC PROBIT procedure?
The different plot options that can be specified with PLOTS= option are-
• CDFPLOT
• IPPPLOT
• PREDPLOT
• LPREDPLOT
• ALL
• NONE
Q18. What is a cluster and what is a cluster analysis?
Cluster analysis is a discovery device that reveals institutions, styles, relationships, and structures in hundreds of facts. in this, cases, data, or gadgets (activities, humans, matters, and so
on.) are sub-divided into organizations (clusters) such that the gadgets in a cluster are very comparable (but now not identical) to one another and really distinct from the items in different
Q19.What are the different procedures offered by SAS STAT for cluster analysis?
• PROC ACECLUS
• PROC TREE
• PROC MODECLUS
• PROC CLUSTER
• PROC DISTANCE
• PROC FASTCLUS
• PROC VARCLUS
Read SAS/STAT Cluster Analysis in detail
Q20. What is the difference between the PROC ACECLUS and PROC CLUSTER procedures?
PROC ACECLUS outputs a fact set containing canonical variable scores to be used in the SAS/STAT cluster analysis while A PROC CLUSTER shows a history of the clustering technique, displaying
information beneficial for estimating the number of clusters in the population from which the data are sampled.
SAS-STAT Interview Questions For Beginners. Q- 12,15,17,18,20
SAS-STAT Interview Questions For Professional. Q- 11,13,14,16,19
Q21. What does the PROC DISTANCE in SAS STAT do?
The PROC DISTANCE process in SAS/STAT is used to degree exclusive measures of distance, dissimilarity, or similarity among the rows (observations) of an enter SAS information set, that could contain
numeric or person variables, or each.
Q22. What do the POPULATION and REFERENCE statement in the PROC STDRATE procedure signify?
The PROC STDRATE declaration within the STDRATE manner calls the procedure, names the statistics sets specifies the standardization approach, and identifies the statistic for standardization.
the specified populace assertion specifies the price or risk information in observe populations, and the REFERENCE announcement specifies the rate or danger facts in the reference populace.
Q23. What is the Kernel Density Estimation technique?
The kernel density estimation method is a way used for density estimation in which a regarded density feature, referred to as a kernel, is averaged throughout the records to create an approximation.
Q24. What is the use of the UNIVAR and BIVAR statement inside the PROC KDE procedure?
The UNIVAR statement inside the PROC KDE procedure performs a univariate kernel density estimates and further, the BIVAR statement computes bivariate kernel density estimate.
Q25. What is group sequential design and analysis?
The organization sequential layout affords unique specs for a collection sequential trial. similarly to the standard specifications, it gives the overall variety of tiers (the quantity of period
in-between ranges plus a very last degree) and a preventing criterion to reject, accept, or either reject or receive the null hypothesis at each period in-between stage. It also affords vital values
and the sample size at each level of the trial.
Q26. What are the procedures for group sequential design and analysis?
PROC SEQDESIGN and PROC SEQTEST are the two procedures.
Q27. What are the steps involved in group sequential trial?
• Specify the statistical info of the design
• Compute the boundary values
• Gather additional information
• Evaluate the take a look at statistic with the corresponding boundary values.
Click here, to know more about SAS/STAT Group Sequential Design and Analysis
Q28. What is longitudinal data?
Longitudinal data arises when you measure a reaction variable of hobby multiple numbers of instances on more than one subjects. for that reason, longitudinal data has the traits of each
cross-sectional facts and time-series statistics.
Q29. What are the two approaches for modeling longitudinal data?
they’re marginal models (additionally called populace-common models) and blended fashions (additionally referred to as situation-specific models).
Let’s Explore SAS/STAT Longitudinal Data Analysis Procedures
Q30. What is the syntax for the PROC GEE procedure and also mention required statements?
CLASS <variable>;
MODEL response= effects <options>;
REPEATED subject=subject effects/<options>;
The PROC GEE, MODEL, and REPEATED statements are required.
SAS-STAT Interview Questions For Beginners. Q- 21,22,24,25,26,27,28,29
SAS-STAT Interview Questions For Professional. Q- 23,30
So, this all about SAS-STAT Interview Questions and Answers. Hope you like our explanation.
Hence, we have studied the detailed list of latest SAS-STAT Interview Questions and the best possible answers. Thus, we really hope these SAS-STAT Interview Questions will help you to understand the
nature of SAS/STAT. Although, if you want to ask any query regarding SAS-STAT Interview Questions, feel free to ask in the comment section.
Your opinion matters
Please write your valuable feedback about DataFlair on Google
Leave a Reply Cancel reply | {"url":"https://data-flair.training/blogs/stat-interview-questions/","timestamp":"2024-11-05T00:24:43Z","content_type":"text/html","content_length":"270262","record_id":"<urn:uuid:98bc2261-1d4f-417c-bdb7-e0b9f2109a1c>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00609.warc.gz"} |
How Deloitte Italy built a digital payments fraud detection solution using quantum machine learning and Amazon Braket
As digital commerce expands, fraud detection has become critical in protecting businesses and consumers engaging in online transactions. Implementing machine learning (ML) algorithms enables
real-time analysis of high-volume transactional data to rapidly identify fraudulent activity. This advanced capability helps mitigate financial risks and safeguard customer privacy within expanding
digital markets.
Deloitte is a strategic global systems integrator with over 19,000 certified AWS practitioners across the globe. It continues to raise the bar through participation in the AWS Competency Program with
29 competencies, including Machine Learning.
This post demonstrates the potential for quantum computing algorithms paired with ML models to revolutionize fraud detection within digital payment platforms. We share how Deloitte built a hybrid
quantum neural network solution with Amazon Braket to demonstrate the possible gains coming from this emerging technology.
The promise of quantum computing
Quantum computers harbor the potential to radically overhaul financial systems, enabling much faster and more precise solutions. Compared to classical computers, quantum computers are expected in the
long run to have to advantages in the areas of simulation, optimization, and ML. Whether quantum computers can provide a meaningful speedup to ML is an active topic of research.
Quantum computing can perform efficient near real-time simulations in critical areas such as pricing and risk management. Optimization models are key activities in financial institutions, aimed at
determining the best investment strategy for a portfolio of assets, allocating capital, or achieving productivity improvements. Some of these optimization problems are nearly impossible for
traditional computers to tackle, so approximations are used to solve the problems in a reasonable amount of time. Quantum computers could perform faster and more accurate optimizations without using
any approximations.
Despite the long-term horizon, the potentially disruptive nature of this technology means that financial institutions are looking to get an early foothold in this technology by building in-house
quantum research teams, expanding their existing ML COEs to include quantum computing, or engaging with partners such as Deloitte.
At this early stage, customers seek access to a choice of different quantum hardware and simulation capabilities in order to run experiments and build expertise. Braket is a fully managed quantum
computing service that lets you explore quantum computing. It provides access to quantum hardware from IonQ, OQC, Quera, Rigetti, IQM, a variety of local and on-demand simulators including
GPU-enabled simulations, and infrastructure for running hybrid quantum-classical algorithms such as quantum ML. Braket is fully integrated with AWS services such as Amazon Simple Storage Service
(Amazon S3) for data storage and AWS Identity and Access Management (IAM) for identity management, and customers only pay for what you use.
In this post, we demonstrate how to implement a quantum neural network-based fraud detection solution using Braket and AWS native services. Although quantum computers can’t be used in production
today, our solution provides a workflow that will seamlessly adapt and function as a plug-and-play system in the future, when commercially viable quantum devices become available.
Solution overview
The goal of this post is to explore the potential of quantum ML and present a conceptual workflow that could serve as a plug-and-play system when the technology matures. Quantum ML is still in its
early stages, and this post aims to showcase the art of the possible without delving into specific security considerations. As quantum ML technology advances and becomes ready for production
deployments, robust security measures will be essential. However, for now, the focus is on outlining a high-level conceptual architecture that can seamlessly adapt and function in the future when the
technology is ready.
The following diagram shows the solution architecture for the implementation of a neural network-based fraud detection solution using AWS services. The solution is implemented using a hybrid quantum
neural network. The neural network is built using the Keras library; the quantum component is implemented using PennyLane.
The workflow includes the following key components for inference (A–F) and training (G–I):
1. Ingestion – Real-time financial transactions are ingested through Amazon Kinesis Data Streams
2. Preprocessing – AWS Glue streaming extract, transform, and load (ETL) jobs consume the stream to do preprocessing and light transforms
3. Storage – Amazon S3 is used to store output artifacts
4. Endpoint deployment – We use an Amazon SageMaker endpoint to deploy the models
5. Analysis – Transactions along with the model inferences are stored in Amazon Redshift
6. Data visualization – Amazon QuickSight is used to visualize the results of fraud detection
7. Training data – Amazon S3 is used to store the training data
8. Modeling – A Braket environment produces a model for inference
9. Governance – Amazon CloudWatch, IAM, and AWS CloudTrail are used for observability, governance, and auditability, respectively
For training the model, we used open source data available on Kaggle. The dataset contains transactions made by credit cards in September 2013 by European cardholders. This dataset records
transactions that occurred over a span of 2 days, during which there were 492 instances of fraud detected out of a total of 284,807 transactions. The dataset exhibits a significant class imbalance,
with fraudulent transactions accounting for just 0.172% of the entire dataset. Because the data is highly imbalanced, various measures have been taken during data preparation and model development.
The dataset exclusively comprises numerical input variables, which have undergone a Principal Component Analysis (PCA) transformation because of confidentiality reasons.
The data only includes numerical input features (PCA-transformed due to confidentiality) and three key fields:
• Time – Time between each transaction and first transaction
• Amount – Transaction amount
• Class – Target variable, 1 for fraud or 0 for non-fraud
Data preparation
We split the data into training, validation, and test sets, and we define the target and the features sets, where Class is the target variable:
The Class field assumes values 0 and 1. To make the neural network deal with data imbalance, we perform a label encoding on the y sets:
The encoding applies to all the values the mapping: 0 to [1,0], and 1 to [0,1].
Finally, we apply scaling that standardizes the features by removing the mean and scaling to unit variance:
The functions LabelEncoder and StandardScaler are available in the scikit-learn Python library.
After all the transformations are applied, the dataset is ready to be the input of the neural network.
Neural network architecture
We composed the neural network architecture with the following layers based on several tests empirically:
• A first dense layer with 32 nodes
• A second dense layer with 9 nodes
• A quantum layer as neural network output
• Dropout layers with rate equals to 0.3
We apply an L2 regularization on the first layer and both L1 and L2 regularization on the second one, to avoid overfitting. We initialize all the kernels using the he_normal function. The dropout
layers are meant to reduce overfitting as well.
Quantum circuit
The first step to obtain the layer is to build the quantum circuit (or the quantum node). To accomplish this task, we used the Python library PennyLane.
PennyLane is an open source library that seamlessly integrates quantum computing with ML. It allows you to create and train quantum-classical hybrid models, where quantum circuits act as layers
within classical neural networks. By harnessing the power of quantum mechanics and merging it with classical ML frameworks like PyTorch, TensorFlow, and Keras, PennyLane empowers you to explore the
exciting frontier of quantum ML. You can unlock new realms of possibility and push the boundaries of what’s achievable with this cutting-edge technology.
The design of the circuit is the most important part of the overall solution. The predictive power of the model depends entirely on how the circuit is built.
Qubits, the fundamental units of information in quantum computing, are entities that behave quite differently from classical bits. Unlike classical bits that can only represent 0 or 1, qubits can
exist in a superposition of both states simultaneously, enabling quantum parallelism and faster calculations for certain problems.
We decide to use only three qubits, a small number but sufficient for our case.
We instantiate the qubits as follows:
‘default.qubit’ is the PennyLane qubits simulator. To access qubits on a real quantum computer, you can replace the second line with the following code:
device_ARN could be the ARN of the devices supported by Braket (for a list of supported devices, refer to Amazon Braket supported devices).
We defined the quantum node as follows:
The inputs are the values yielded as output from the previous layer of the neural network, and the weights are the actual weights of the quantum circuit.
RY and Rot are rotation functions performed on qubits; CNOT is a controlled bitflip gate allowing us to embed the qubits.
qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(2)) are the measurements applied respectively to the qubits 0 and the qubits 1, and these values will be the neural network output.
Diagrammatically, the circuit can be displayed as:
The transformations applied to qubit 0 are fewer than the transformations applied to qbit 2. This choice is because we want to separate the states of the qubits in order to obtain different values
when the measures are performed. Applying different transformations to qubits allows them to enter distinct states, resulting in varied outcomes when measurements are performed. This phenomenon stems
from the principles of superposition and entanglement inherent in quantum mechanics.
After we define the quantum circuit, we define the quantum hybrid neural network:
KerasLayer is the PennyLane function that turns the quantum circuit into a Keras layer.
Model training
After we have preprocessed the data and defined the model, it’s time to train the network.
A preliminary step is needed in order to deal with the unbalanced dataset. We define a weight for each class according to the inverse root rule:
The weights are given by the inverse of the root of occurrences for each of the two possible target values.
We compile the model next:
custom_metric is a modified version of the metric precision, which is a custom subroutine to postprocess the quantum data into a form compatible with the optimizer.
For evaluating model performance on imbalanced data, precision is a more reliable metric than accuracy, so we optimize for precision. Also, in fraud detection, incorrectly predicting a fraudulent
transaction as valid (false negative) can have serious financial consequences and risks. Precision evaluates the proportion of fraud alerts that are true positives, minimizing costly false negatives.
Finally, we fit the model:
At each epoch, the weights of both the classic and quantum layer are updated in order to reach higher accuracy. At the end of the training, the network showed a loss of 0.0353 on the training set and
0.0119 on the validation set. When the fit is complete, the trained model is saved in .h5 format.
Model results and analysis
Evaluating the model is vital to gauge its capabilities and limitations, providing insights into the predictive quality and value derived from the quantum techniques.
To test the model, we make predictions on the test set:
Because the neural network is a regression model, it yields for each record of x_test a 2-D array, where each component can assume values between 0 and 1. Because we’re essentially dealing with a
binary classification problem, the outputs should be as follows:
• [1,0] – No fraud
• [0,1] – Fraud
To convert the continuous values into binary classification, a threshold is necessary. Predictions that are equal to or above the threshold are assigned 1, and those below the threshold are assigned
To align with our goal of optimizing precision, we chose the threshold value that results in the highest precision.
The following table summarizes the mapping between various threshold values and the precision.
│Class │Threshold = 0.65│Threshold = 0.70│Threshold = 0.75│
│No Fraud│1.00 │1.00 │1.00 │
│Fraud │0.87 │0.89 │0.92 │
The model demonstrates almost flawless performance on the predominant non-fraud class, with precision and recall scores close to a perfect 1. Despite far less data, the model achieves precision of
0.87 for detecting the minority fraud class at a 0.65 threshold, underscoring performance even on sparse data. To efficiently identify fraud while minimizing incorrect fraud reports, we decide to
prioritize precision over recall.
We also wanted to compare this model with a classic neural network only model to see if we are exploiting the gains coming from the quantum application. We built and trained an identical model in
which the quantum layer is replaced by the following:
In the last epoch, the loss was 0.0119 and the validation loss was 0.0051.
The following table summarizes the mapping between various threshold values and the precision for the classic neural network model.
│Class │Threshold=0.65│Threshold = 0.70 │Threshold = 0.75 │
│No Fraud│1.0 │1.00 │1.00 │
│Fraud │0.83 │0.84 │0. 86 │
Like the quantum hybrid model, the model performance is almost perfect for the majority class and very good for the minority class.
The hybrid neural network has 1,296 parameters, whereas the classic one has 1,329. When comparing precision values, we can observe how the quantum solution provides better results. The hybrid model,
inheriting the properties of high-dimensional spaces exploration and a non-linearity from the quantum layer, is able to generalize the problem better using fewer parameters, resulting in better
Challenges of a quantum solution
Although the adoption of quantum technology shows promise in providing organizations numerous benefits, practical implementation on large-scale, fault-tolerant quantum computers is a complex task and
is an active area of research. Therefore, we should be mindful of the challenges that it poses:
• Sensitivity to noise – Quantum computers are extremely sensitive to external factors (such as atmospheric temperature) and require more attention and maintenance than traditional computers, and
this can drift over time. One way to minimize the effects of drift is by taking advantage of parametric compilation—the ability to compile a parametric circuit such as the one used here only one
time, and feed it fresh parameters at runtime, avoiding repeated compilation steps. Braket automatically does this for you.
• Dimensional complexity – The inherent nature of qubits, the fundamental units of quantum computing, introduces a higher level of intricacy compared to traditional binary bits employed in
conventional computers. By harnessing the principles of superposition and entanglement, qubits possess an elevated degree of complexity in their design. This intricate architecture renders the
evaluation of computational capacity a formidable challenge, because the multidimensional aspects of qubits demand a more nuanced approach to assessing their computational prowess.
• Computational errors – Increased calculation errors are intrinsic to quantum computing’s probabilistic nature during the sampling phase. These errors could impact accuracy and reliability of the
results obtained through quantum sampling. Techniques such as error mitigation and error suppression are actively being developed in order to minimize the effects of errors resulting from noisy
qubits. To learn more about error mitigation, see Enabling state-of-the-art quantum algorithms with Qedma’s error mitigation and IonQ, using Braket Direct.
The results discussed in this post suggest that quantum computing holds substantial promise for fraud detection in the financial services industry. The hybrid quantum neural network demonstrated
superior performance in accurately identifying fraudulent transactions, highlighting the potential gains offered by quantum technology. As quantum computing continues to advance, its role in
revolutionizing fraud detection and other critical financial processes will become increasingly evident. You can extend the results of the simulation by using real qubits and testing various outcomes
on real hardware available on Braket, such as those from IQM, IonQ, and Rigetti, all on demand, with pay-as-you-go pricing and no upfront commitments.
To prepare for the future of quantum computing, organizations must stay informed on the latest advancements in quantum technology. Adopting quantum-ready cloud solutions now is a strategic priority,
allowing a smooth transition to quantum when hardware reaches commercial viability. This forward-thinking approach will provide both a technological edge and rapid adaptation to quantum computing’s
transformative potential across industries. With an integrated cloud strategy, businesses can proactively get quantum-ready, primed to capitalize on quantum capabilities at the right moment. To
accelerate your learning journey and earn a digital badge in quantum computing fundamentals, see Introducing the Amazon Braket Learning Plan and Digital Badge.
Connect with Deloitte to pilot this solution for your enterprise on AWS.
About the authors
Federica Marini is a Manager in Deloitte Italy AI & Data practice with a strong experience as a business advisor and technical expert in the field of AI, Gen AI, ML and Data. She addresses research
and customer business needs with tailored data-driven solutions providing meaningful results. She is passionate about innovation and believes digital disruption will require a human centered approach
to achieve full potential.
Matteo Capozi is a Data and AI expert in Deloitte Italy, specializing in the design and implementation of advanced AI and GenAI models and quantum computing solutions. With a strong background on
cutting-edge technologies, Matteo excels in helping organizations harness the power of AI to drive innovation and solve complex problems. His expertise spans across industries, where he collaborates
closely with executive stakeholders to achieve strategic goals and performance improvements.
Kasi Muthu is a senior partner solutions architect focusing on generative AI and data at AWS based out of Dallas, TX. He is passionate about helping partners and customers accelerate their cloud
journey. He is a trusted advisor in this field and has plenty of experience architecting and building scalable, resilient, and performant workloads in the cloud. Outside of work, he enjoys spending
time with his family.
Kuldeep Singh is a Principal Global AI/ML leader at AWS with over 20 years in tech. He skillfully combines his sales and entrepreneurship expertise with a deep understanding of AI, ML, and
cybersecurity. He excels in forging strategic global partnerships, driving transformative solutions and strategies across various industries with a focus on generative AI and GSIs.
Leave a Comment | {"url":"https://www.meishulabs.com/index.php/2024/07/18/how-deloitte-italy-built-a-digital-payments-fraud-detection-solution-using-quantum-machine-learning-and-amazon-braket/","timestamp":"2024-11-09T04:12:53Z","content_type":"text/html","content_length":"172658","record_id":"<urn:uuid:d793bbff-1a2c-49f8-b507-9109b53e7362>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00504.warc.gz"} |
Labs WMT ROMSLIte SettlingRates
Introduction to Regional Ocean Modeling - Settling Rates and Critical Shear Stress
This lab has been designed and developed by Courtney Harris, Julia Moriarty, and Danielle Tarpley, Virginia Institute of Marine Sciences, Gloucester Point, VA
with assistance of Irina Overeem, CSDMS, University of Colorado, CO
Classroom organization
This is the second lab in a mini series to introduce a Web-Based version of the Regional Ocean Modeling System (ROMS) for inexperienced users. ROMS is a three-dimensional hydrodynamic ocean model
(see Haidvogel et al. 2008; myroms.org). ROMS solves the conservation of mass and three-dimensional momentum equations and includes transport equations for temperature and salinity. The version
implemented here also accounts for suspended sediment transport and deposition, following Warner et al. (2008). Here we present a basic configuration of ROMS in the framework of the Web Modeling Tool
(WMT). This series of labs is designed for inexperienced modelers to gain some experience with running a numerical model, changing model inputs, and analyzing model output. The example provided looks
at the influence of a river plume on the hydrodynamics and sediment transport within an idealized continental shelf.
This lab focuses on sediment settling rates and critical shear stress for motion. Basic theory on settling rates and suspended sediment is presented in these slides File:ROMS Lite Introduction.pptx.
This lab will likely take ~ 3hours to complete in the classroom.
If you have never used the Web Modeling Tool, learn how to use it here. The WMT allows you to set up simulations, but once you are ready to run them, you will need an account on the CSDMS
supercomputer to successfully submit and run your job. More information on getting an account can be found here HPCC Access. Note that getting permission for access takes a few days after your
Learning objectives
• familiarize with a basic configuration of the Regional Ocean Modeling System
• learn how to manipulate parameters in ROMS-Lite and set up different experiments
• physics of settling rates
• bed shear stress and threshold to incipient motion
• Rouse number
• influence of settling velocity and critical shear stress on fluvial deposition
Lab Notes
>> Open a new browser window and open the Web Modeling Tool here and select the ROMS project
>> This WMT project is unique in that there is only a single driver, ROMS-Lite. It is a pre-compiled instance of the larger ROMS system specially configured to the river plume case for teaching use.
For this lab, you will need to visualize in Matlab, you can download a library here File:Riverplume mfiles.tar.gz.
The numerical experiment has been designed to use idealized inputs and a configuration considered representative for a medium-sized river draining into the coastal ocean. This ROMS model
implementation represents sediment using three separate sources: two classes are used to represent sediment discharged by the river, and the third class represents sediment from the seabed. Each
sediment class has fixed attributes of grain diameter, density, settling velocity, critical shear stress for erosion, and the erodibility constant. The user can modify the settling velocity, critical
shear stress for erosion, and erodibility constant from the WMT GUI interface.
Sediment suspended in the water column is transported, like other conservative tracers (e.g., salinity) by solving the advection–diffusion equation with a source/sink term for vertical settling and
erosion. The ROMS model represents sediment using separate cohesive and non-cohesive categories, in this ROMS-Lite model there are 3 non-cohesive sediment classes. Each class has fixed attributes of
grain diameter, density. For the duration of the model run the settling velocity, critical shear stress for erosion, and erodibility are constant. These properties are used to help determine the bulk
properties of each bed layer.
Settling Velocity
The settling velocity, fall velocity, or terminal velocity of a sediment particle is defined as the rate the sediment particle settles in still fluid. The settling velocity equals the velocity at the
point when the weight of the sediment particle is balanced by frictional drag with the fluid. It is diagnostic of grain size, but is also sensitive to the shape (roundness and sphericity) and density
of the grain as well as to the viscosity and density of the fluid. It integrates all of these into a key transport parameter. In general, larger, more dense particles have higher settling velocities.
Specification of settling velocity for fine-grained particles (muds, clays, fine silts) is especially difficult because these tend to flocculate and form large, less dense, groups of particles. The
settling velocities of these will be larger than individual disaggregated grains in the water column; and the settling velocities of these aggregates vary over several orders of magnitude (e.g. Hill
and McCave, 2001).
The base case assigned settling velocities to the two sediment types delivered by the river as 0.05 mm/s and 0.1 mm/s (these are size classes 0 and 1 in the WMT ROMS-LITE).
Look at the difference in sediment distribution for the two sediment types delivered by the river. Which of the two sediment types do you expect to travel further from the river mouth before settling to near the bed? Test your ideas by plotting the near-bed suspended sediment concentrations for each of these two size classes.
How do you expect the near-bed concentrations to change if you increase the settling velocities by a factor of 10? Change the settling velocities in the WMT for size classes 0 and 1, and resubmit the job. Then download the new results and plot the near bed concentrations.
Resuspension and Rouse Number
Sediment suspension depends on turbulent diffusion overpowering settling. The shear velocity of a flow provides a scale for the turbulent diffusion, and the shear velocity, u* , is defined as
u* = √(τb/ρ);
where τb is the bed shear stress, and ρ is the fluid density. For sediment to be suspended, the ratio of settling velocity over shear velocity must be low (less than about 1). This is often expressed
as the Rouse Number, defined as
P = ws/( κ u* )
where κ is von Karman’s constant (κ= 0.408). Sediment can be suspended when P < 2.5.
Calculate the Rouse Numbers for the sediment classes in the base case. To do this you will first need to find the bed shear stress from the model output file. ROMS stores the bed shear stress as a vector having components in both the x- and the y-directions, with the variable names for this implementation being τb,x = “bustrcwmax” and τb,y = “bvstrcwmax”. Pull the bed stress variables out of the netcdf output file, these will be two-dimensional in space, and time dependent. Calculate the magnitude of the stress vector at the last time step τb = √(τb,x2 + τb,y2). Where on the continental shelf is bed stress high?
Now: calculate the Rouse number for the two sediment size classes that are delivered by the river. Given the way that the Rouse numbers change with water depth, where on the continental shelf do you expect sediment to be most easily suspended?
Critical Shear Stress
Another important hydrodynamic property of sediment is its “critical shear stress”, τcr. This defines the threshold where the drag exerted by the fluid on the seabed moves sediment. Like settling
velocity, the critical shear stress depends on grain size, density, shape of the particle, among other factors. In general, larger more dense sediment particles have higher critical shear stresses.
Researchers generally use curves that are based on empirical data to estimate the critical shear stress of sediment; the curve below, based on Miller et al. (1977) relates the diameter of quartz
–density sediment grains to the critical shear velocity (u* in the figure), and critical shear stress (τo in the figure).
Critical shear velocity as a function of sediment size for quartz-density sediment
Based on the shear velocities calculated previously, and the Miller et al. (1977) plot, what sediment grain diameter could be mobilized for the base case at a water depth of 20 m?
The critical shear stresses assumed in the base case for the sediment delivered by the river was 0.04 Pa and 0.14 Pa. Compared to the bed shear stresses calculated above, at what water depths would the flows in the base case be sufficient to mobilize these sediments?
How do you expect sediment deposition to depend on critical shear stress for erosion? Decrease the critical shear stresses used in the base case for sediment types 0 and 1, and re-run the model. Plot the results for sediment deposition of each size class for the base case, and the reduced – critical shear stress models to test your ideas.
• Warner, Sherwood, Signell, Harris, and Arango, 2008 "Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model", Computers & Geosciences.
• Threshold of sediment motion under unidirectional currents, M. C. Miller, I. N. McCave, P. D. Komar, Sedimentology (1977) 24, 507-527.
• Hill, P.S., McCave, I.N., 2001. Suspended particle transport in benthic boundary layers. In: Boudreau, B.P., Jorgensen, B.B.(Eds.), The Benthic Boundary Layer. Oxford University Press, pp. | {"url":"https://csdms.colorado.edu/wiki/Labs_WMT_ROMSLIte_SettlingRates","timestamp":"2024-11-11T04:49:12Z","content_type":"text/html","content_length":"36898","record_id":"<urn:uuid:ba81b0c9-7726-4644-892e-c7b46b082076>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00774.warc.gz"} |
Why Sklearn’s Logistic Regression Has no Learning Rate Hyperparameter?
A common and fundamental way of training a logistic regression model, as taught in most lectures/blogs/tutorials, is using SGD.
Essentially, given an input $X$ and the model parameters $\theta$, the output probability ($\hat y$) is computed as follows:
Next, we compute the loss function ($J$), which is log-loss:
The final step is to update the parameters $\theta$ using gradient descent as follows:
As depicted above, the weight update depends on the learning rate hyperparameter ($\alpha$), which we specify before training the model.
We execute the above steps (summarized again below) over and over for some epochs or until the parameter converges:
• Step 1) Initialize model parameters $\theta$.
• Step 2) Compute output probability $\hat y$ for all samples.
• Step 3) Compute the loss function $J(\theta)$, which is log-loss.
• Step 4) Update the parameters $\theta$ using gradient descent.
• Repeat steps 2-4 until convergence.
Simple, isn't it?
I am sure this is the method that you must also be thoroughly aware of.
However, if that is true, why don’t we see a learning rate hyperparameter $(\alpha)$ in the sklearn logistic regression implementation:
As depicted above, there is no learning rate parameter in this documentation.
However, we see a max_iter parameter that intuitively looks analogous to the epochs.
But how does that make sense?
We have epochs but no learning rate $\alpha$, so how do we even update the parameters of our model, as we do in SGD below?
Are we missing something here?
As it turns out, we are indeed missing something here.
More specifically, there are a few more ways to train a logistic regression model, but most of us are only aware of the above SGD procedure, which depends on the learning rate.
But most of us never happen to consider them.
However, the importance of these alternate mechanisms is entirely reflected by the fact that even sklearn, one of the most popular libraries of data science and machine learning, DOES NOT use SGD in
its logistic regression implementation.
Thus, in this article, I want to share the overlooked details of logistic regression and introduce you to one more way of training this model, which does not depend on the learning rate
Let’s begin!
Before understanding the alternative training mechanism of training logistic regression, it is immensely crucial to know how we model data while using logistic regression.
In other words, let’s understand how we frame its modeling mathematically.
The blog ahead is a bit math-intensive. Yet, I have simplified it as much as possible. If you have any queries, feel free to comment and I'll help you out.
Essentially, whenever we model data using logistic regression, the model is instructed to maximize the likelihood of observing the given data $(X, y)$.
More formally, a model attempts to find a specific set of parameters $\theta$ (also called model weights), which maximizes the following function:
The above function $L$ is called the likelihood function, and in simple words, it says:
• maximize the likelihood of observing y
• given X
• when the prediction is parameterized by some parameters $\theta$ (also called weights)
When we begin modeling:
• We know $X$.
• We also know $y$.
• The only unknown is $\theta$, which we are trying to estimate.
Thus, the instructions given to the model are:
• Find the specific set of parameters $\theta$ that maximizes the likelihood of observing the data $(X, y)$.
This is commonly referred to as maximum likelihood estimation (MLE) in machine learning.
MLE is a method for estimating the parameters of a statistical model by maximizing the likelihood of the observed data.
MLE: Find the parameter values that maximize the likelihood of data
It is a common approach for parameter estimation in various models, including linear regression, logistic regression, and many others.
The key idea behind MLE is to find the parameter values that make the observed data most probable.
The steps are simple and straightforward:
1. Define the likelihood function for the entire dataset: Here, we typically assume that the observations are independent. Thus, the likelihood function for the entire dataset is the product of the
individual likelihoods. Also, the likelihood function is parameterized by a set of parameters $\theta$, which are trying to estimate.
2. Take the logarithm (the obtained function is called log-likelihood): To simplify calculations and avoid numerical issues, it is common to take the logarithm of the likelihood function.
3. Maximize the log-likelihood: Finally, the goal is to find the set of parameters $\theta$, which maximizes the log-likelihood function.
In fact, it’s the MLE that helps us derive the log-loss used in logistic regression.
Formulating logistic regression MLE
We all know that in logistic regression, the model outputs the probability that a sample belongs to a specific class.
Let’s call it $\hat y$.
Assuming that you have a total of N independent samples $(X, y) = \{(x_{1}, y_{1}), (x_{2}, y_{2}), \dots, (x_{N}, y_{N})\}$, the likelihood estimation can be written as:
Essentially, we assume that all samples are independent.
Thus, the likelihood of observing the entire data is the same as the product of the likelihood of observing individual points.
Next, we should determine these individual likelihoods $L(y_{i}|x_{i};\theta)$ as a function of the output probability of logistic regression $\hat y_i$:
Logistic regression output to likelihood function conversion
While training logistic regression, the model returns a continuous output $\hat y$, representing the probability that a sample belongs to a specific class.
In logistic regression, the “specific class” is the one we have assigned the label of $y_{i} = 1$.
In other words, it is important to understand that a logistic regression model, by its very nature, outputs the probability that a sample belongs to one of the two classes.
More specifically, it is the class with true label $y_{i} = 1$.
The output of the logistic regression model
The higher the output, the higher the probability that the sample has a true label $y_{i} = 1$.
Thus, we can say that when the true label $y_{i} = 1$, the likelihood of observing that data point is the output of logistic regression, i.e., $\hat y$.
But how do we determine the likelihood when the true label $y_{i} = 0$?
For simplicity, consider the illustration below:
Deriving the probability of the “Dog” class (Class 0) from the probability of the “Cat” class (Class 1)
Assume that the label “Cat” is denoted as “Class 1” and the label “Dog” is denoted by “Class 0”.
Class labels
Thus, all the logistic regression model outputs inherently denote the probability that an input is “Cat.”
But if we need the probability that the input is a “Dog,” we should take the complement of the output of the logistic regression model.
In other words, the likelihood when the true label $y_{i} = 0$ can be derived from the output of logistic regression $\hat y$.
Therefore, we get the following likelihood function for observing a specific data point $i$:
The likelihood of observing a sample with true label $y_{i} = 1$ is $\hat y_{i}$ (or the output of the model).
But the likelihood of observing a sample with true label $y_{i} = 0$ is $(1-\hat y_{i})$.
Final MLE step
We can dissolve the piecewise notation above to get the following:
Let’s plug the likelihood function of individual data points back into the likelihood estimation for all samples:
We can simplify the product to a summation by taking the logarithm on both sides.
In practice, maximizing the log-likelihood function is often more convenient than the likelihood function.
Since the logarithm is a monotonically increasing function, maximizing the log-likelihood is equivalent to maximizing the likelihood.
On further simplification, we get the following:
And to recall, $\hat y_i$ is the output probability by the logistic regression model:
The above derivation gave us the log-likelihood of the logistic regression model.
If we take negative (-) on both sides, it will give us the log loss, which can be conveniently minimized by gradient descent.
However, there is another way to manipulate the above log-likelihood formulation for more convenient optimization.
Let’s understand below.
Log-likelihood manipulation
Read the full article
Sign up now to read the full article and get access to all articles for paying subscribers only.
Join today!
RAG • 22 min read
A Crash Course on Building RAG Systems – Part 1 (With Implementations)
A practical and beginner-friendly crash course on building RAG apps (with implementations).
NLP • 24 min read
AugSBERT: Bi-encoders + Cross-encoders for Sentence Pair Similarity Scoring – Part 2
A deep dive into extensions of cross-encoders and bi-encoders for sentence pair similarity.
NLP • 20 min read
Bi-encoders and Cross-encoders for Sentence Pair Similarity Scoring – Part 1
A deep dive into why BERT isn't effective for sentence similarity and advancements that shaped this task forever. | {"url":"https://www.dailydoseofds.com/why-sklearns-logistic-regression-has-no-learning-rate-hyperparameter/","timestamp":"2024-11-03T06:51:10Z","content_type":"text/html","content_length":"92637","record_id":"<urn:uuid:0a3a549c-4e79-47ca-a95d-677c18709a27>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00656.warc.gz"} |
This is documentation for Orange 2.7. For the latest documentation, see Orange 3.
Classifier (orange.Classifier)
A classifier (either naive Bayesian classifier or logistic regression)
Nomogram is a simple and intuitive, yet useful and powerful representation of linear models, such as logistic regression and naive Bayesian classifier. In statistical terms, the nomogram plots log
odds ratios for each value of each attribute. We shall describe its basic properties here, though we recommend reading the paper in which we introduced the nomograms for naive Bayesian classifier,
Nomograms for Visualization of Naive Bayesian Classifier. This description will show the nomogram for a naive Bayesian classifier; nomograms for other types of classifiers are similar, though they
lack some functionality due to inherent limitations of these models.
The snapshot below shows a naive Bayesian nomogram for the heart disease data. The first attribute, gender, has two values, where log odds ratio for females is -1 (as read from the axis on the top)
and for males it is around 0.4. For the next attribute, the type of chest pain, the asymptotic pain votes for the target class (having narrowed vessels), and the other three have negative odds of
different magnitudes. Note that these are odds for naive Bayesian classifier, where, unlike in logistic regression, there is no “base value” which would have a odds ratio of zero.
The third attribute, SBP at rest, is continuous. To get log odds ratios for a particular value of the attribute, find the value (say 175) of the vertical axis to the left of the curve corresponding
to the attribute. Then imagine a line to the left, at the point where it hits the curve, turn upwards and read the number on the top scale. The SBP of 175 has log odds ration of approximately 1
(0.93, to be precise). The curve thus shows a mapping from attribute values on the left to log odds at the top.
Nomogram is a great data exploration tool. Lengths of the lines correspond to spans of odds ratios, suggesting importance of attributes. It also shows impacts of individual values; being female is
good and being male is bad (w.r.t. this disease, at least); besides, being female is much more beneficial than being male is harmful. Gender is, however, a much less important attribute than the
maximal heart rate (HR) with log odds from -3.5 to +2.2. SBP’s from 125 to 140 are equivalent, that is, have the same odds ratios...
Nomograms can also be used for making probabilistic prediction. A sum of log odds ratios for a male with asymptomatic chest pain, a rest SBP of 100, cholesterol 200 and maximal heart rate 175 is 0.38
+ 1.16 + -0.51 + -0.4 = -0.58, which corresponds to a probability 32 % for having the disease. To use the widget for classification, check Show predictions. The widget then shows a blue dots on
attribute axes, which can be dragged around - or left at the zero-line if the corresponding value is unknown. The axes at the bottom then show a mapping from the sum of log odds to probabilities.
Now for the settings. Option Target Class defines the target class, Attribute values to the right of the zero line represent arguments for that class and values to the left are arguments against it.
Log odds for naive Bayesian classifier are computed so that all values can have non-zero log odds. The nomogram is drawn as shown above, if alignment is set to Align by zero influence. If set to
Align left, all attribute axes are left-aligned. Logistic regression compares the base value with other attribute values, so the base value always has log odds ratio of 0, and the attribute axes are
always aligned to the left.
The influence of continuous attribute can be shown as two dimensional curves (2D curve) or with the values projected onto a single line (1D projection). The latter make the nomogram smaller, but can
be unreadable if the log odds are not monotonous. In our sample, the nomogram would look OK for the heart rate and SBP, but not for cholesterol.
The widget can show either log odds ratios (Log odds ratios), as above, or “points” (Point scale). In the latter case, log OR are simply scaled to the interval -100 to 100 for easier (manual)
calculation, for instance, if one wishes to print out the nomogram and use it on the paper.
Show prediction puts a blue dot at each attribute which we can drag to the corresponding value. The widget sums the log odds ratios and shows the probability of the target class on the bottom axes.
Confidence intervals adds confidence intervals for the individual log ratios and for probability prediction. Show histogram adds a bar whose height represents the relative number of examples for each
value of discrete attribute, while for continuous attributes the curve is thickened where the number of examples is higher.
For instance, for gender the number of males is about twice as big than the number of females, and the confidence interval for the log OR is correspondingly smaller. The histograms and confidence
intervals also explain the strange finding that extreme cholesterol level (600) is healthy, healthier than 200, while really low cholesterol (50) is almost as bad as levels around 300. The big
majority of patients have cholesterol between 200 and 300; what happens outside this interval may be a random effect, which is also suggested by the very wide confidence intervals.
To draw a nomogram, we need to get some data (e.g. from the File widget, induce a classifier and give it to the nomogram. | {"url":"https://docs.biolab.si/orange/2/widgets/rst/classify/nomogram.html","timestamp":"2024-11-10T18:09:24Z","content_type":"application/xhtml+xml","content_length":"12363","record_id":"<urn:uuid:335fe713-ba51-4d43-8446-11f140f1c1b4>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00411.warc.gz"} |
Convert Nanosiemens (nS) (Electric conductance)
Convert Nanosiemens (nS)
Direct link to this calculator:
Convert Nanosiemens (nS) (Electric conductance)
1. Choose the right category from the selection list, in this case 'Electric conductance'.
2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), square root (√), brackets and
π (pi) are all permitted at this point.
3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'Nanosiemens [nS]'.
4. The value will then be converted into all units of measurement the calculator is familiar with.
5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so.
Utilize the full range of performance for this units calculator
With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '390 Nanosiemens'. In so doing, either the full name of the unit or
its abbreviation can be usedas an example, either 'Nanosiemens' or 'nS'. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case
'Electric conductance'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally
sought. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units.
All of that is taken over for us by the calculator and it gets the job done in a fraction of a second.
Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(59 * 33) nS'. But different
units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '12 Nanosiemens + 85 Nanosiemens' or '7mm x 80cm x 54dm = ? cm^3'. The
units of measure combined in this way naturally have to fit together and make sense in the combination in question.
The mathematical functions sin, cos, tan and sqrt can also be used. Example: sin(π/2), cos(pi/2), tan(90°), sin(90) or sqrt(4).
If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 5.461 748 098 446 2×1021. For this form of presentation, the number
will be segmented into an exponent, here 21, and the actual number, here 5.461 748 098 446 2. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket
calculators, one also finds the way of writing numbers as 5.461 748 098 446 2E+21. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at
this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 5 461 748 098 446 200 000 000. Independent of the presentation of the
results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications. | {"url":"https://www.convert-measurement-units.com/convert+Nanosiemens.php","timestamp":"2024-11-04T15:21:35Z","content_type":"text/html","content_length":"53577","record_id":"<urn:uuid:319ae770-fb1c-4b27-bd6f-3839a8d586df>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00563.warc.gz"} |
All point correlation functions in SYK
Large N melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams
that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together. We uncover an incredibly useful property of these theories: the six-point
function, or equivalently, the three-point function of the primary O( N ) invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions,
to leading nontrivial order in 1/ N , through simple Feynman-like rules. The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point
functions. We explicitly calculate the bilinear three-point function for q-body SYK, at any q. This leads to the bilinear four-point function, as well as all higher-point functions, expressed in
terms of higher-point conformal blocks, which we discuss. We find universality of correlators of operators of large dimension, which we simplify through a saddle point analysis. We comment on the
implications for the AdS dual of SYK.
Journal of High Energy Physics
Pub Date:
December 2017
□ 1/N Expansion;
□ AdS-CFT Correspondence;
□ Conformal Field Theory;
□ Integrable Field Theories;
□ High Energy Physics - Theory;
□ Condensed Matter - Strongly Correlated Electrons
67 pages, v2 | {"url":"https://ui.adsabs.harvard.edu/abs/2017JHEP...12..148G/abstract","timestamp":"2024-11-01T18:57:06Z","content_type":"text/html","content_length":"40024","record_id":"<urn:uuid:5fbfebbf-6539-4397-ba90-5e092af3d86d>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00101.warc.gz"} |
Filter rows based on numerical/expression column
2 Brief description
Only those rows are kept that have a value in the numerical column fulfilling the equation or inequality relation.
Output: The filtered matrix.
3 Parameters
3.1 Number of columns
The filtering is based on relations of expression/numerical columns. Up to five columns (default: 1) can be selected. Depending on the number of chosen columns drop down box(es) appear on the pop-up
window named “x”, “y”, “z”, “a” and “b”. In these drop down boxes expression/numerical columns can be specified, which can then be used in the relations that should be applied for filtering the
3.2 Number of relations
Up to five relations using the previously specified columns can be included in the filtering process (default:1). Depending on the selected number of relations text fields on the pop-up window appear
named “Relation 1”, “Relation 2”, “Relation 3”, “Relation 4” and “Relation 5”.
In each text field a relation for the filtering process can be defined using the variables of the parameter “Number of columns”. For the relations numbers with “.” as decimal point, “+”, “-”, “*”, “/
” and “^” as well as scientific notation (e.g. “5.4e-12”) can be used.
3.3 Combine through
Defines how the specified relations are combined (default: intersection). Depending on the specified combination mode either rows, which fulfill the “intersection” (default) of the relations are kept
or the ones fulfilling the “union”.
3.4 Filter mode
The “Filter mode” defines, whether the input matrix will be reduced (“Reduce matrix” = default) or a new categorical column called “Filter” will be generated containing the categories “Keep” and
“Discard” (“Filter mode” = “Add categorical column”). | {"url":"https://cox-labs.github.io/coxdocs/filternumericalcolumn.html","timestamp":"2024-11-12T23:27:24Z","content_type":"application/xhtml+xml","content_length":"27671","record_id":"<urn:uuid:1f7e73f0-3cfb-4f33-847c-1be73dae7a48>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00844.warc.gz"} |
This function Gcross and its companions Gdot and Gmulti are generalisations of the function Gest to multitype point patterns.
A multitype point pattern is a spatial pattern of points classified into a finite number of possible ``colours'' or ``types''. In the spatstat package, a multitype pattern is represented as a single
point pattern object in which the points carry marks, and the mark value attached to each point determines the type of that point.
The argument X must be a point pattern (object of class "ppp") or any data that are acceptable to as.ppp. It must be a marked point pattern, and the mark vector X$marks must be a factor. The
arguments i and j will be interpreted as levels of the factor X$marks. (Warning: this means that an integer value i=3 will be interpreted as the number 3, not the 3rd smallest level).
The ``cross-type'' (type \(i\) to type \(j\)) nearest neighbour distance distribution function of a multitype point process is the cumulative distribution function \(G_{ij}(r)\) of the distance from
a typical random point of the process with type \(i\) the nearest point of type \(j\).
An estimate of \(G_{ij}(r)\) is a useful summary statistic in exploratory data analysis of a multitype point pattern. If the process of type \(i\) points were independent of the process of type \(j\)
points, then \(G_{ij}(r)\) would equal \(F_j(r)\), the empty space function of the type \(j\) points. For a multitype Poisson point process where the type \(i\) points have intensity \(\lambda_i\),
we have $$G_{ij}(r) = 1 - e^{ - \lambda_j \pi r^2} $$ Deviations between the empirical and theoretical \(G_{ij}\) curves may suggest dependence between the points of types \(i\) and \(j\).
This algorithm estimates the distribution function \(G_{ij}(r)\) from the point pattern X. It assumes that X can be treated as a realisation of a stationary (spatially homogeneous) random spatial
point process in the plane, observed through a bounded window. The window (which is specified in X as Window(X)) may have arbitrary shape. Biases due to edge effects are treated in the same manner as
in Gest.
The argument r is the vector of values for the distance \(r\) at which \(G_{ij}(r)\) should be evaluated. It is also used to determine the breakpoints (in the sense of hist) for the computation of
histograms of distances. The reduced-sample and Kaplan-Meier estimators are computed from histogram counts. In the case of the Kaplan-Meier estimator this introduces a discretisation error which is
controlled by the fineness of the breakpoints.
First-time users would be strongly advised not to specify r. However, if it is specified, r must satisfy r[1] = 0, and max(r) must be larger than the radius of the largest disc contained in the
window. Furthermore, the successive entries of r must be finely spaced.
The algorithm also returns an estimate of the hazard rate function, \(\lambda(r)\), of \(G_{ij}(r)\). This estimate should be used with caution as \(G_{ij}(r)\) is not necessarily differentiable.
The naive empirical distribution of distances from each point of the pattern X to the nearest other point of the pattern, is a biased estimate of \(G_{ij}\). However this is also returned by the
algorithm, as it is sometimes useful in other contexts. Care should be taken not to use the uncorrected empirical \(G_{ij}\) as if it were an unbiased estimator of \(G_{ij}\). | {"url":"https://www.rdocumentation.org/packages/spatstat.explore/versions/3.0-6/topics/Gcross","timestamp":"2024-11-06T15:47:58Z","content_type":"text/html","content_length":"96152","record_id":"<urn:uuid:5007c108-6171-44ce-911d-3b0422fe8a66>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00785.warc.gz"} |
Othmar Winkler
Othmar W. Winkler is Professor Emeritus of business and economic statistics at the McDonough School of Business at Georgetown University.
RIP: Obituary 8/14/2022. Wilhelm Winkler's bio (Othmar's father) Statisticians of the Centuries (Table of Contents)
2021: A Simple Graphic Method to Assess Correlation 2021 Biometrics and Biostatistics International Journal (BBIJ)
2019: A Statistical Mystery Resolved May 2019 Biometrics & Biostatistics International Journal. Vol 8, Iss 3. P 101-102
2019: Interpreting the CDF of Socio-Economic Data. January 2019 Biometrics & Biostatistics International Journal. Vol 8, Iss 1. P 13-15.
2018: Different Approach to Socio-Economic Statistics compared to the classical Statistics Approach. Biom. Biostat Int. Jl. 2018 7(1)
2012: How Economic and Social Statistics became the Stepchildren of the Profession. Presented at 2012 Joint Statistical Meeting of American Statistical Association
2011: Interpreting Socio-Economic Data. Presented at the 2011 conference of the International Statistical Institute (ISI) in Dublin.
2009: Interpreting the Cumulative Frequency Distribution of Socio-Economic Data. Talk at the 2009 Joint Statistical Meeting of the American Statistical Association (ASA)
Interpreting Economic and Social Data: A Foundation of Descriptive Statistics (2009)
Back Cover
"Interpreting Economic and Social Data aims at rehabilitating the descriptive function of socio-economic statistics, bridging the gap between today's statistical theory on one hand, and econometric
and mathematical models of society on the other. it does this by offering a deeper understanding of data and methods with surprising insights, the result of the author's six decades of teaching,
consulting and involvement in statistical surveys. The author challenges many preconceptions about aggregation, time series, index numbers, frequency distributions, regression analysis and
probability, nudging statistical theory in a different direction.
Interpreting Economic and Social Data also links statistics with other quantitative fields like accounting and geography. it is aimed at students and professors in business, economics and social
science courses, and in general at users of socio-economic data, requiring only an acquaintance with elementary statistical theory."
First section: 1.1 Stating the Problem
"Statisticians accept as a self evident principle that there is one general theory of statistics that applies equally to all fields,' biology, economics, engineering, demography, environmental
sciences, sociology, etc. (Fig. 1.1). Yet, important applications in economics and the social sciences in general are not covered by what today is considered 'the theory of statistics.' This calls
for a review of the situation, of methods that do not apply, and important aspects of socio-economic applications that are not supported by statistical theory. The peculiar nature of the data in
socio-economic statistics requires a different basis than is available at present and makes it unlikely that a general `Theory of Statistics' can satisfy the needs of this scientific field.
Historically, the turn toward inference came from the discovery of random sampling, from experimentation in agriculture and other applications in the natural sciences. We proceed as if socioeconomic
statistical data are like those in the sciences, ignoring that they differ in important ways. Because of this, the applications of social, business and economic statistics are not adequately
supported by today's statistical theory."
Preface: Introduction
"On a snowy winter morning I boarded a crowded city bus, unable to use my bicycle for the usual 10 km commute to Georgetown University. In preparation for teaching that morning, I began perusing the
textbook on business and economic statistics that I had adopted for this course. At the next stop, a young woman took the seat next to me, the only one remaining in the full bus. Shortly after
settling in, she turned to me:: `Excuse me sir, is this statistics?' she motioned to the textbook. `Yes', I responded, surprised, `Business and Economic Statistics.' At this, a look of revulsion
overcame her "Ugh... Statistics was the only subject I could never handle in college..." She trembled at a memory that still haunted and upset her. At this reaction a series of similar, though less
dramatic, occurrences came to mind. Few other academic subject seem to evoke the distaste that the mention of statistics seems to elicit. Does it have to be that way? I grappled with possible
explanations for a long time.
This book is my response that evolved gradually over decades of teaching a variety of business, economic and general statistics courses, using the newest textbooks available, and being involved in
survey work and statistical consulting. I wondered why these textbooks on business and economic statistics presented the subject matter as a watered-down version of mathematical statistics, which
itself evolved from problems of measurement and observation in the natural sciences. These textbooks treat socio-economic data like the measurements in the natural sciences and present the subject as
an application of probability, grouped around the Gaussian, Poisson, F, C^2 and other statistical distributions, sampling and statistical inference. There was no interest or concern about how to
interpret the messages about society contained in the wealth of published economic and social data. They fail to see that this is the raison d'etre of the entire statistical enterprise which also
should be the main purpose of statistics courses for social scientists. These courses fail to present statistics as the instrument for scanning the economic and social environment and to monitor
important aspects of social reality.
It is the aim of this book to re-orient statistics towards making sense of economic and social data. It is an attempt to rehabilitate 'descriptive statistics' as a respectable part of statistics,
re-orienting it toward the description of society which in fact was its original purpose and still is the ultimate goal of all statistical endeavors. This book is addressed to the literate and
numerate public, trying to open their eyes to various basic facts that are commonly overlooked, in short, to lead them to a fuller awareness of simple basics, to encourage asking questions and to
look for answers in the fine print that accompanies tabulations of socio-economic data.
It is also the aim of this book to draw attention to the neglected twilight zone, the no-man's land between the partisan efforts of statisticians who, inspired by applications in the natural
sciences, turned to probability, controlled experiments, model building, etc. on one hand, and the applied fields of social sciences on the other. Statistical theorists feel that they are the
guardians of a true science, concerned with the purity of its theoretical core with little regard for interpreting economic and social data. On the other side are social scientists and economists
concerned about discovering timeless laws of economics, intent on condensing them into mathematical models. They too are less concerned about using statistical data to monitor and also influence
events in society. And last, but not least, there are the dedicated statistical foot soldiers who take censuses and surveys, and prepare tabulations. They too have no time for making sense of their
data about society.
As you may notice from the `Outline,' this book departs from the usual structure, but instead follows the steps of the statistical process in a rather abstract, theoretical manner, from the very
start of conceptualizing the socio-economic phenomenon to be investigated to the final tabulation of the data. Standard topics, like the Gaussian curve, probability theory and symmetrical,
well-behaved frequency distributions are treated at the end of the book, if at all. The initial chapters deal at length with topics that are usually missing in textbooks such as aggregation,
statistical aggregates and ratios. They form the backbone for the interpretation of socio-economic data. Then follow three chapters on time series as the most frequent form in which data are
published. These chapters are given priority over frequency distributions in one or more dimensions, treated toward the end.
This book, by the way, is not meant as an introduction to statistics, nor as a "how-to-do, hands-on" manual. Its concern is to make sense of socio-economic data. and to shine new light on various
misconceptions the reader may have acquired in previous statistics courses. Only a minimum of mathematics will be required. Calculations are relegated to the five optional appendices. Although
mathematical statisticians may find this book pedestrian and simplistic, some abstract thinking is involved and the reader is asked to be patient with unfamiliar ideas.
This book is intended for everyone who has to deal with data about society: students and teachers in business, economics and social science courses, economists, social scientists, financial analysts,
market researchers, business and economic forecasters, sociologists, managers, demographers, even geographers. It is my hope that the chapters of this book will open up a new understanding of
socio-economic data for their meaningful interpretation, allay bad feelings toward our field, and stimulate further developments in the indicated direction.
Description of Chapters:
Chapter 1 provides a short view of the developments that led to the present situation in socio-economic statistics. The powerful influence and the band wagon effect of the developments in statistics
in biology, agriculture came to dominate all fields of statistical application. This chapter points out that socio-economic statistical data are quite different from the measurements in the sciences.
Chapter 2 traces the statistical process, from the conception and formulation of a socio-economic phenomenon, such as unemployment, poverty, productivity or crime; to the identification and recording
of the relevant `real-life-objects' which portray that social or economic phenomenon: human beings, entities such as corporations, or events, such as births, work accidents or business mergers. The
simplified records of these `real-life-objects' then become the 'statistical-counting units'.
In Chap. 3 the subsequent grouping of these `statistical-counting-units' into suitable aggregates is discussed. These new entities, the statistical aggregates, are defined by their three
`dimensions': the subject matter, the time period, and the extent of the geographic area covered. As to the subject-matter "dimension", the qualitative characteristics of the statistical counting
units are important for the formation of a hierarchy of sub-aggregates. The magnitude of each of the three `dimensions' of an aggregate determines how to interpret the gains and losses from
aggregating the `statistical-counting-units'. These statistical aggregates represent the bulk of the data in socio-economic statistics. They are quite distinct from the data in the natural sciences,
an important matter that has not received due attention.
In Chap. 4 a variety of ratios is discussed as simple and effective analytical tools. These ratios allow us to perceive and make sense of the underlying economic and social reality conveyed by these
aggregates. Despite their pervasiveness and importance, ratios have rarely been discussed.
Chapters 5, 6 and 7 study the development, over time, of economic and social phenomena through time-series of socio-economic data.
Chapter 5 presents a critical view of the customary decomposition of time series into trend, seasonal pattern, business cycle and randomness. Instead of the mathematical decomposition into the
standard components, time-series should be understood as quantitative economic and social history that can be interpreted meaningfully through a hierarchy of simple ratios between aggregates. These
figures are not to be understood as abstract algebraic numbers.
Chapter 6 explores the fact that statistical data lose their relevance over time and become obsolete and less relevant for anticipating the future of a situation in society. Good forecasting requires
acquaintance with the historic development of the underlying economic or social forces. Much depends on the speed with which the data become obsolete. The level of aggregation also affects
obsolescence. All this requires judicious decisions regarding the weight older data should be given in a forecasting model, and the point in the past from which on the data of a time series should be
Chapter 7 has two parts. In the first part, Sect. 7.1, Price-Index-Numbers are discussed as an important type of time series. A simpler, ratio-based approach is presented that is more transparent and
easier to interpret than the historic Price-Index-Number formulations currently in use, allowing for understanding and interpreting the actual changes in price levels. In the second part, Sect. 7.2,
Index-Numbers of Production are critically reviewed. Different production concepts are discussed and simpler ways of measuring production and productivity are developed.
Chapter 8 deals with the interpretation of highly asymmetric frequency distributions that predominate in economic and social data. Simple measures are presented to deal appropriately with these
highly asymmetrical data, to assess and interpret centrality, asymmetry and dispersion.
Chapter 9 discusses the puzzling case of one particular regression analysis that changed my views on cross-sectional data in general. Without going into the algebra of their calculation, specific
problems in Regression and Correlation with aggregate data are discussed.
Chapter 10 explores the relationship between statistics and the calculus of probability. Although socio-economic statistics is numeric, using mathematical symbols, algebra, geometry and graphs, it
must not be considered as a branch of mathematics. Socio-economic statistical data have an important conceptual non-numeric component that defies a numbers-only approach. One must keep in mind that
its purpose is the perception of very real economic and social happenings in historic time, and in geographic and subject-matter space. Misuses of probability, foremost the mis-interpretation and
misuse of "Statistical Significance," are critically reviewed.
Chapters 11 and 12, explore areas that social, business, and economic statistics has in common with subjects that do not readily come to mind as linked with statistics. While exploring these areas in
these two final chapters the nature of socioeconomic statistics is further clarified.
Chapter 11 has more in common than is usually acknowledged. When statistics is not considered as a branch of mathematics, however, it is easier to see that macro economics, really National Accounting
— which is essentially economic statistics - keeps track of the economy like financial accounting keeps track of a business corporation. The discussion reveals surprising affinities between
socio-economic statistics and financial accounting.
Chapter 12 discusses the importance of geographic-spatial distributions, a matter that has been absent from the theory of statistics, though not from statistical field-work. Although specialized
quantitative-statistical research abounds in geography, the geographic-spatial dimension has not been recognized as belonging to statistics and ought to be included in its theory.
Reviews and Comments:
Review by Prof. Thomas R. Dyckman: "Opening this book by Othmar Winkler is like splashing oneself with cold water at 5:30 in the morning. It’s a wakeup call! The author lays out his “call to arms” in
the preface. In our quest to understand or “make sense of socio-economic data” (p. vi), we have come to rely too heavily on statistical inference (F, t, Chisquare) and on assumed symmetry and
continuity. If we seek insights, we are enjoined to adopt instead the descriptive tools of statistics and apply them to aggregate observations and their categorizations. To understand socio-economic
phenomena, it is essential to recognize that the contributing processes are purposeful and not random." Reviewed in "The Accounting Review" by Thomas R. Dyckman: Prof. emeritus in Accounting at
Cornell University.
Review by Prof. Dr. Peter Winker: "Othmar W. Winkler’s book is ... far from providing the usual type of content of a monograph in statistics, but rather challenges conventions by providing
alternative views on the nature of data and how to analyze them." "Instead of being just another textbook in statistics for economists, the book rather targets all experienced statisticians and
econometricians who find it relevant to think carefully about the origin and properties of the data they use." Posted in the journal "Jahrbuecher fuer Nationaloekonomie und Statistik".
Review by Brady T. West: "This insightful text comes from a veteran scholar and targets individuals working with socio-economic (SE) data from business, economics, sociology, and other social
sciences. The book provides a refreshing view on how data from these fields should be approached in a realistic manner. The author strongly and consistently advocates the use of straight-forward
descriptive statistical methods to describe SE realities, rather than forcing SE data to conform to convenient probability models and inferential methods developed by mathematical statisticians for
data from the natural sciences (which are much more likely to be governed by natural laws and “true” probability models). Interpreting Economic and Social Data will appeal to (and should be read
carefully by) students and professional researchers in the social sciences who are responsible for analyzing cross-sectional or longitudinal SE data and generating written reports describing and
interpreting the analysis findings." "this book is an enjoyable read, and it does an excellent job of reinforcing the unique features of SE data and how statistical analyses should be tailored to
these features to produce the most meaningful descriptions of SE phenomena." Michigan Program in Survey Methodology Survey Research Center Institute for Social Research (ISR) University of Michigan.
[Extract from a draft of his review to be published by the Journal of Official Statistics]
Review by Walter Krämer: "Most of what is covered in this book is either taken for granted or not discussed at all in standard textbooks on economic or social statistics, not to mention mathematical
statistics." Institut für Wirtschafts-und Sozialstatistik, Technische Universität Dortmund at Dortmund, Germany.
Review by Thomas Luke Spreen. "Othmar Winkler's Interpreting Economic and Social Data calls into question the tendency of social scientists to treat quantitative summary data as objective
measurements as in the natural sciences. Winkler's observations on the subject are both thought-provoking and insightful." Spreen is an economist, Division of Labor Force Statistics, Office of
Employment and Unemployment, U.S. Bureau of Labor Statistics. Published in the Book Review Section of the August 2011 issue of the BLS Monthly Labor Review.
Comments by Dr. Keith Ord: "I am very impressed by the breadth of coverage and the deep discussion you have provided on a number of topics.
Review by McGee (Biostatistician, SMU) in the American Statistician. Winkler's reply.
Review by Andrey Kostenko in the 2012 International Journal of Forecasting. "In conclusion, the book is written to share the author’s belief that ‘‘social and economic statistics, though numeric, is
essentially quantified history of society, not a branch of mathematics’’ (p. 232). Those who are close to this belief (or those who are yet to form their views on the subject) may find the book
interesting." Winkler's reply. | {"url":"http://statlit.org/Winkler.htm","timestamp":"2024-11-07T23:27:29Z","content_type":"text/html","content_length":"43051","record_id":"<urn:uuid:5a19542d-2473-4f93-91f8-36b27f0d698f>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00542.warc.gz"} |
How to Insert a Text Box in MS Word
Text box allows you to control the position of a block of text in your document. You can also format them with borders and shading. The two commonly used methods to insert Text Boxes are given below:
Method 1:
• Select the Insert tab
• Locate the Text group
• Click the Text Box button
• It displays Built-In text box menu and an option to draw table
• With a left click select the desired text box format from the menu
Method 2:
• Select ‘Draw Text Box’ option
• A cross shaped cursor appears
• Left click the mouse and holding it down drag it to draw the box of desired dimensions
See the image: | {"url":"https://ncert-books.com/how-to-insert-a-text-box-in-ms-word/","timestamp":"2024-11-07T03:31:55Z","content_type":"text/html","content_length":"119510","record_id":"<urn:uuid:e550489e-c498-4bce-b22a-6d4abfc9b13e>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00812.warc.gz"} |
Görkem Paçacı
AI Machine Learning Research
All this talk about Artificial General Intelligence (AGI) made me wonder how far in is GPT towards formal logic? I should clarify: if it turns out it can do a lot of formal logic, I don’t think that
is any kind of sign towards AGI. The two are conceptually related but not correlated. Humans (supposedly) have AGI, but they fail at formal logic often. A lot of computer algorithms have been
invented for formal logic,…
Passing a struct as ref through an interface in C#
Didn’t think it’d be any complicated. I’m in the middle of a large refactoring job that is primarily concerned with memory adjacency. When data lies in memory continuously instead of being
distributed segments, parallel code scales better because of CPU caching. This is currently my problem with the Parallel implementation of CombInduce, the ‘solver’/program synthesiser that forms the
basis of our work in Interpretable AI. This memory adjacency work involves, among other things, to replace…
Bad examples and inheritance
The other day my students were asking about Covariance/Contravariance, they were visibly frustrated because they were trying to grasp them at once together with covariance/contravariance modifiers on
generics. While trying to explain the concept without generics, I came up with an example on the spot about inheritance that didn’t work, so they were even more frustrated. Because the example not
only didn’t make a good case for covariance/contravariance, it didn’t work as an example of…
Special Session on Effective Modelling and Implementation of Quantities – EMIQ 2022
In conjunction with MODELSWARD conference, Steve is organising a special edition on implementation of units / quantities. Misuse/non-use of proper libraries/supporting tools for units is one of the
bleeding failures of Software Engineering, and there’s much work to be done on this in both the research end, and in application. Paper submission by November 26th, 2021. https://
JustOnce delegate wrapper
I found myself in need of returning a delegate but making sure that the receiver gets to call the delegate at most once. The task at hand is a concurrent task queue. Threads take a task, and can put
back a set of tasks back into the queue if they wish. But if they will put back some tasks, TaskQueue needs to make sure they get to do it only once. Simply the thread would… | {"url":"http://gorkempacaci.com/author/admin/","timestamp":"2024-11-11T20:54:44Z","content_type":"text/html","content_length":"37501","record_id":"<urn:uuid:faf18505-ba10-47c5-9a34-91808661a5f8>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00363.warc.gz"} |
| Applications of Differentiation
Rate of change: conical tank [Solved!]
Ana 25 Nov 2015, 09:46
My question
Please help me solve a rate of change problem about a conical tank wit vertex down. i dont know the equation i have to use
Relevant page
What I've done so far
I read the examples on the page, but none of them were like my one. | {"url":"https://www.intmath.com/forum/applications-differentiation-27/rate-of-change-conical-tank:18","timestamp":"2024-11-12T15:47:12Z","content_type":"text/html","content_length":"109337","record_id":"<urn:uuid:9fe72b72-f2f5-4c54-b5b6-d09381cff497>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00667.warc.gz"} |
The dgl.geometry package contains geometry operations:
• Farthest point sampling for point cloud sampling
• Neighbor matching module for graclus pooling
This package is experimental and the interfaces may be subject to changes in future releases.
Farthest Point Sampler¶
Farthest point sampling is a greedy algorithm that samples from a point cloud data iteratively. It starts from a random single sample of point. In each iteration, it samples from the rest points that
is the farthest from the set of sampled points.
class dgl.geometry.farthest_point_sampler[source]¶
Farthest Point Sampler without the need to compute all pairs of distance.
In each batch, the algorithm starts with the sample index specified by start_idx. Then for each point, we maintain the minimum to-sample distance. Finally, we pick the point with the maximum such
distance. This process will be repeated for sample_points - 1 times.
☆ pos (tensor) – The positional tensor of shape (B, N, C)
☆ npoints (int) – The number of points to sample in each batch.
☆ start_idx (int, optional) – If given, appoint the index of the starting point, otherwise randomly select a point as the start point. (default: None)
The sampled indices in each batch.
Return type
tensor of shape (B, npoints)
The following exmaple uses PyTorch backend.
>>> import torch
>>> from dgl.geometry import farthest_point_sampler
>>> x = torch.rand((2, 10, 3))
>>> point_idx = farthest_point_sampler(x, 2)
>>> print(point_idx)
tensor([[5, 6],
[7, 8]])
Neighbor Matching¶
Neighbor matching is an important module in the Graclus clustering algorithm.
class dgl.geometry.neighbor_matching[source]¶
The neighbor matching procedure of edge coarsening in Metis and Graclus for homogeneous graph coarsening. This procedure keeps picking an unmarked vertex and matching it with one its unmarked
neighbors (that maximizes its edge weight) until no match can be done.
If no edge weight is given, this procedure will randomly pick neighbor for each vertex.
The GPU implementation is based on A GPU Algorithm for Greedy Graph Matching
NOTE: The input graph must be bi-directed (undirected) graph. Call dgl.to_bidirected
if you are not sure your graph is bi-directed.
☆ graph (DGLGraph) – The input homogeneous graph.
☆ edge_weight (torch.Tensor, optional) – The edge weight tensor holding non-negative scalar weight for each edge. default: None
☆ relabel_idx (bool, optional) – If true, relabel resulting node labels to have consecutive node ids. default: True
The following example uses PyTorch backend.
>>> import torch, dgl
>>> from dgl.geometry import neighbor_matching
>>> g = dgl.graph(([0, 1, 1, 2], [1, 0, 2, 1]))
>>> res = neighbor_matching(g)
tensor([0, 1, 1]) | {"url":"https://doc.dgl.ai/en/0.7.x/api/python/dgl.geometry.html","timestamp":"2024-11-06T05:18:21Z","content_type":"text/html","content_length":"20574","record_id":"<urn:uuid:dd5719a1-2037-406b-b7a8-c0f1ebc447e3>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00654.warc.gz"} |
FAQ - Kinetic Math Center
Kinetic Math is your TRUE Math enrichment center. It offers energizing and engaging learning activities which help students develop numerical fluency, creativity, critical thinking and problem
solving skills while enjoying math.
Kinetic Math aims to:
• equip students with numeracy, reasoning, problem solving skills and critical thinking skills that are necessary for life.
• provide students venue to reason logically, communicate mathematically, learn cooperatively and independently.
• develop the children’s love for mathematics through engaging and challenging learning activities.
Kinetic Math offers the following Math programs to Kinder to Grade 10 students:
Click the links below for more details.
In Kinetic Math, we give the children an assessment test before starting any program with us. That way, we can recommend the best program that suits your child’s needs.
No. The programs offered by Kinetic Math complement the traditional Math lessons in school. They not only help the children with their current lessons, but also teach them more strategies to help
them compute mentally and solve word problems.
Each session lasts for an hour. However, other parents or students request for 2 slots (hours) in a day.
The frequency of the child’s session depends on the needs of and the goal for each child. After taking the assessment test, the Kinetic Math teacher will recommend the number of Kinetic Math sessions
that the child needs in a week in order to master the necessary skills needed.
Children as young as 4 years old may already enroll at Kinetic Math. However, we also accept students younger than four years old if their assessment test result shows that they are ready for the
The teacher-student ratio in Kinetic Math is 1:3.
Kinetic Math can help your child in his or her current lessons in class. We also hold review sessions for quizzes and exams. In addition, the center may also go back to past lessons that the child
failed to master. For some children, advanced lessons may also be discussed.
Yes, we welcome students with special needs who can sit down and do the Kinetic Math activities. One-on-one sessions may also be recommended as needed. However, there is a different rate for
one-on-one sessions.
Yes, we can help him prepare for the entrance exam. We will help him review his past lessons and teach him the lessons that he failed to master. In addition, we will also help him develop his
test-taking skills.
Yes, in addition to the regular programs, we also offer various summer programs to help the children develop certain Math skills. Please call the Kinetic Math branch near you for more details.
For Kinetic Math Katipunan and Kinetic Math San Juan, one-on-one sessions are only offered to those who really need one. However, Kinetic Math BGC offers one-on-one Math sessions to everyone.
Yes, Kinetic Math teachers are highly trained in Singapore Math. All the teachers underwent Singapore Math training. | {"url":"https://kineticmathcenter.net/faqs/","timestamp":"2024-11-10T09:48:14Z","content_type":"text/html","content_length":"59687","record_id":"<urn:uuid:cd4d8223-2e04-44cf-a91a-2c12d7a70c9e>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00844.warc.gz"} |
In this paper we introduce a sub-family of SAPDA, one-turn Synchronized Alternating Pushdown Automata, and prove that they are equivalent to Linear Conjunctive Grammars
— Linear Conjunctive Grammars and One-Turn Synchronized Alternating Pushdown Automata ↗, 2009
This is similar to the pushdown automata of 2.4. As, we have shown that the class of context-free grammars is equal to the class of languages accepted by PDAs, we will show the equivalence of the
class of conjunctive languages with the class of languages accepted by SAPDA. The original paper introducing this concept is [11]. For making our model similar to automata and to pushdown
automata as introduced in 2.4, we give a different but equivalent definition of SAPDA as it’s given in [11]. So, the proof of equivalence of the class of conjunctive grammars with the class of
SAPDA is also different than the one given in the orininal paper. | {"url":"https://parsing.stereobooster.com/sapda/","timestamp":"2024-11-09T15:44:08Z","content_type":"text/html","content_length":"36458","record_id":"<urn:uuid:bb21f67c-f94a-4c9d-96a0-176b94046985>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00170.warc.gz"} |
UI Scripting contextual menus
How to choose and execute a menu item in a contextual menu with UI Scripting?
Namely in iTunes: choosing “Convert ID3 Tags.” in a track contextual menu (might not be there) and “Export.” in a Playlist contextal menu.
tell application "System Events"
tell process "iTunes"
set theSelectedRow to (row 1 of outline 1 of scroll area 3 of window "iTunes" whose selected is true)
set {x, y} to position of theSelectedRow
key down control
tell me to do shell script "/usr/local/bin/cliclick c:" & x & "," & y
key up control
keystroke "Convert" & return
delay 1
implies intalling cliclick and keystroke “Convert” to select the menu item. Is there a better way?
Here is a handler which I used to trigger a contextual menu in Numbers.
It was designed to convert the selected standard row 1 into a header one.
It does the trick but there is a long pause before really triggering the menu item.
Maybe it may be used with iTunes.
tell application "Numbers"
set dname to name of document 1
tell document 1 to tell sheet 1 to tell table 1
set selection range to range "A1:A1"
end tell
end tell
my convertRow1ToHeaderRow(dname)
on convertRow1ToHeaderRow(d_Name)
local boutonMenu, avant, tempsRequis, errmsg, errNbr, xPos, yPos
tell application "Numbers"
tell application "System Events" to tell application process "Numbers"
tell window d_Name to tell first splitter group to tell last splitter group to tell first splitter group to tell last scroll area to tell (first UI element whose role is "AXLayoutArea") to tell first UI element to tell first UI element to tell last group
set boutonMenu to first menu button
Reveal the contextual menu *)
tell current application to set avant to current date
click boutonMenu
tell current application to set tempsRequis to (current date) - avant
repeat 50 times
if exists menu 1 of boutonMenu then exit repeat
delay 0.5
end repeat
tell boutonMenu to set {xPos, yPos} to position
end tell -- window.
click at {xPos + 26, yPos + 28}
end tell -- System Events
display dialog "Waited " & tempsRequis & " seconds" & return & "before giving hand back to the script !" buttons {"Continue"} default button 1
end tell
end convertRow1ToHeaderRow
Oops, the phone rang and I clicked [ Submit ] erroneously :rolleyes:
Yvan KOENIG (VALLAURIS, France) mardi 9 octobre 2012 18:55:54
I think you forgot the handler Yvan.
Thanks, it was helpful to get me started. Unfortunately there is no menu button
The progress so far:
tell window d_Name
tell scroll area 3
get it
tell outline 1
get it
tell row 19
--click --row 19
perform action "AXShowMenu"
keystroke "Convert" & return
And hop, there it is the wanted dialog!
Can we say perform action “AXShowMenu” is a reasonably general solution for contextual menus?
Hello, I’m really puzzled.
activate application "iTunes"
tell application "System Events" to tell application process "iTunes"
tell window 1
--class of every UI element
-->{button, button, button, button, slider, button, scroll area, radio group, text field, scroll area, UI element, scroll area, scroll area, browser, button, button, button, button, static text, button, button, static text, button, button, button, button}
position of every scroll area
--> {{665, 44}, {303, 91}, {1290, 114}, {673, 91}}
size of every scroll area
--> {{475, 44}, {185, 827}, {213, 804}, {616, 827}}
class of every UI element of scroll area 3
--> {UI element}
class of every UI element of first outline of scroll area 3
--> error number -1719 from outline 1 of scroll area 3 of window 1 of application process "iTunes"
class of every UI element of last scroll area
--> {outline, scroll bar, scroll bar}
class of every UI element of first outline of last scroll area
--> {group, column, column, column, column, column, column, column, column, column, column, column, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row, row}
tell first outline of last scroll area
tell row 25
--> {1456, 1014}
--> {1177, 19}
value of first text field
--> "Little Numbers"
end tell # row 25
tell (first row whose value of text field 1 is "1901")
if not value of attribute "AXSelected" then
set value of attribute "AXSelected" to true
repeat until value of attribute "AXSelected" is true
delay 0.1
end repeat
end if
# Now the wanted row is selected
set {xTop, yTop} to position
tell application "ASObjC Runner"
{xTop + 1, yTop + 1}
click button once at result holding down {control}
{xTop + 5, yTop + 2}
set mouse location to result
# The contextual menu is visible
end tell
delay 0.5
class of UI elements
end tell # (first row whose value of text field 1 is
end tell # first outline of last scroll area
class of UI elements
# I am really puzzled, I don't see the menu object.
--> {button, button, button, button, slider, button, scroll area, radio group, text field, scroll area, UI element, scroll area, scroll area, browser, button, button, button, button, static text, button, button, static text, button, button, button, button}
end tell # window 1
end tell # System Events & process
(1) Here, the tracks aren’t listed in scroll area 3 but in scroll area 4.
(2) the script reveal the pop up menu but I’m unable to find its descriptor.
Yvan KOENIG (VALLAURIS, France) mercredi 10 octobre 2012 19:49:02
The iTunes sidebar is showing.
Under most circumstances last scroll area works, but not if the sidebar is opened after the playlist is showing. Thanks for poniting me to a future bug!
I guess that explains why I was having so much problems (besides my complete noobiness).
In my script above (soon edited) click is not needed and the script leaves the selection as is, a good thing. Thanks for showing a few things about the process. | {"url":"https://www.macscripter.net/t/ui-scripting-contextual-menus/64702","timestamp":"2024-11-02T09:23:07Z","content_type":"text/html","content_length":"37045","record_id":"<urn:uuid:d9547242-5035-46fb-afd2-c010b9e48b54>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00432.warc.gz"} |
What is behind Einstein’s turbulence?
Numerical calculations by scientists at the AEI give an initial insight into the relativistic properties of this mysterious process
The American Nobel Prize Laureate for Physics Richard Feynman once described turbulence as “the most important unsolved problem of classical physics”, because a description of the phenomenon from
first principles does not exist. This is still regarded as one of the six most important problems in mathematics today. David Radice and Luciano Rezzolla from the Max Planck Institute for
Gravitational Physics (Albert Einstein Institute / AEI) in Potsdam have now taken a major step towards solving this problem: For the first time, a new computer code has provided relativistic
calculations that give scientists a better understanding of turbulent processes in regimes that can be found in astrophysical phenomena.
Turbulent flows are very common and play a major role in the dynamics of physical processes. We all come across turbulence on a daily basis, for example every time we mix milk and coffee, or in
gasoline -air mixture in combustion engines, or in the diluted hot plasma of the intergalactic medium.
Already as far back as in the 15th century, turbulent vortices were studied by Leonardo da Vinci. In the 19th century, Claude Navier and George Stokes formulated equations that described the motion
of fluids and gases. The corresponding “Navier-Stokes equations” can also be used to describe turbulence. However, using simple geometrical and energetic arguments, the Russian mathematician Andrey
Kolmogorov developed during the Second World War a phenomenological theory for turbulence that is still valid today.
Snapshots at different times of a simulation of the energy density of a driven turbulent flow in a hot plasma. Bright regions represent portions of the flow with the largest energies and
© D. Radice, L. Rezzolla (Max Planck Institute for Gravitational Physics)
Despite Kolmogorov’s predictions have been validated in a number of conditions, a fundamental mathematical theory of turbulence is still lacking. As a result, the “Analysis of the existence and
regularity of solutions to the three-dimensional incompressible Navier-Stokes equations” is on the list of unsolved mathematical problems, for which the Clay Mathematics Institute in Cambridge/
Massachusetts offered prize money to the tune of one million US dollars in the year 2000 for its solution.
“Our calculations have not solved the problem, but we are demonstrating that the previous theory has to be modified and how this should be done. This brings us one step closer to a basic theory for
the description of turbulence,” says Luciano Rezzolla, head of the Numerical Relativity Theory working group at the AEI.
Snapshots at different times of the logarithm of the Lorentz factor, an important dimensionless quantity in relativity. It measures the size of the velocity of the plasma. Dark regions represent
portions of the flow with the highest velocities and up to 99.95% of the speed of light.
© D. Radice, L. Rezzolla (Max Planck Institute for Gravitational Physics)
Rezzolla and his colleague David Radice researched turbulence in relativistic conditions of speed and energies, such as those expected near a black hole or in the early universe; in both cases, the
fluid motion is close to the speed of light. The researchers used a virtual laboratory to simulate these situations taking relativistic effects into account. The corresponding nonlinear differential
equations of relativistic hydrodynamics were solved on the supercomputers at AEI and the Garching-based Computing Centre.
“Our studies showed that Kolmogorov’s basic predictions for relativistic phenomena must be modified, because we are observing anomalies and new effects,” says Rezzola. “Interestingly, however, the
most important prediction of Kolmogorov’s theory appears to be still valid”, notes Rezzolla when referring to the so-called -5/3 Kolmogorov law, which describes how the energy of a system is
transferred from large to small vortices.
With their work, the scientists also want to help formulate a comprehensive model. “We have now taken the first step,” says Luciano Rezzolla. “We intend to improve the computer codes to acquire
further knowledge on the basic properties of relativistic turbulence.” | {"url":"https://www.aei.mpg.de/197497/what-is-behind-einstein-s-turbulence","timestamp":"2024-11-12T00:43:00Z","content_type":"text/html","content_length":"354065","record_id":"<urn:uuid:3db0af9e-1d9e-4db2-85bd-18fd5ef1846c>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00602.warc.gz"} |
Name Description
Computes class-label decisions for a given set of input vectors.
(Inherited from ClassifierBaseTInput, TClasses.)
Computes a class-label decision for a given input.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a class-label decision for a given input.
Decide(TInput, TClasses)
(Inherited from ClassifierBaseTInput, TClasses.)
Computes class-label decisions for the given input.
Decide(TInput, Boolean)
(Inherited from MulticlassClassifierBaseTInput.)
Computes class-label decisions for the given input.
Decide(TInput, Double)
(Inherited from MulticlassClassifierBaseTInput.)
Computes class-label decisions for the given input.
Decide(TInput, Int32)
(Inherited from MulticlassClassifierBaseTInput.)
Computes a class-label decision for a given input.
Decide(TInput, Double)
(Inherited from MulticlassClassifierBaseTInput.)
Distortion Calculates the average square distance from the data points to the nearest clusters' centroids.
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
GetEnumerator Returns an enumerator that iterates through the collection.
Serves as the default hash function.
(Inherited from Object.)
Gets the Type of the current instance.
(Inherited from Object.)
Creates a shallow copy of the current Object.
(Inherited from Object.)
Randomize Randomizes the clusters inside a dataset.
Computes a numerical score measuring the association between the given input vector and its most strongly associated class (as predicted by the classifier).
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and its most strongly associated class (as predicted by the classifier).
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
Score(T, Int32)
(Overrides MulticlassScoreClassifierBaseTInputScore(TInput, Int32).)
Predicts a class label for the input vector, returning a numerical score measuring the strength of association of the input vector to its most strongly related class.
Score(TInput, Int32)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and its most strongly associated class (as predicted by the classifier).
Score(TInput, Double)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
Score(TInput, Int32)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
Score(TInput, Int32)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Predicts a class label for each input vector, returning a numerical score measuring the strength of association of the input vector to the most strongly related class.
Score(TInput, Int32)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Score(TInput, Int32, Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Score(TInput, Int32, Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Score(TInput, Int32, Predicts a class label for each input vector, returning a numerical score measuring the strength of association of the input vector to the most strongly related class.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and each class.
Scores(TInput, Double)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Predicts a class label vector for the given input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible
Scores(TInput, Int32) classes.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Computes a numerical score measuring the association between the given input vector and each class.
Scores(TInput, Double)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Predicts a class label vector for each input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible
Scores(TInput, Int32) classes.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Predicts a class label vector for the given input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible
Scores(TInput, Int32, classes.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Predicts a class label vector for each input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible
Scores(TInput, Int32, classes.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Views this instance as a multi-class generative classifier.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Views this instance as a multi-label distance classifier, giving access to more advanced methods, such as the prediction of one-hot vectors.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Returns a string that represents the current object.
(Inherited from Object.)
Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
Applies the transformation to a set of input vectors, producing an associated set of output vectors.
(Inherited from TransformBaseTInput, TOutput.)
Transform(TInput, Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Boolean)
(Inherited from MulticlassClassifierBaseTInput.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Int32)
(Inherited from MulticlassClassifierBaseTInput.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Boolean)
(Inherited from MulticlassClassifierBaseTInput.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Double)
(Inherited from MulticlassClassifierBaseTInput.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Int32)
(Inherited from MulticlassClassifierBaseTInput.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Double)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Applies the transformation to an input, producing an associated output.
Transform(TInput, Double)
(Inherited from MulticlassScoreClassifierBaseTInput.)
Transform(T, Double, Transform data points into feature vectors containing the distance between each point and each of the clusters.
Transform(T, Int32, Transform data points into feature vectors containing the distance between each point and each of the clusters.
Double, Double) | {"url":"http://accord-framework.net/docs/html/Methods_T_Accord_MachineLearning_KModesClusterCollection_1.htm","timestamp":"2024-11-02T11:43:01Z","content_type":"text/html","content_length":"70866","record_id":"<urn:uuid:4b1dc9df-d23d-449e-824b-e1f83d71c747>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00825.warc.gz"} |
Average True Range (ATR) - Volatility Indicator
Average True Range (ATR) – Volatility Indicator
What is the ATR?
The ATR is a technical indicator that measures the volatility of the market. As such, the indicator does not provide information on the direction of the price, but on the degree of movement of the
price, or volatility. It was developed by J. Welles Wilder and disseminated in his book, New Concepts in Technical Trading Systems (1978).
Wilder designed several indicators applying them mainly to commodity markets and especially with daily prices. At the time Wilder designed the ATR, commodity markets were among the most volatile
markets where price gaps and limit movements were frequent, and continue to be. These gaps result in jumps in the price not reflected in the session data: opening price, maximum price, minimum price
and closing price, and therefore this amplitude of movement is not reflected in the range of movement typically calculated using the maximum-minimum range. Wilder began designing the True Range (TR)
concept in an effort to appropriately reflect volatility. Unlike the calculations based on maximum and minimum ranges, the TR takes into account the gaps and the limit movements, and is defined as
the greater of the following values:
• Current maximum minus current minimum.
• Absolute value of the current maximum minus the closing of the previous candle.
• Absolute value of the current minimum minus the closing of the previous candle.
Observing the three possibilities, we can deduce that if the last two possibilities are greater than the current maximum-minimum range, it can indicate that there has been a gap or limit movement.
Let’s look at an example where you can see three situations where the TR will not use the current maximum-minimum range. Two of the examples show a wide gap, all three have a narrow maximum-minimum
current candle range.
Methods to calculate the True Range (TR). Source: https://school.stockcharts.com/doku.php?id=technical_indicators:average_true_range_atr
1. We see a formation with a small maximum-minimum range after a bullish gap. The TR is the absolute value of the difference between the current maximum and the close of the previous candle, which
is, in this case, the highest value among the possibilities described above.
2. In this case, there is also a small maximum-minimum range. We see a bearish gap. The TR is the absolute value of the difference between the current low and the previous close.
3. The third example shows that the current maximum-minimum range is still small, and although the absolute value of the difference between the current maximum and the previous close is also small,
it is greater than that range.
For tango, the TR reflects the range of movement that has taken place much more realistically than the simple minimum-maximum range. If we take for example the illustration 1 in the image above you
can see how the maximum-minimum range is small when in fact there has been a much greater movement that is reflected in the TR.
After explaining what is the TR, we can now define the ATR indicator. The ATR, as its name suggests (Average True Range), is the average true range calculated for a given period, typically this
period is 14.
ATR calculation
The most typical period to calculate the Average True Range (ATR) for any time frame is 14. Let’s see an example of a calculation for daily data. The calculation period will, therefore, be 14 days.
To calculate the ATR you must first calculate the TR. For the first day (first data) the TR is the maximum minus the minimum of the same day since it is the beginning of the series and there are no
previous data. To calculate the first ATR value we need to have as many previous TR data as the calculation period we are using, in this case, we need a minimum of 14 TR data, so we will obtain the
first ATR value at the end of day 14 (including the TR of the day 14). This first data is the simple average of the TR of the previous 14 days. For the following data of the ATR, Wilder added a
calculation formula in which he incorporated the ATR from the previous session, thus softening the results obtained. The calculation for the following sessions is:
((ATRprev x 13) + TRp)/14
ATRprev is the ATR value from the previous session, which is multiplied by 13 and the closest TR value is added to the result. All this is divided by 14.
As you have read, there is always a start for the calculation of the ATR in which the values are not calculated in the same way as the following. This fact makes that the current value of the ATR
obtained vary depending on how much historical data you have. However, the difference will not be very large if you compare the ATR calculated from data of 500 sessions with an ATR obtained from data
of 600 sessions, but this difference can be significant if you compare the current ATR obtained with data from 30 sessions or 500.
The calculations made in this table correspond to the ATR shown in the following chart:
Uses of the Average True Range (ATR)
As an indicator based on volatility, like the Bollinger bands, the ATR does not predict (nor can it predict) direction or duration of a trend, but rather measures market activity and volatility.
• High ATR values indicate high activity in the market and, therefore, that price movements have high volatility. Very high values occur as a result of a large rise or fall in price and it is
highly unlikely that the ATR will remain at high values for a long time.
• Low ATR values indicate little activity and volatility, a calm market in which movements will be short.
• Long-term low ATR values indicate price consolidation and maybe the starting or continuing point of a trend.
In the following image, you can see a M30 price chart of the EUR/USD pair. Look at the ATR’s high and low marks and see how both high and low ATR values can denote a turn in the trend direction.
Also, note how the market has little activity when the ATR decreases and how a continuation or trend change follows.
How to use stop loss orders based on the ATR?
Expert traders consider that supports and resistances can be used, among other things, to establish stop loss orders. However, there are also other tools that allow the stop loss to be established in
a more objective way, based on market volatility. For this purpose, the ATR can be considered quite useful. For example, we can use this indicator to place a stop loss equal to 25% of the daily ATR
for a given trade. Let suppose that the ATR reported that day a valued of 140, therefore, we are going to calculate 25% of that value, which gives us 140 x 0.25 = 35 pips. Already acquired this
information you could place a “Stop Loss Order” of 35 pips from your entry point. Based on this result, we can place the stop loss 35 pips from the entry point for that position.
We can also use multiples of the ATR to determine market exit points. For example, the Chandelier stop is a technique that can also be used to define stop loss levels based on market volatility.
This is just an example of how to use the ATR to trade in the market, but the general idea can be applied to trade in other scenarios. Just remember that the ATR is a measure of the market
volatility, no of its trend. | {"url":"https://www.forexdominion.com/average-true-range-atr.html","timestamp":"2024-11-09T09:19:16Z","content_type":"text/html","content_length":"91723","record_id":"<urn:uuid:0cb93dac-89ee-416c-bd8b-eb7c2ebcf10a>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00563.warc.gz"} |
Introduction Class 11 Statistics Notes And Questions
Please refer to Introduction Class 11 Statistics notes and questions with solutions below. These Class 11 Statistics revision notes and important examination questions have been prepared based on the
latest Statistics books for Class 11. You can go through the questions and solutions below which will help you to get better marks in your examinations.
Class 11 Statistics Introduction Notes and Questions
1. CONCEPT OF ECONOMICS
We advise the young learners of Class XI to comprehend the concept of economics through the following discussion relating to ordinary (or routine) business (or activities) of our life.
Every individual, ranging from a child to an old man, is engaged in some economic activity or the other. Consumption is an important economic activity; and we all are consumers, consuming different
goods and services for the satisfaction of our wants.
Who is a Consumer?
A consumer is one who consumes goods and services for the satisfaction of his wants.
What is Consumption?
Consumption is the process of using up utility value of goods and services for the direct satisfaction of our wants. Utility value of goods means inherent capacity of goods and services to satisfy
human wants.
Production is another economic activity, and many of us are producers, engaged in the production of different goods and services for the generation of income.
Who is a Producer?
A producer is one who produces and/or sells goods and services for the generation of income.
What is Production?
Production is the process of converting raw material into useful things. Things become useful as they acquire utility value in the process of production.
Saving and investment are also economic activities, and many of us are savers and investors. We save a part of our income for future consumption or for investment in shares and bonds to generate
What is Saving?
It is that part of income which is not consumed. It is an act of abstinence from consumption.
What is Investment?
It is expenditure by the producers on the purchase of such assets which help to generate income.
Thus, we are consumers, producers, savers and investors. We are all engaged in diverse economic activities. Economic activities include consumption, production, saving,
investment, and many more.
What is Economic Activity?
It is an activity which is related to the use of scarce means (also called scarce resources).
Means are always scarce in relation to our wants. Imagine yourself as the richest person on the earth. Still you can’t have everything you wish to have at a point of time. It implies the scarcity of
your means/ resources in relation to your wants.
Engaged in diverse economic activities, we are performing ‘ordinary business of life’, according to Alfred Marshall, a great pro founder of Modern Economics. Thus, he defines economics as “the study
of mankind in the ordinary business of life.”
Scarcity is the Undercurrent of Economic Problem and therefore of Economics
Resources are always scarce in relation to our wants. Also, resources have alternative uses: A ten-rupee note in your pocket may be spent on a cup of coffee or a cold drink. Likewise, a worker may
render his services in factory A, rather than B and C. Because, resources are scarce and have alternative uses, we cannot escape from the problem of allocation of limited means to alternative uses.
This is what we call economic problem or the problem of choice.
What is Economic Problem?
It is the problem of choice (or the problem of allocating scarce resources to alternative uses) arising on account of the fact that resources are scarce and these have alternative uses.
Economics is essentially the study of economic problems that we must confront owing to the fact that our means are scarce in relation to our wants, and that the means have alternative uses. If there
is no scarcity, there is no economic problem, and there is no economics if there is no economic problem. Thus, Robbins defines economics as “A science that studies human behaviour as a relationship
between ends and scarce means which have alternative uses.”
Three Distinct Components of Economics: Consumption, Production and Distribution Consumption
Here, we, as students of economics, study behaviour of human beings as consumers or buyers of different goods and services for the satisfaction of their wants. As consumers, people have limited
means, while their wants are unlimited. How do they allocate their given means (or income) to the purchase of different goods and services, (given their market prices) so that their satisfaction is
maximised? This is the study of consumption or the study of consumer behaviour. When we formulate a set of standard relationships (like the inverse elationship between price of good and its purchase)
explaining how consumers tend to behave, we call it consumption theory.
Producers also have limited means while they have a wide range of goods and services to choose from for their firms and factories. Given prices of different inputs, how do they choose such
combination(s) which are least expensive, so that they are able to minimise their cost of production. Also, given prices of different goods, how do they choose to produce those, the production of
which offers them maximum revenue, so that their profit (profit = revenue – costs) is maximised. This is the study of production, or the study of producers’ behaviour. When we formulate a set of
standard relationships (like greater the productivity of a factor, greater is its employment) explaining the behaviour of producers or their production decisions, we call it production theory.
As students of economies we are also interested in knowing how income (generated in the process of production) is distributed among those who have worked as agents of production. Who are agents of
production? These are owners of factors of production, viz. land, labour, capital and entrepreneurship. A part of income generated will go to the owners of land (used in production) in the form of
rent; a part will go to labourers (for rendering their services) in the form of wage; a part will go to the owners of capital (used in production) in the form of interest; and a part will go to the
entrepreneurs in the form of profits. Distribution of income refers to the distribution of GDP (gross domestic product) among the owners of the factors of production (land, labour, capital and
entrepreneurship). What are the economic principles on the basis of which income is distributed among owners of the factors of production? Such a study is called distribution theory in economics.
Besides these three major components of economics, the economists also address such questions which are of social significance, like the question of poverty and unemployment, the question of growth
with social justice and the question of environmental degradation as linked to various economic activities. Issues of social significance or collective significance are categorised as issues of
macroeconomics. These are distinct from the issues of microeconomics which revolve around the problems of choice confronted by microeconomic units like a household, a firm or an industry.
Microeconomics and Macroeconomics
Microeconomics deals with economic issues or economic problems related to microeconomic units like a household, a firm or an industry. These issues and problems are studied and addressed largely with
a view to maximising individual welfare. Macroeconomics deals with economic issues or economic problems at the level of economy as a whole. These issues or problems are studied and addressed keeping
in mind the goals of social welfare or collective welfare.
2. WHAT IS STATISTICS?
Even to a layman this should not be a difficult question. If asked to define Statistics, we can expect a layman to say that Statistics is something like a store of quantitative information. Yes, it
is true. Statistics means quantitative information or quantification of the facts and findings. But, how do we get quantitative information? There must be a system, method or technique to collect
quantitative information. Also, statistical information may be a raw information. It needs to be classified, tabulated or it needs to be systematically presented. One must learn the system of
presentation and classification of data. Also, there must be a set of methods and techniques to condense the data. May be, we find averages or percentages. And above all, there must be a set of
methods or techniques on the analysis and interpretation of quantitative information. A student of economics has to study all these methods and techniques to understand and master the subject matter
of Statistics.
Thus, unlike a layman, a student of economics cannot relax taking Statistics just as a pool of quantitative information. Instead he is also to look into the methods or techniques relating to its
collection, classification, presentation, analysis as well as interpretation.
In view of such a vastness of the subject matter, Statistics is defined both in singular sense and plural sense, as under:
Statistics—A Plural Noun
In its plural sense, Statistics refers to information in terms of numbers or numerical data, such as Population Statistics, Employment Statistics, Statistics concerning Public Expenditure, etc.
However, any numerical information is not Statistics. Example: Ram gets Rs. 100 per month as pocket allowance is not Statistics (it is neither an aggregate nor an average) whereas average pocket
allowance of the students of Class X is Rs. 100 per month, or there are 80 students in Class XI compared to just 8 in Class XII of your school are Statistics.
The following table shows a set of data which is Statistics, and another set which is not Statistics. The figures used are hypothetical.
Distinction between Quantitative and Qualitative Data
This is related to the distinction between quantitative variables and qualitative attributes. There are quantitative variables like income, expenditure and investment which can be expressed in
numerical terms, viz., per capita income in India was (say) Rs. 40,000 per month, per capita expenditure was (say) Rs. 30,000 per month, and net investment (or capita formation) was (say) Rs. 10,000
crore in the year 2017-18. All such data are called quantitative data. On the other hand, there are qualitative attributes like ‘IQ’ level of different individuals or beauty of the individuals which
cannot be expressed in numerical terms.
These attributes refer to qualitative characteristics of the objects. These can be ranked or rated as good, very good, or excellent. We may give them ranks as 1, 2, 3, etc. All such data are called
qualitative data. Briefly, while quantitative data refers to quantitative variables, qualitative data refers to qualitative attributes of the different objects.
All Statistics are data, but all data are not Statistics.
In its plural sense, this is how Statistics is defined by different authors:
“Statistics are numerical statements of facts in any department of enquiry placed in relation to each other. ” —Bowley
“By Statistics we mean quantitative data affected to a marked extent by multiplicity of causes. ” —Yule and Kendall
Features or Characteristics of Statistics in the Plural Sense or as Numerical Data
Main characteristics of Statistics in terms of numerical data are as follows:
(1) Aggregate of Facts: A single number does not constitute Statistics. No conclusion can be drawn from it. It is only the aggregate number of facts that is called Statistics, as the same can be
compared and conclusions can be drawn from them. For example, if it is stated that there are 1,000 students in our college, then it has no statistical significance. But if it is stated that there are
300 students in arts faculty, 400 in commerce faculty and 300 in science faculty in our college, it makes statistical sense as this data conveys statistical information. Similarly, if it is stated
that population of India is 121 crore or that the value of total exports from India is Rs. 14,41,420 crore, then these aggregate of facts will be termed as Statistics. It can, therefore, be concluded
‘All Statistics are expressed in numbers but all numbers are not Statistics’.
(2) Numerically Expressed: Statistics are expressed in terms of numbers. Qualitative aspects like ‘small’ or ‘big’; ‘rich’ or ‘poor’; etc. are not called Statistics. For instance, to say, Irfan
Pathan is tall and Sachin is short, has no statistical sense. However, if it is stated that height of Irfan Pathan is 6 ft and 2-inches and that of Sachin is 5 ft and 4-inches, then these numericals
will he called Statistics.
(3) Multiplicity of Causes: Statistics are not affected by any single factor; but are influenced by many factors. Had they been affected by one factor alone then by removing that factor they would
lose all their significance. For instance, 30 per cent rise in prices may have been due to several causes, like reduction in supply, increase in demand, shortage of power, rise in wages, rise in
taxes, etc.
(4) Reasonable Accuracy: A reasonable degree of accuracy must be kept in view while collecting statistical data. This accuracy depends on the purpose of investigation, its nature, size and available
(5) Mutually related and Comparable: Such numericals alone will be called Statistics as are mutually related and comparable. Unless they have the quality of comparison they cannot be called
For example, if it is stated “Ram is 40 years old, Mohan is 5 ft tall, Sohan has 60 kg of weight”, then these numbers will not be called Statistics, as they are not mutually related nor subject to
comparison. However, if the age, height and weight of all the three are inter-related, then the same will be considered as Statistics.
(6) Pre-determined Objective: Statistics are collected with some pre-determined objective. Any information collected without any definite objective will only be a numerical value and not Statistics.
If data pertaining to the farmers of a village is collected, there must be some pre-determined objective. Whether the Statistics are collected for the purpose of knowing their economic position, or
distribution of land among them or their total population, or for any other purpose, all these objectives must be pre-determined.
(7) Enumerated or Estimated: Statistics may be collected by enumeration or are estimated. If the field of investigation is vast, the procedure of estimation may be helpful. For example, 1 lakh people
attended the rally addressed by the Prime Minister in Delhi and 2 lakh in Mumbai. These Statistics are based on estimation. As against it, if the field of enquiry is limited, the enumeration method
is appropriate. For example, it can be verified by enumeration whether 20 students are present in the class or 10 workers are working in the factory.
(8) Collected in a Systematic Manner: Statistics should be collected in a systematic manner. Before collecting them, a plan must be prepared. No conclusion can be drawn from Statistics collected in
haphazard manner. For instance, data regarding the marks secured by the students of a college without any reference to the class, subject, examination or maximum marks, etc., will lead to no
conclusion. In short, it can safely be concluded that “all numerical data cannot be called Statistics but all Statistics are called numerical data. ”
Statistics-A Singular Noun
In the singular sense, Statistics means science of Statistics or statistical methods. It refers to techniques or methods relating to collection, classification, presentation, analysis and
interpretation of quantitative data.
Focus of the Study
Statistics as a singular noun is focus of the study for the students of Class XI. You are to learn and understand how to collect data, organise data, present data as well as analyse and interpret
“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data. ” —Croxton and Cowden
“Statistics is the science which deals with the collection, classification and tabulation of numerical facts as a basis for the explanation, description and comparison of phenomena. ” —Lovitt “
Statistics is the science which deals with the methods of collecting, classifying, presenting, comparing and. interpreting numerical data, collected to th row some light on any sphere of enquiry. ”
Stages of Statistical
Study Studying Statistics as a singular noun implies the knowledge of various stages of statistical study. These stages are:
Obviously, at the first stage, we collect statistical data. Second, we organise the data in some systematic order. Third, we present the data in the form of graphs, diagrams or tables. Fourth, we
analyse the data in terms of averages or percentages. Fifth, and finally, we interpret the data to find certain conclusions.
Statistical Tools
Each stage of the statistical study involves the use of certain standard techniques or methods. These techniques or methods are called statistical tools. Thus, there are statistical tools used for
the collection of data, like the ‘Sample’ and ‘Census’ techniques. Array of data and tally bars are the standard techniques used for organisation of data. Tables, graphs and diagrams are the
well-known statistical tools for the presentation of data.
Averages and percentages are the commonly used techniques for the analysis of data. Interpretation of data is often done in terms of the magnitude of averages, percentages or coefficients of
correlation/regression. The following table gives an overall view of the various stages of statistical study and the related sets of statistical tools.
What are Statistical Tools? These refer to the methods or techniques used for the collection, organisation and presentation of data, as well as for the analysis and interpretation of data.
Stages of Statistical Study and the Related Statistical Tools
3. SCOPE OF STATISTICS
Study of the scope of statistics includes:
(1) Nature of Statistics,
(2) Subject Matter of Statistics, and
(3) Limitations of Statistics.
Nature of Statistics
Here, the basic question is whether Statistics is a science or an art. Prof. Tippet, has rightly observed that “Statistics is both a science as well as an art.” As a science, Statistics studies
numerical data in a scientific or systematic manner. As an art, Statistics relates to quantitative data to the real life problems. By using statistical data, we are able to analyse and understand
real life problems much better than otherwise. Thus, the problem of unemployment in India is more meaningfully analysed when the size of unemployment is supported with quantitative data.
Subject Matter of Statistics
Subject matter of statistics includes two components: Descriptive Statistics and Inferential Statistics.
The Concept of Universe or Population
It should be interesting for the students of Clsss XI to note that the concept of universe or population has a specific meaning in Statistics. It refers to the aggregate of all items or units
relating to your statistical study. Example:
Universe or population size is 1,000 if you are studying 1,000 students for your statistical study.
(1) Descriptive Statistics: Descriptive Statistics refers to those methods which are used for the collection, presentation as well as analysis of data. These methods relate to such estimations as
‘measurement of central tendencies’ (average mean, median, mode), ‘measurement of dispersion’ (mean deviation, standard deviation, etc.), ‘measurement of correlation’, etc. Example: Descriptive
statistics is used when you estimate average height of the secondary students in your school. Likewise, descriptive statistics is used when you find that marks in science and mathematics of the
students in all classes are intimately related to each other.
(2) Inferential Statistics: Inferential Statistics refers to all such methods by which conclusions are drawn relating to the universe or population on the basis of a given sample. (In Statistics, the
term universe or population refers to the aggregate of all items or units relating to any subject.) For example, if your class teacher estimates average weight of the entire class (called universe or
population) on the basis of average weight of only a sample of students of the class, he is using inferential statistics.
Limitations of Statistics
In modern times. Statistics has emerged to be of crucial significance in all walks of life. However, it has certain limitations. Thus, writes Newshome that, “Statistics must be regarded as an
instrument of research of great value but barring severe limitations which are not possible to overcome.” Following are some notable limitations of Statistics:
(1) Study of Numerical Facts only: Statistics studies only such facts as can be expressed in numerical terms, it does not study qualitative phenomena like honesty, friendship, wisdom, health,
patriotism, justice, etc.
(2) Study of Aggregates only: Statistics studies only the aggregates of quantitative facts. It does not study statistical facts relating to any particular unit. Example: It may be a statistical fact
that your class teacher earns Rs. 50,000 per month. But, as this fact relates to an individual, it is not to be deemed as a subject matter of Statistics. However, it becomes a subject matter of
Statistics if we study income of school teachers across all parts of the country, for purpose of finding regional differences in income.
(3) Homogeneity of Data, an essential Requirement: To compare data, it is essential that statistics are uniform in quality. Data of diverse qualities and kinds cannot be compared. For example,
production of food grains cannot be compared with the production of cloth. It is because cloth is measured in meters and food grains in tonnes. Nevertheless, it is possible to compare their value
instead of the volume.
(4) Results are True only on an Average: Most statistical findings are true only as averages. They express only the broad tendencies. Unlike the laws of natural sciences, statistical observations are
not error-free. They are not always valid under all conditions. For instance, if it is said that per capita income in India is Rs. 50,000 per annum, it does not mean that the income of each and every
Indian is Rs. 50,000 per annum. Some may have more and some may have less,
(5) Without Reference, Results may Prove to be Wrong: In order to understand the conclusions precisely, it is necessary that the circumstances and conditions under which these conclusions have been
drawn are also studied. Otherwise, they may prove to be wrong.
(6) Can be used only by the Experts: Statistics can be used only by those persons who have special knowledge of statistical methods. Those who are ignorant about these methods cannot make sensible
use of statistics. It can, therefore, be said that data in the hands of an unqualified person is like a medicine in the hands of a quack who may abuse it, leading to disastrous consequences. In the
words of Yule and Kendall, “Statistical methods are most dangerous tools in the hands of an inexpert.”
(7) Prone to Misuse: Misuse of Statistics is very common. Statistics may used to support a pre-drawn conclusion even when it is absolutely false. It is usually said, “Statistics are like clay by
which you can make a god or a devil, as you please.” Misuse of statistics is indeed its greatest limitation.
Following words of Prof. Tippet very aptly capture the importance of Statistics in economics: “A day might come when the department of economics in the universities will go out of the control of
economic theoreticians and come under the control of statistical workshops, in the same manner as the department of physics and chemistry have come under the control of experimental laboratories.”
Indeed, Statistics has emerged as the lifeline of economics. It is because of the growing use of Statistics by the economists that the subjects like econometrics have been added to the horizons of
economics. Students of Class XI may note the following points to highlight the significance (functions and importance) of Statistics in economics.
(1) Quantitative Expression of Economic Problems:
Consider any economic problem, be it the problem of unemployment, the problem of price rise or the problem of shrinking exports. The first task of the economists is to understand its magnitude
through its quantitative expression.
For example, if it is the problem of unemployment, we make its quantitative expression stating that (say) 20 per cent of the India’s working population is unemployed or that between the years
1995-2010 the percentage of unemployed working population has tended to increase from 18 per cent to 9.4 per cent.
(2) Inter-sectoral and Inter-temporal Comparisons: Economists do not stop merely at the quantitative expression of the problems. They would try to further comprehend it through inter-sectoral and
inter-temporal comparisons. From inter-sectoral comparisons we mean, comparisons across different sectors of the economy. Thus, analysing the problem of unemployment, the economists would like to
know the magnitude of unemployment across rural and urban sectors of the economy. They would like to know what percentage of rural population is unemployed compared to the urban population.
Inter-temporal comparison means understanding of change in the magnitude of the problem over time. This would mean making a comparison (say) over different plan periods of the rural and urban
(3) Working out Cause and Effect Relationship:
Economists try to find out cause and effect relationship between different sets of data. This enables them to attempt an effective diagnosis of the problem and accordingly to suggest some effective
remedies. Thus, through their statistical studies, if the economists come to know that it is because of the decline in demand that investment in the economy has tended to shrink, they can suggest the
government to adopt such measures as would increase the level of demand in the economy.
Two Important points on the Significance of Statistics in Economics
(i) Statistics facilitates inter-sectoral and inter-temporal comparison.
(ii) Statistics helps to establish cause and effect relationship between different economic variables that have facilitated the construction of economic theories.
(4) Construction of Economic Theories or Economic Models: What is economic theory? It is an established statistical relationship between different sets of statistical data, offering conclusions of
economic significance. The well-known inverse relationship between price of a commodity and its demand (i.e., more is purchased when price falls) is an established statistical relationship, and
therefore, is a part of economic theory. Is the construction of theoretical relationships or models possible without statistical experiments? Certainly not.
(5) Economic Forecasting: Economists do forecasting through statistical studies. By the term forecasting we do not mean some astrological predictions. We only mean to assess and ascertain the future
course of certain events which are of economic significance. Thus, on studying the behaviour of price level over several years, the economists can make statistical forecasting about the likely trend
or pattern of the price level in the near future. This helps us in future planning.
(6) Formulation of Policies: How does the finance minister decide to increase or decrease taxation as a source of government revenue? Obviously through statistical studies. It is through statistical
investigations that the finance minister gets a feedback on the taxpaying capacity of the people, and revenue needs of the government. Accordingly, tax rates are fixed to get maximum possible revenue
with minimum possible discomfort to the people.
(7) Economic Equilibrium: What is economic equilibrium? It is a state of balance for the producer or the consumer where the producer finds that his profits are maximum or where the consumer finds
that his satisfaction is maximum. It is through the use of statistical methods that the economists have evolved some eco-fundamentals (which you will study in Class XII) telling us how profits of the
producers are maximised or how consumers get maximum satisfaction. Thus, so much is the significance of Statistics in economics that Marshall (a great economist of the past century) had to concede
that “Statistics are the straw out of which I, like every other economist, have to make bricks.” Surely, Statistics is the hub of the wheel of economic studies, and the beginners of Class XI must
focus on the hub to precisely understand the movement of the entire wheel.
Statistical Methods are No Substitute for Common Sense
This is a statement of caution to the students of Statistics. It urges the students not to use Statistics devoid of their common sense. You may find some spurious relationships, like larger the
number of doctors in an area greater are the deaths in that area. It may be true statistically, but does not match with common sense. Hence, never propagate any statistical conclusion in case it
offends your common sense. Likewise, average size of shoes for the 50 students in your class may be ‘six’. But it would be foolish if the school authorities place an order of 50 shoes of the size-six
for all of you. Surely this size may not fit many of you.
Distrust of Statistics
Some people have misgivings about Statistics and make observations like the following:
(i) Statistics is a rainbow of lies.
(ii) Statistics are tissues of falsehood.
(iii) Statistics can prove anything.
(iv) Statistics cannot prove anything.
(v) Statistics are like clay of which you can make a god or a devil, as you please.
According to Disraeli, “There are three kinds of iies-lies, damned lies and Statistics.”
Indeed, one can present statistical information in a manner that tends to distort the facts and thereby mislead the people. For instance, the government claimed that in 2018, per capita income in
India increased by about 17 per cent. On the other hand, the opposition party claimed that in 2018, per capita income increased by 5 per cent only. But the difference lies in the fact that whereas
government estimates are based on current prices, those of the opposition party are based on the 2011-12 prices, it is difficult for a layman to understand this difference. He will just be confused
or perhaps be fooled by the claims and counterclaims of the government and the opposition party.
What Causes Distrust?
Distrust of Statistics arises not because there is anything wrong with Statistics as a subject matter. It arises because the users of Statistics tend to manipulate it to suit or support their
pre-drawn conclusions or observations. Main causes for the distrust of Statistics are as under:
(i) Different kinds of Statistics are obtained in respect of a given problem.
(ii) Statistics can be altered to match the predetermined conclusions.
(iii) Authentic Statistics can also be presented in such a manner as to confuse the reader.
(iv) When Statistics are collected in a partial manner, the results are generally wrong. Consequently, people lose faith in them.
However, it may be noted that if Statistics are presented wrongly, then the fault does not lie with Statistics as a subject matter. The fault lies with those people who collect wrong Statistics or
those who draw wrong conclusions. Statistics, as such, do not prove anything. They are simply tools in the hands of the statisticians. If a statistician misuses the data, then the blame lies squarely
on him and not on the subject matter, A competent doctor can cure a disease by making good use of the medicine but the same medicine in the hands of an incompetent doctor becomes a poison. The fault
in this case is not of the medicine but of the unqualified doctor. In the same way, Statistics is never faulty but the fault lies with the users.
In fact, Statistics should not be relied upon blindly nor distrusted outright. “Statistics should not be used as a blind man uses a lamp post for support rather than for illumination, whereas its
real purpose is to serve as illumination and not as a support.”
In making use of Statistics one should be cautious and vigilant. In the words of King, “The science of Statistics is the most useful servant, but only of great value to those who understand its
proper use.”
It is the duty of the students of economics to make use of know-how of Statistics to discover the truth rather than to cover the truth.
How to Remove Distrust?
Following are some essential remedies of the distrust of Statistics:
(i) Consideration of Statistical Limitations: While making use of Statistics, limitations of Statistics must be taken care of.
(ii) No Bias: The user should be impartial. He should make use only of the relevant data and draw conclusions without any bias or prejudice.
(iii) Application by Experts: Statistics should be used only by the experts to minimise the possibility of misuse. | {"url":"https://www.cbsencertsolutions.com/introduction-class-11-statistics-notes-and-questions/","timestamp":"2024-11-06T20:22:34Z","content_type":"text/html","content_length":"168073","record_id":"<urn:uuid:bd80eb43-f6b2-4e7f-865d-f6914bda7f38>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00589.warc.gz"} |
From Dance Artist to Schrodinger's Lover
As I sat in the library, struggling through first-semester chemistry, I began chapter 6, Quantum Chemistry. Here I was, a former ballet dancer with a B.A. in dance, turned nontraditional pre-med
student earning her second degree, who wouldn't have been caught dead in a science course 5 years before.
Then comes Schrödinger...
Or rather, the Schrödinger equation.
Now before your eyes glaze over, the first thing to keep in mind is that mathematics is a language, and there are folks who spend a lifetime learning how to understand and use it. The fact that this
may look like Greek to you is completely normal. All this equation says is, (on the left), is the potential and kinetic energy of some quantum system, like light, an electron, or even a crystal, is
equal to (on the right) the total energy of that system. I'll go into the deeper subtleties in another blog post.
I was so fascinated by this equation that I naively tried to solve this equation having only completed a pre-calculus course, which is four courses behind the math skills needed. Nevertheless, by the
time I stopped trying to solve this equation to finish the studying this chapter, the physics seed had been planted.
And so I switched and am now earning a B.S. in physics and computational math. The transition wasn't easy and required mental shifts I hadn't anticipated that I will also go into a future blog posts,
but is hands down the best life decision I've made.
So here's to becoming one of the next of too few Black woman physicists. Stay tuned... | {"url":"https://www.latoyascisoftwaredev.com/post/from-dance-artist-to-schrodinger-s-lover","timestamp":"2024-11-03T20:06:50Z","content_type":"text/html","content_length":"1050499","record_id":"<urn:uuid:cbad79bd-a4dc-4688-9779-4c0a49b1747a>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00115.warc.gz"} |
Astronomical Units to Perch Converter
Enter Astronomical Units
β Switch toPerch to Astronomical Units Converter
How to use this Astronomical Units to Perch Converter π €
Follow these steps to convert given length from the units of Astronomical Units to the units of Perch.
1. Enter the input Astronomical Units value in the text field.
2. The calculator converts the given Astronomical Units into Perch in realtime β using the conversion formula, and displays under the Perch label. You do not need to click any button. If the input
changes, Perch value is re-calculated, just like that.
3. You may copy the resulting Perch value using the Copy button.
4. To view a detailed step by step calculation of the conversion, click on the View Calculation button.
5. You can also reset the input by clicking on button present below the input field.
What is the Formula to convert Astronomical Units to Perch?
The formula to convert given length from Astronomical Units to Perch is:
Length[(Perch)] = Length[(Astronomical Units)] / 3.361812555665857e-11
Substitute the given value of length in astronomical units, i.e., Length[(Astronomical Units)] in the above formula and simplify the right-hand side value. The resulting value is the length in perch,
i.e., Length[(Perch)].
Calculation will be done after you enter a valid input.
Consider that the average distance from Earth to the Sun is 1 astronomical unit (AU).
Convert this distance from astronomical units to Perch.
The length in astronomical units is:
Length[(Astronomical Units)] = 1
The formula to convert length from astronomical units to perch is:
Length[(Perch)] = Length[(Astronomical Units)] / 3.361812555665857e-11
Substitute given weight Length[(Astronomical Units)] = 1 in the above formula.
Length[(Perch)] = 1 / 3.361812555665857e-11
Length[(Perch)] = 29745858326.1771
Final Answer:
Therefore, 1 AU is equal to 29745858326.1771 perch.
The length is 29745858326.1771 perch, in perch.
Consider that the distance from Earth to Mars at its closest approach is approximately 0.5 astronomical units (AU).
Convert this distance from astronomical units to Perch.
The length in astronomical units is:
Length[(Astronomical Units)] = 0.5
The formula to convert length from astronomical units to perch is:
Length[(Perch)] = Length[(Astronomical Units)] / 3.361812555665857e-11
Substitute given weight Length[(Astronomical Units)] = 0.5 in the above formula.
Length[(Perch)] = 0.5 / 3.361812555665857e-11
Length[(Perch)] = 14872929163.0886
Final Answer:
Therefore, 0.5 AU is equal to 14872929163.0886 perch.
The length is 14872929163.0886 perch, in perch.
Astronomical Units to Perch Conversion Table
The following table gives some of the most used conversions from Astronomical Units to Perch.
Astronomical Units (AU) Perch (perch)
0 AU 0 perch
1 AU 29745858326.1771 perch
2 AU 59491716652.3542 perch
3 AU 89237574978.5313 perch
4 AU 118983433304.7085 perch
5 AU 148729291630.8856 perch
6 AU 178475149957.0627 perch
7 AU 208221008283.2398 perch
8 AU 237966866609.4169 perch
9 AU 267712724935.594 perch
10 AU 297458583261.7711 perch
20 AU 594917166523.5422 perch
50 AU 1487292916308.8557 perch
100 AU 2974585832617.7114 perch
1000 AU 29745858326177.113 perch
10000 AU 297458583261771.1 perch
100000 AU 2974585832617711.5 perch
Astronomical Units
An astronomical unit (AU) is a unit of length used in astronomy to measure distances within our solar system. One astronomical unit is equivalent to approximately 149,597,870.7 kilometers or about
92,955,807.3 miles.
The astronomical unit is defined as the mean distance between the Earth and the Sun.
Astronomical units are used to express distances between celestial bodies within the solar system, such as the distances between planets and their orbits. They provide a convenient scale for
describing and comparing distances in a way that is more manageable than using kilometers or miles.
A perch is a unit of length used primarily in land measurement and surveying. One perch is equivalent to 16.5 feet or approximately 5.0292 meters.
The perch is defined as 16.5 feet, which is the same length as a rod or a pole, and is used in various practical applications such as land measurement and construction.
Perches are used in land surveying, property measurement, and agricultural contexts. The unit provides a convenient measurement for shorter distances and has historical significance in land
measurement practices.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Astronomical Units to Perch in Length?
The formula to convert Astronomical Units to Perch in Length is:
Astronomical Units / 3.361812555665857e-11
2. Is this tool free or paid?
This Length conversion tool, which converts Astronomical Units to Perch, is completely free to use.
3. How do I convert Length from Astronomical Units to Perch?
To convert Length from Astronomical Units to Perch, you can use the following formula:
Astronomical Units / 3.361812555665857e-11
For example, if you have a value in Astronomical Units, you substitute that value in place of Astronomical Units in the above formula, and solve the mathematical expression to get the equivalent
value in Perch. | {"url":"https://convertonline.org/unit/?convert=astronomical_unit-perch","timestamp":"2024-11-10T20:34:12Z","content_type":"text/html","content_length":"92105","record_id":"<urn:uuid:3334718f-eec3-44fe-a6da-d432a23b8705>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00565.warc.gz"} |
Living Like an Asymptote - Indian Thoughts
The word ‘asymptote’ may appear strange to many, particularly to those who have not studied higher mathematics. Though the word finds a place in all English dictionaries, I feel it needs an
explanation. To understand ‘asymptote’, one has to understand certain mathematical terms. First the term ‘curve’ is to be understood. It is a geometrical figure following a defined relationship in
its two coordinates, a simple example of a curve being a circle. The second term to be understood is ‘tangent’. It is a line which meets the curve only at one point. Normally a line intersects a
curve at two or more points depending upon the shape of the curve, but when it intersects or meets only at one point, the same line becomes a tangent. We have two types of curves. Some have a finite
size while the others are infinite in size. The examples of finite size curves are a circle, an ellipse, etc., and the examples of infinite size curves are parabola, hyperbola, etc. Both types of
curves have tangents. In fact, each point on the curve can have a tangent and these tangents follow certain mathematical rules.
Of course, there are no such rules for lines which are not tangents. Having understood this, the term ‘asymptote’ can also be explained. An ‘asymptote’ is a line which is just like a tangent but is
not a tangent. This is so because the point of contact between an asymptote and the curve is at infinity. At infinity, the curve and the tangent merge into each other. Only a curve of infinite size
can have an ‘asymptote’. It is quite difficult to grasp the concept of contact at infinity as it is only creation of the
imagination. ‘Asymptotes’ also follow certain mathematical laws. I studied this concept about thirty years back and it fascinated me greatly. Generally, students found it too difficult to grasp, but
those who understood its concept, found it easy. I shall now relate the concept of tangent and asymptote with life in order to make it easy and interesting. The world we live in is like a limited
size curve. A person living a worldly life is like a line which is a non-tangent. He has no rules to guide him and follows the path which suits him at a particular point of time. In other words, he
lives a directionless
life, resulting in frequent intersection with the worldly curve which may be compared to the clashes or conflicts he comes across in his worldly life. The answer to this lies in living a properly
directed life so that life becomes a tangent to the world. It means that the contact with the world is reduced to just a point. Such a person has very few clashes or conflicts with the world and
leads a smooth life with the right direction. Tangents at various points means that it is possible to live smoothly, if one wishes to.
Having achieved this stage, one can switch on to a higher state of living. For this, one has to enlarge one’s vision to infinity. This is like shifting to infinite curves, from limited or finite
curves. While one can draw tangents on each point here, an asymptote can also be drawn on such curves, meaning that while the line goes along the curve, it does not touch it at all, at least in the
finite dimension. In terms of living, it is like living a life above the world. However, this is possible only when we have our vision
focused on infinity and is not possible in the case of finite vision. In such a state, there is no clash with the world and one can be above it while living in it. It is like the movement of a
hovercraft which is above the water despite being in it. A comparison can also be drawn with the meeting or merger of an asymptote with the curve. As said earlier, this is possible at the infinite
only. In terms of living it means that the ultimate aim of life is to achieve divinity, that is, to merge with the infinity. However, this is not possible as long as we identify ourselves only with
the body and remain limited in our vision. As the bodily sense reduces, the vision gets widened. If the physical consciousness goes completely, the vision becomes infinite and a complete merger which
is possible only after the body is gone, takes place. It is then like meeting or merging of an asymptote with the curve at infinite distance. This is, perhaps, the ultimate aim of living. The Creator
or God can be compared with an infinite curve. Let us try to become its asymptote so that all along we are with it, and the gap narrows as we go through the path of life and ultimately merge into it
when the body is totally gone. | {"url":"https://indianthoughts.in/living-like-an-asymptote/","timestamp":"2024-11-01T21:54:18Z","content_type":"text/html","content_length":"167272","record_id":"<urn:uuid:123f9811-4228-4ab6-b6e5-8c4285a3e1bb>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00682.warc.gz"} |