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seminars - Balanced wall for random groups
Gromov showed that one way to obtain a word-hyperbolic group is to choose a presentation "at random". I will survey random group properties in Gromov's model at various values of the density
parameter. We will then focus on Ollivier-Wise cubulation of random groups for density parameter <1/5. I will indicate how to construct new walls that work at higher densities. This is joint work
with John Mackay. | {"url":"https://www.math.snu.ac.kr/board/index.php?mid=seminars&l=en&sort_index=date&order_type=desc&page=85&document_srl=636033","timestamp":"2024-11-02T11:06:54Z","content_type":"text/html","content_length":"46535","record_id":"<urn:uuid:577115bb-b75f-403b-8d45-3e57c972a2dd>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00325.warc.gz"} |
A demo of K-Means clustering on the handwritten digits data
A demo of K-Means clustering on the handwritten digits data
A demo of structured Ward hierarchical clustering on an image of coins
A demo of structured Ward hierarchical clustering on an image of coins
A demo of the mean-shift clustering algorithm
A demo of the mean-shift clustering algorithm
Adjustment for chance in clustering performance evaluation
Adjustment for chance in clustering performance evaluation
Agglomerative clustering with and without structure
Agglomerative clustering with and without structure
Agglomerative clustering with different metrics
Agglomerative clustering with different metrics
An example of K-Means++ initialization
An example of K-Means++ initialization
Bisecting K-Means and Regular K-Means Performance Comparison
Bisecting K-Means and Regular K-Means Performance Comparison
Color Quantization using K-Means
Color Quantization using K-Means
Compare BIRCH and MiniBatchKMeans
Compare BIRCH and MiniBatchKMeans
Comparing different clustering algorithms on toy datasets
Comparing different clustering algorithms on toy datasets
Comparing different hierarchical linkage methods on toy datasets
Comparing different hierarchical linkage methods on toy datasets
Comparison of the K-Means and MiniBatchKMeans clustering algorithms
Comparison of the K-Means and MiniBatchKMeans clustering algorithms
Demo of DBSCAN clustering algorithm
Demo of DBSCAN clustering algorithm
Demo of HDBSCAN clustering algorithm
Demo of HDBSCAN clustering algorithm
Demo of OPTICS clustering algorithm
Demo of OPTICS clustering algorithm
Demo of affinity propagation clustering algorithm
Demo of affinity propagation clustering algorithm
Demonstration of k-means assumptions
Demonstration of k-means assumptions
Empirical evaluation of the impact of k-means initialization
Empirical evaluation of the impact of k-means initialization
Feature agglomeration
Feature agglomeration
Feature agglomeration vs. univariate selection
Feature agglomeration vs. univariate selection
Hierarchical clustering: structured vs unstructured ward
Hierarchical clustering: structured vs unstructured ward
Inductive Clustering
Inductive Clustering
K-means Clustering
K-means Clustering
Online learning of a dictionary of parts of faces
Online learning of a dictionary of parts of faces
Plot Hierarchical Clustering Dendrogram
Plot Hierarchical Clustering Dendrogram
Segmenting the picture of greek coins in regions
Segmenting the picture of greek coins in regions
Selecting the number of clusters with silhouette analysis on KMeans clustering
Selecting the number of clusters with silhouette analysis on KMeans clustering
Spectral clustering for image segmentation
Spectral clustering for image segmentation
Various Agglomerative Clustering on a 2D embedding of digits
Various Agglomerative Clustering on a 2D embedding of digits
Vector Quantization Example
Vector Quantization Example | {"url":"https://scikit-learn.org/1.4/auto_examples/cluster/index.html","timestamp":"2024-11-02T21:08:10Z","content_type":"text/html","content_length":"30735","record_id":"<urn:uuid:0afb30ae-5c76-4775-b8a4-5194383bdb32>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00343.warc.gz"} |
Read Кто Заплачет, Когда Ты Умрешь? Уроки Жизни От Монаха, Который Продал Свой ?феррари\\\'
Read Кто Заплачет, Когда Ты Умрешь? Уроки Жизни От Монаха, Который Продал Свой ?феррари\\'
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HP-80 CHS Exponent Curiosity
My one and only classic HP is an HP-80, like many with the 1247... serial number but the ROM chip shows a date of 1/73.
It exhibits a strage characteristic when in exponential display mode with a number less than 1, and CHS is pressed. Instead of only inserting a negative sign in the left-most position, it also
changes the exponential value to -99.
Toggling CHS leaves the exponential value at -99 but toggles the left-most negative sign as expected. However, pressing SAVE resets the exponential to the original value, switching back to decimal
display shows the correct value and calculations are correct even when the exponential value shows -99.
For an example keystrokes and display:
Power on " 0.00 "
.1 SAVE " 0.10 "
Shift 7 " 1. -01"
CHS "-1. -99"
Shift 2 "-0.10 "
So it seems the CHS induced exponential -99 display is just a display curiosity, but I cannot find any reference to it anywhere. Is this something other people have seen on the HP-80?
Kind regards, MAX
10-21-2013, 08:03 PM
HP's original serial number system used the four digit date code as the first week of production of machines of a particular revision level, rather than the week a particular unit was actually
manufactured. For calculators the production volume quickly ramped to a high enough rate to make that scheme unusable, so at some point before 1976, for calculators only, the scheme was changed to
have the date code reflect the actual production week, without regard to the revision level of the product.
10-21-2013, 08:29 PM
I don't remember coming across this before, but my early HP-80 and later one (with a "Hewlett Packard 80" nameplate on the front) both exhibit this same display problem. The HP-81 I have doesn't have
this issue, but the display system is somewhat different.
10-21-2013, 10:50 PM
I'm fairly certain that it's a firmware bug, and they probably fixed it before releasing the HP-81. It's possible that late production HP-80 units that used the quad ROMs (two HP-45/55/70 style DIPs
rather than a hybrid) might have it fixed, but I don't have such a unit to try.
10-22-2013, 02:39 PM
Thanks guys for the feedback. Maybe it should be added under the 'Bugs' section? | {"url":"https://archived.hpcalc.org/museumforum/thread-253502-post-253505.html","timestamp":"2024-11-13T12:37:31Z","content_type":"application/xhtml+xml","content_length":"41509","record_id":"<urn:uuid:5446a4f0-6c9d-4ae0-8d64-90ac8a23bdf7>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00733.warc.gz"} |
MaffsGuru.com - Making maths enjoyableIndex Laws 4 and 5
This video looks at the final two Index laws; namely, Index Law 4 and 5. These look at extending the laws we have previously discovered. Using Rule 3, we can adapt it to help us use index laws with
Fractions! I know .. who likes fractions, right? But I show how to make it easy with lots of worked examples and explanations which just make sense! | {"url":"https://maffsguru.com/videos/index-laws-4-and-5/","timestamp":"2024-11-14T08:24:40Z","content_type":"text/html","content_length":"29447","record_id":"<urn:uuid:90506926-f2c2-4028-80de-784dbacb68b9>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00431.warc.gz"} |
Tatakau is the Japanese verb for 'to fight', explained
What does “tatakau” mean in Japanese?
Native speakers say “tatakau” to mean ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese. Perhaps, some Japanese learners know this verb as it is sometimes used in Japanese movies, songs, novels,
manga, anime, and the like. In this blog post, however, I will explain this verb with its major conjugations. And also, I will explain how to use them through example sentences. My explanations would
help Japanese learners to use “tatakau” more properly. Then, let’s get started!
Definition and meanings of “tatakau”
Let me start with the definition and meanings of “tatakau”.
• tatakau – 戦う/闘う (たたかう) : a verb meaning ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
This verb has two different kanji expressions. The first one is more commonly used; the second one is used purposely for specific cases. Basically, therefore, we can focus on the first one.
The definition and meanings are not that difficult, I think. Then, let me explain how to use this verb through the example sentence below.
Example #1: how to say “fight” in Japanese
boku tachi wa kono uirusu to tatakau – 僕達はこのウイルスと戦う (ぼくたちはこのういるすとたたかう)
We fight against this virus.
Below are the new words used in the example sentence.
• boku – 僕 (ぼく) : a pronoun meaning ‘I’ in Japanese. This is used mainly by boys and young males.
• tachi – 達 (たち) : a suffix used after a noun or pronoun to make its plural form. In the example, this is used after “boku” to make its plural form, “boku tachi”, which means ‘we’ in Japanese.
Learn more about Japanese plural.
• wa – は : a binding particle working as a case marker or topic marker. In the example, this works after “boku tachi” to make the subject in the sentence.
• kono – この : a determiner used before a noun referring to a thing close to the speaker. In the example, this is used before “uirusu” to say “this virus” in Japanese.
• uirusu – ウイルス (ういるす) : a noun meaning ‘virus’ in Japanese. This is an imported word.
• to – と : a case particle used to say with whom someone does something. In the example, this is used after “kono uirusu” to indicate the object which the speakers fight against.
This is a typical usage of “tatakau”. In the example, it works together with the case particle, “to”, to have the object. This usage is worth knowing, I think. When we want to mean ‘to fight’ in
Japanese, anyway, this verb is a good option.
So far, I’ve explained the definition and meanings of “tatakau” and how to use it through the example sentence. In the rest part of this blog post, I will explain its major conjugations. The first
one is “tatakawanai”.
Tatakawanai: the nai form of “tatakau”
Below are the definition and meanings of “tatakawanai”.
• tatakawanai – 戦わない/闘わない (たたかわない) : the nai form of “tatakau”, which means ‘not to fight’, ‘not to battle’, or ‘not to contend’ in Japanese.
Grammatically, “tatakawanai” consists of the following two parts:
• tatakawa – 戦わ/闘わ (たたかわ) : one conjugation of “tatakau”. This can have a smooth connection with “nai”.
• nai – ない : an auxiliary verb used after a verb, adjective, or auxiliary verb to deny its meaning. Word orders in Japanese and English are different, but the role of this auxiliary verb is very
similar to that of “not”.
From these two parts, we can understand that “tatakawanai” is literally the nai form of “tatakau” and means ‘not to fight’, ‘not to battle’, or ‘not to contend’ in Japanese. Then, let me explain this
form through the example sentence below.
Example #2: how to say “don’t fight” in Japanese
watashi tachi wa shizen to tatakawanai – 私達は自然と戦わない (わたしたちはしぜんとたたかわない)
We don’t fight against nature.
Below are the new words used in the example sentence.
• watashi – 私 (わたし) : a pronoun meaning ‘I’ in Japanese.
• shizen – 自然 (しぜん) : a noun meaning ‘nature’ in Japanese.
This is a typical usage of “tatakawanai”. When we want to mean ‘not to fight’ in Japanese, this nai form is a good option.
Tatakaou: the volitional form of “tatakau”
Below are the definition and meanings of “tatakaou”.
• tatakaou – 戦おう/闘おう (たたかおう) : the volitional form of “tatakau”, which expresses volition to fight, battle, or contend.
Grammatically, “tatakaou” consists of the following two parts:
• tatakao – 戦お/闘お (たたかお) : one conjugation of “tatakau”. This can have a smooth connection with “u”.
• u – う : an auxiliary verb used after a verb to make its volitional form.
From these two parts, we can understand that “tatakaou” is literally the volitional form of “tatakau” and expresses volition to fight, battle, or contend. Then, let me explain how to use this form
through the example sentence below.
Example #3: how to say “let’s fight” in Japanese
kono byouki to tatakaou – この病気と戦おう (このびょうきとたたかおう)
Let’s fight against this disease!
Below is the new word used in the example sentence.
• byouki – 病気 (びょうき) : a noun meaning ‘disease’ or such in Japanese.
This is a typical usage of “tatakaou”. In this example, it works to make the suggestion. When we want to say “let’s fight” in Japanese, this volitional form is a good option.
Tatakaimasu: the masu form of “tatakau”
Below are the definition and meanings of “tatakaimasu”.
• tatakaimasu – 戦います/闘います (たたかいます) : the masu form of “tatakau”, which means ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
Grammatically, “tatakaimasu” consists of the following two parts:
• tatakai – 戦い/闘い (たたかい) : one conjugation of “tatakau”. This can have a smooth connection with “masu”.
• masu – ます : an auxiliary verb used after a verb to make it polite. Probably, this is well known as a part of Japanese masu form.
From these two parts, we can understand that “tatakaimasu” is literally the masu form of “tatakau” and means ‘to fight’, ‘to battle’, or ‘to contend’ politely in Japanese. Then, let me explain how to
use this form through the example sentence below.
Example #4: how to say “fight” politely in Japanese
kodomo tachi mo kono uirusu to tatakaimasu – 子供達もこのウイルスと戦います (こどもたちもこのういるすとたたかいます)
Children fight against this virus, too.
Below are the new words used in the example sentence.
• kodomo – 子供 (こども) : a noun meaning ‘child’ or ‘kid’ in Japanese. This can also work as plural.
• mo – も : a binding particle making the subject word or the object word in a sentence with adding the meaning of ‘also’, ‘as well’, or ‘too’. In the example, this works after “kodomo tachi” to
make the subject in the sentence with adding the meaning of ‘too’.
This is a typical usage of “tatakaimasu”. Its politeness has not been reflected in the English sentence, but the Japanese sentence sounds polite thanks to the masu form. When we want to say “fight”
politely in Japanese, this form is a very good option.
Tatakatta: the ta form of “tatakau”
Below are the definition and meanings of “tatakatta”.
• tatakatta – 戦った/闘った (たたかった) : the ta form of “tatakau”, which means ‘fought’, ‘battled’, or ‘contended’ in Japanese.
Grammatically, “tatakatta” consists of the following two parts:
• tatakat – 戦っ/闘っ (たたかっ) : one conjugation of “tatakau”. This can have a smooth connection with “ta”.
• ta – た : an auxiliary verb used after a verb, adjective, or auxiliary verb to make its past tense form. Probably, this is well known as a part of Japanese ta form.
From these two parts, we can understand that “tatakatta” is literally the ta form of “tatakau” and means ‘fought’, ‘battled’, or ‘contended’ in Japanese. Let me explain how to use it through the
example sentence below.
Example #5: how to say “fought” in Japanese
boku tachi wa yami no senshi to tatakatta – 僕達は闇の戦士と戦った (ぼくたちはやみのせんしとたたかった)
We fought against dark warriors.
Below are the new words used in the example sentence.
• yami – 闇 (やみ) : a noun meaning ‘darkness’ or ‘the dark’ in Japanese.
• no – の : a case particle used to join two nouns. Normally, the first one can work as a modifier to describe the second. In the example, this is used to join “yami” and “senshi”. The formed
phrase literally means ‘dark warriors’ in Japanese.
• senshi – 戦士 (せんし) : a noun meaning ‘soldier’ or ‘warrior’ in Japanese. This can also work as plural.
This is a typical usage of “tatakatta”. When we want to say “fought” in Japanese, this ta form is a good option.
Tatakatte: the te form of “tatakau”
Below are the definition and meanings of “tatakatte”.
• tatakatte – 戦って/闘って (たたかって) : the te form of “tatakau”, which means ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
Grammatically, “tatakatte” consists of the following two parts:
• tatakat – 戦っ/闘っ (たたかっ) : one conjugation of “tatakau”. This can have a smooth connection with “te”.
• te – て : a conjunctive particle used after a verb, adjective, or auxiliary verb to make its te form.
From these two parts, we can understand that “tatakatte” is literally the te form of “tatakau”. In Japanese, te-formed words have some important roles. One of them is make smooth connections of
words. So, “tatakatte” is very useful when we want to use “tatakau” in front of another verb, an adjective, or an auxiliary verb. Let me explain this usage through the example sentence below.
Example #6: how to say “fight and” in Japanese
hikari no senshi wa tokidoki yami no senshi to tatakatte taosu – 光の戦士は時々闇の戦士と戦って倒す (ひかりのせんしはときどきやみのせんしとたたかってたおす)
Light warriors sometimes fight against the dark warriors and beat them.
Below are the new words used in the example sentence.
• hikari – 光 (ひかり) : a noun meaning ‘light’ in Japanese.
• tokidoki – 時々 (ときどき) : an adverb of frequency meaning ‘sometimes’ in Japanese.
• taosu – 倒す (たおす) : a verb meaning ‘to beat’ or such in Japanese.
This is a typical usage of “tatakatte”. In this example, it has the smooth connection with “taosu”. When we want to use “tatakau” in front of another verb, its te form is very useful.
Tatakaeba: the ba form of “tatakau”
Below are the definition and meanings of “tatakaeba”.
• tatakaeba – 戦えば/闘えば (たたかえば) : the ba form of “tatakau”, which makes a conditional clause in a sentence with meaning ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
Grammatically, “tatakaeba” consists of the following two parts:
• tatakae – 戦え/闘え (たたかえ) : one conjugation of “tatakau”. This can have a smooth connection with “ba”.
• ba – ば : a conjunctive particle used after a verb, adjective, or auxiliary verb to make its ba form.
From these two parts, we can understand that “tatakaeba” is literally the ba form of “tatakau”. In Japanese, ba-formed words can work as their conditional forms. So, we can use “tatakaeba” to make a
conditional clause in a sentence with adding the meaning of ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese. Let me explain this usage through the example sentence below.
Example #7: how to say “if fight” in Japanese
ima tatakaeba, omae wa shinu – 今戦えば、お前は死ぬ (いまたたかえば、おまえはしぬ)
If you fight now, you’ll die.
Below are the new words used in the example sentence.
• ima – 今 (いま) : an adverb meaning ‘now’ in Japanese.
• omae – お前 (おまえ) : a pronoun rudely meaning ‘you’ in Japanese.
• shinu – 死ぬ (しぬ) : a verb meaning ‘to die’ in Japanese.
This is a typical usage of “tatakaeba”. In this example, it works as a part of the conditional clause, “ima tatakaeba”, which means ‘if you fight now’ in Japanese. When we want to make a conditional
clause in a sentence with adding the meaning of ‘to fight’, this ba form is a good option.
In this blog post, I’ve explained “tatakau” and its major conjugations. And also, I’ve explained how to use them through the example sentences. Let me summarize them as follows.
• tatakau – 戦う/闘う (たたかう) : a verb meaning ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
• tatakawanai – 戦わない/闘わない (たたかわない) : the nai form of “tatakau”, which means ‘not to fight’, ‘not to battle’, or ‘not to contend’ in Japanese.
• tatakaou – 戦おう/闘おう (たたかおう) : the volitional form of “tatakau”, which expresses volition to fight, battle, or contend.
• tatakaimasu – 戦います/闘います (たたかいます) : the masu form of “tatakau”, which means ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
• tatakatta – 戦った/闘った (たたかった) : the ta form of “tatakau”, which means ‘fought’, ‘battled’, or ‘contended’ in Japanese.
• tatakatte – 戦って/闘って (たたかって) : the te form of “tatakau”, which means ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
• tatakaeba – 戦えば/闘えば (たたかえば) : the ba form of “tatakau”, which makes a conditional clause in a sentence with meaning ‘to fight’, ‘to battle’, or ‘to contend’ in Japanese.
Hope my explanations are understandable and helpful for Japanese learners.
Learn more vocabulary on the app!
You can improve your Japanese vocabulary with our flashcards. | {"url":"https://japaneseparticlesmaster.xyz/tatakau-in-japanese/","timestamp":"2024-11-07T15:32:03Z","content_type":"text/html","content_length":"83569","record_id":"<urn:uuid:79a14875-0a0d-47f3-8d7e-bf71ee8a6932>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00688.warc.gz"} |
Examples of non-local time dependent or parabolic Dirichlet spaces
Colloquium Mathematicum 65 (1993), 241-265 DOI: 10.4064/cm-65-2-241-265
In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families $(E^{(τ)})_{τ ∈ ℝ}$ of Dirichlet forms. He developed a rather far-reaching and
general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M.
Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second order. To our knowledge, only very recently, when Y. Oshima in [20] was able to
construct a Markov process associated with a time dependent or parabolic Dirichlet space, these parabolic Dirichlet spaces attracted the attention of probabilists. The proof of the existence of such
a Markov process depends much on the potential theory developed by M. Pierre. Moreover, in [21] Y. Oshima proved that a lot of results valid for symmetric Dirichlet spaces (see [7] as a standard
reference) also hold for time dependent Dirichlet spaces. The purpose of this note is to give some concrete examples of time dependent Dirichlet spaces which are generated by pseudo-differential
operators and therefore are non-local. In Section 1 we recall the basic definition of a time dependent Dirichlet space and in Section 2 we give some auxiliary results. Sections 3-5 are devoted to
examples. In Section 3 we discuss some spatially translation invariant operators. We do not really give there any surprising examples, but we emphasize the relation to the theory of balayage spaces.
In Section 4 we consider time dependent Dirichlet spaces constructed from a special class of symmetric pseudo-differential operators analogous to those handled in our joint paper [9] with W. Hoh.
Finally, in Section 5 we construct time dependent generators of (symmetric) Feller semigroups following [15]. The estimates used in this construction already ensure that we get non-local time
dependent Dirichlet spaces. We would like to mention that non-local Dirichlet forms have recently been investigated by U. Mosco [19] in his study of composite media. | {"url":"https://www.impan.pl/en/publishing-house/journals-and-series/colloquium-mathematicum/all/65/2/107965/examples-of-non-local-time-dependent-or-parabolic-dirichlet-spaces","timestamp":"2024-11-04T02:05:09Z","content_type":"text/html","content_length":"43790","record_id":"<urn:uuid:60a119ff-edbd-4853-88cd-6ea5ee7ddcf1>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00414.warc.gz"} |
Characters, genericity, and multiplicity one for U(3)
Let ψ: U → ℂ^x be a generic character of the unipotent radical U of a Borel subgroup of a quasisplit p-adic group G. The number (0 or 1) of ψ-Whittaker models on an admissible irreducible
representation π of G was expressed by Rodier in terms of the limit of values of the trace of π at certain measures concentrated near the origin. An analogous statement holds in the twisted case.
This twisted analogue is used in [F, p. 47] to provide a local proof of the multiplicity one theorem for U(3). This asserts that each discrete spectrum automorphic representation of the quasisplit
unitary group U(3) associated with a quadratic extension E/F of number fields occurs in the discrete spectrum with multiplicity one. It is pointed out in [F, p. 47] that a proof of the twisted
analogue of Rodier's theorem does not appear in print. It is then given below. Detailing this proof is necessitated in particular by the fact that the attempt in [F, p. 48] at a global proof of the
multiplicity one theorem for U(3), although widely quoted, is incomplete, as we point out here.
Dive into the research topics of 'Characters, genericity, and multiplicity one for U(3)'. Together they form a unique fingerprint. | {"url":"https://cris.ariel.ac.il/en/publications/characters-genericity-and-multiplicity-one-for-u3-3","timestamp":"2024-11-03T09:38:02Z","content_type":"text/html","content_length":"52671","record_id":"<urn:uuid:34819df0-3c61-4f00-8c90-edf1ee8a2c64>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00406.warc.gz"} |
Flashcards - Honors Math
• 1. Volume of irregular shape (crown in tub, Eureka)
• 2. Single-handedly pull a ship to dock with pulley system.
• 3. Pulley networks used in war fare to pick up enemy ships and drop them.
• 4. Archimedean Screw to move water.
• 5. Rumor of using a system of mirrors to catch enemy ships on fire.
• 1. Measuring the volume of an irregular shape (crown in bath tub)
• 2. Archimedean screw
• 3. Pulley
• 1. Attacks by Arabs in 641 A.D.
• 2. Cairo was built in 969 A.D.
• 3. Shipping route discovered around the Cape of Good Hope
What is tallying, and why is it important in the development of early number systems?
Tallying is the method of makng notches to record how much of an item is present. They were used to record ownership of currency and items of trade before a simpler way of recording numbers was in
use. Tallies were used until the early 1800 in Britain to track money kept by clients in the bank. | {"url":"https://freezingblue.com/flashcards/119894/preview/honors-math","timestamp":"2024-11-13T02:02:08Z","content_type":"text/html","content_length":"17057","record_id":"<urn:uuid:d02af048-c077-492c-be28-c6824af19a7f>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00326.warc.gz"} |
Verifying Newton’s Second Law — Adam Cap
Verifying Newton’s Second Law
↘︎ … 2′ … download⇠ | skip ⇢
To determine the relationship between force, mass, and acceleration using a cart attached to a pulley with varying weights.
If the mass of the weights attached to the pulley is increased, the force exerted on the cart and the acceleration of the cart will also increase.
See attached sheet.
Weight of Cart and Sensor (N) 6.624
Weight of Cart System (kg) 0.6759
Weight of Pulley (g) 60 50 40 30 20 10
Force Exerted on Cart (N) 0.5472 0.4921 0.4059 0.3227 0.2321 0.1404
Average Acceleration of Cart (m/s^2) 0.8252 0.736 0.7222 0.4469 0.3395 0.2148
Weight of Cart and Sensor and 300 g (N) 9.718
Weight of Cart System (kg) 0.9916
Weight of Pulley (g) 60 50 40 30 20 10
Force Exerted on Cart (N) 0.588 0.5049 0.418 0.3323 0.2385 0.1442
Average Acceleration (m/s^2) 0.6655 0.5182 0.4263 0.3478 0.2633 0.1476
See attached sheets.
1. Is the graph of force vs. acceleration for the cart a straight line? If so, what is the value of the slope?
Yes, the graph produces nearly a straight line; the correlation for a linear fit is 0.9787. The value of the slope is 0.6129 N/(m/s^2).
2. What are the units of the slope of force vs. acceleration graph? Simplify the units of the slope to fundamental units (m, kg, s). What does the slope represent?
The units of the slope of force vs. acceleration are N/(m/s^2). This simplifies to kg. The slope represents the mass of the pulley.
3. What is the total mass of the system (both with and without extra weight) that you measured?
The total mass of the system without the extra weight was 0.6759 kg and the mass of the system with the extra weight (300 g) was 0.9916 kg, which seems to make sense. 0.9916 kg is almost exactly 300
g more than 0.6759 kg.
4. How does the slope of your graph compare (percent difference) with the total mass of the system that you measured?
The slope of the graph without any added weights was 0.6129 kg, which is a 9.78% difference. The slope of the graph with the added weights was 0.8939 kg, which is a 10.36% difference.
5. Are the net force on an object and the acceleration of the object directly proportional?
Yes, as the net force is increased, the acceleration is also increased.
6. Write a general equation that relates all three variables: force, mass, and acceleration.
F = ma
Lab Summarized
The overall goal of the lab was to determine and show the relationship between force, mass, and acceleration. The goal was achieved using a cart and pulley system with varying weights to measure
force and acceleration. The forces and accelerations collected were then graphed against each other the construct a linear fit line, whose slope showed the mass of the system (the cart, sensor, and
any added weights). This value could then be compared to the mass calculated from the force of the free hanging system. The force and acceleration from each trial run could also be analyzed to show
any relationship between the two values.
The data collected seemed to show a direct correlation between force and acceleration. Thus, the stated hypothesis was confirmed that if the force was increased, the acceleration would also increase.
The compared values for the masses of the cart systems were about 10% different in each case. For the trial without any added weight, the calculated value of 0.6759 kg is 9.78% different from the
extrapolated value of 0.6129 kg. In regards to the trial with the added weight, the calculated value of 0.9916 kg is 10.36% different than the extrapolated value of 0.8939 kg. This error could have
been caused by a number of factors. For instance, the air resistance from the weight on the pulley dropping could have caused error, and any possible friction from the track could have attributed to
this, too. It could also be thought that if the pulley did not drop straight downward, i.e. it was swaying at all, this would have further error. Lastly, if the rope was not completely taught when
the system was put in motion, that could have caused error as well.
F = ma
a = 9.8 m/s^2
N/(m/s^2) = kg
circa 2018 (30 y/o) | {"url":"https://adamcap.com/schoolwork/3000/","timestamp":"2024-11-15T04:37:13Z","content_type":"text/html","content_length":"95174","record_id":"<urn:uuid:f202e7a4-a469-4710-bb5d-243e9d038d97>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00849.warc.gz"} |
World long-distance running elite: ethnicity-specific run energy efficiency analysis
World long-distance running elite: ethnicity-specific run energy efficiency analysis
Dr.Hab. V.D. Kryazhev^1
Dr. Hab., Professor V.Y. Karpov^2
PhD, Professor K.K. Skorosov^3
PhD, Associate Professor V.I. Sharagin^4
^1Federal Scientific Center for Physical Culture and Sports, Moscow
^2Russian State Social University, Moscow
^3Penza State University, Penza
^4Moscow State University of Psychology and Education, Moscow
Corresponding author: kryzev@mail.ru
Keywords: long-distance running, mathematical modeling, run energy cost, run energy efficiency.
Background. Di Prampero (Italy) [4] and F. Peronne, G. Thibault (Canada) [7] have developed a middle-/ long-distance run energy cost rating method based on the aerobic/ anaerobic metabolism capacity
and kinetics rating formulae, with the resulting values calculated with only 0.68% error. Their calculations of VO2max were only 2-3 mm/kg/min different from the published individual long-distance
running elite test data. It is commonly assumed that the long-distance running elite energy cost varies at around 3.86 J/kg/m, and the maximal oxygen consumption at 80 ml/kg/min [7]. Later it was
found, however, that the East African long-distance running elite (from Ethiopia, Kenya and other nations) runs in much more energy efficient manner that the Europeans [5, 6]. We believe that it may
be pertinent in this context to have the common long-distance running energy efficiency analysis and findings revised.
Objective of the study was to analyze, on a mathematical and statistical basis, the African and European long-distance running elite energy efficiency.
Methods and structure of the study. We collected for analysis the individual competitive performance data of the top-five European and top-five African runners from the 2019 top-100 list: see Table
Table 1. Individual competitive performance data of the top-five European and top-five African competitors in 3000m, 5000m and 10000m
│ │Athlete │Nation│Rank │3000m │5000m │10000m │
│1 │T. Bekele │ETH │1-5000 │7:32.55 │12:52.98│ │
│2 │S. Barega │ETH │1-5000 │7:32.17 │12:43.02│26:49.46│
│3 │H. Gebhriwet │ETH │1-10000 │7:30.36 │12:45.82│26:48.95│
│4 │A. Hadis │ETH │3-10000 │7:39.10 │12:56.27│26:56.46│
│5 │J. Cheptegey │UGA │1-10000 │7: 33.26│12:57.41│26:38.36│
│6 │R. Ringer │GER │11-10000│7:53.81 │13:23.04│28:44.17│
│7 │J. Wanders │SWI │15-5000 │7:43.62 │13:13.84│27:17.29│
│8 │S. McSweyn │AUS │7-10000 │7:34.79 │13:05.23│27:23.20│
│9 │S.N. Moen │NOR │27-10000│7:52.55 │13:20.16│27:24.78│
│10│P. Tiernan │AUS │12-5000 │7:37.76 │13:12.68│27:29.40│
Sports results (LnT times) were converted into mean distance speed (V) and processed in Excel to produce V-LnT correlations. The critical running speed (Vcrit) was found based on the seventh-minute
LnT (Ln 420 = 6.04) [7, 8]. Based on the critical running speed concept [1] and using the ∆MAP = Crtot ∙ Vcrit, W ratio, we computed the maximum aerobic power (MAP) above the quiescent level (∆MAP)
using the equation VO2max = (∆MAP + 1.2) ∙ 2.87 ml/kg/min. Note that Crtot means the run energy cost net of the air resistance. Run energy efficiency (net energy cost Cr) was estimated at 3.76 J/kg/m
for the Europeans and 3.30 J/kg/m for the Ethiopians [4, 5]. Note that the aerobic maximum aerobic power, run energy cost and endurance ratio (E, rated by the regression curve tilt angle V - LnT [8]
as provided by Péronnet-Thibault model [7]) may be used to compute the individual energy efficiency [2].
Results and discussion. Given on Figure hereunder are the regression equations for the African and European runners with virtually the same tilt angles indicative of the similar E ratios and
endurance indices EI. The critical speeds generated by the regression equations show advantage of the African group. Thus the Ethiopian runners demonstrate higher energy efficiencies i.e. energy
costs per meter net of the air resistance; and, hence, lower metabolic demand (MD) on the distances. It should be emphasized that the African runners are generally more successful than the Europeans
in spite of the lower aerobic maximums. The mathematical models that we applied give fairly accurate energy efficiency rates based on the known energy costs [2, 7].
Figure 1. Elite long-distance runners’ distance speed variations on three distances
Note that the mean values for the European/ African long-distance running elites vary within the range of around 7% [4, 6], although the intergroup energy efficiencies are quite significant.
Table 2. Calculated energy cost and performance test data of the European and African elite long-distance runners on 3000m distance
│ │ │ │VO2max, │Vcrit, │ │
│Elite long-distance runners │V, m/s │Pv, W/kg │ │ │Cr, J/kg/m │
│ │ │ │ml/kg/m │m/s │ │
│Africans │6,12 ±0,01 │26.76 ±0.03│76.2 ±0.11│6.65 ±0.011│3.80 ±0.006│
│Europeans │6,14 ±0,013│28.62 ±0.06│82.4 ±0.17│6.51 ±0.014│4.21 ±0.009│
Note: р≤0.05; V – running speed; Pv – metabolic demand; VO2max – maximum oxygen consumption; Vcrit – critical running speed; Cr – energy cost per meter net of air resistance
The high run energy efficiencies of the world leading Ethiopian and Kenyan middle- and long-distance runners may be due to the genetically predetermined lower limb metrics and habitual high-altitude
living conditions [3] that develop more energy efficient aerobic metabolism. The shorter shin circumference (minus 3 cm on average) secures more efficient mass-inertial performance of the distal leg
segments and eases the mechanical work [6]; plus the lower shoulder of forces acting in the Achilles tendon contributes to the energy efficiency of the elastic elements in the musculoskeletal system
Conclusion. Mathematical analysis of the competitive performance data and energy efficiency of elite long-distance runners demonstrated serious advantages of the East African runners over their
European competitors secured by the lower metabolic demands on the distances and, hence, better energy efficiencies as a sound basis for their great competitive accomplishments despite the relatively
lower aerobic maximums.
1. Kryazhev V.D., Volodin R.N., Solovyev V.B. et al. Critical running speed concept and its assessment in middle distance runners. Vestnik sportivnoy nauki. 2019. No. 6. pp. 4-6.
2. Kryazhev V.D., Kryazhev S.V. Individual rating of bioenergetic indicators of middle distance runners. Vestnik sportivnoy nauki. 2019. No. 1. pp. 15-20.
3. Barnes K.R. and Klding A.E. (2015). Running Economy: measurement, norm, and determining factors. Sport Med Open. Dec; 1: 8.
4. Di Prampero P.E., Capelli C., Pagliaro P., Antonutto G., Girardis M., Zamparo P., Soule R.G. Energetics of best performances of middle-distance running. Journal of Applied Physioliogy. 1993; 74.
рp. 2318-2324.
5. Faster C. and Lucia A. Running Economy. The Forgotten Factor in Elite Performance. Sport Med. 2007: 37 (4-5).
6. Lucia A. Esteve-Lanao J., Olivan J., Gomez-Gallego F., San Juan A.F., Santiago C. et al. Physiological characteristics of the best Eritrean runners-exceptional running economy. Appl Physiol Nutr
Metab. 2006;31(5):530-40.
7. Péronnet F., Thibault G. Mathematical analysis of running performance and world running records. Journal of Applied Physiology, 67, 1989. рp. 453-465.
8. Zinoubi B., Vandewalle, H. and Driss. (2017). Modeling of Running Performances in Human: Comparison of Power Laws and Critical Speed. The Journal of Strength and Conditioning Research, Vol. 31,
pp. 1859-1868.
9. Vandewalle H. (2017). Mathematical modeling of running performances in endurance exercises: comparison of the models of Kennely and Peronnet-Thibault for World records and elite endurance
running. American Journal of Engineering Research FJER) e-ISSN:2320-0847 p-ISSN: 2320-0936. V- 6, I-9. pp-317-323. | {"url":"http://www.teoriya.ru/en/node/14131","timestamp":"2024-11-02T01:50:36Z","content_type":"text/html","content_length":"40368","record_id":"<urn:uuid:93c8265e-1079-4f30-a5b1-e3db0b547424>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00482.warc.gz"} |
Advanced Excel Unit 4 | Administrative Career Training Institute
Unit 3 IF function - Part 1
Nested IF statement
You can also nest IF functions to perform more complex logical tests.
For example, suppose you have a cell containing a student's score in cell A1, and you want to display "A" if the score is greater than or equal to 90, "B" if it's greater than or equal to 80, "C" if
it's greater than or equal to 70, and "D" if it's greater than or equal to 60.
You can use the following nested IF formula:
=IF(A1>=90, "A", IF(A1>=80, "B", IF(A1>=70, "C", IF(A1>=60, "D", "F"))))
This formula checks the score against multiple conditions in sequence. If the score meets the first condition (A1>=90), it returns "A"; otherwise, it moves on to the next condition (A1>=80), and so
In this dataset:
Column A contains the test scores of the students.
Column B will contain the letter grades assigned based on the test scores using the nested IF formula provided earlier.
Example 2
You work as an administrative assistant at a small office supplies company. Your company offers discounts on bulk purchases to its customers. However, the discount rate varies depending on the total
amount spent by the customer. Your task is to create an Excel spreadsheet to calculate the discount amount for each customer based on their total purchase.
For example, if a customer's total purchase amount is greater than or equal to $500, they are eligible for a 10% discount. Otherwise, they receive no discount.
The formula might look like this:
=IF(B2>=500, B2*0.1, 0)
Where B2 is the total purchase amount for the customer. If the total purchase amount is greater than or equal to $500, the discount amount is calculated as 10% of the total purchase amount.
Otherwise, no discount is applied.
MIN and MAX functions with arrays in Microsoft Excel allows you to find the smallest an largest values respectively within a range of cells. A
Scenario: You work as an administrative assistant at a small retail store. Your task is to categorize customers based on their purchase history and loyalty status to determine the type of discount
they are eligible for.
Create an IF statement and Dataset (using any suitable details) to show how you would complete such a task.
Submit your answer to actira.tt@gmail.com | {"url":"https://admincareerstt.com/advanced-excel-unit-4","timestamp":"2024-11-10T08:16:45Z","content_type":"text/html","content_length":"349764","record_id":"<urn:uuid:b024277a-b19f-4049-9ed4-de8e026ecfff>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00166.warc.gz"} |
Re: st: Difference in Difference for Proportions
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Re: st: Difference in Difference for Proportions
From Jeph Herrin <[email protected]>
To [email protected]
Subject Re: st: Difference in Difference for Proportions
Date Thu, 17 Sep 2009 16:53:47 -0400
Not sure whether this helps you, but I would normally test this
with an interaction term in a model. For instance
gen txsouth=t*south
binreg f t south txsouth, n(pop)
Then testing the coefficient on -txsouth- is the same as
testing whether there is a significant difference in differences.
Misha Spisok wrote:
Hello, Statalist,
In brief, how does one test a difference in difference of proportions?
My question is re-stated briefly at the end with reference to the
variables I present. A formula and/or reference would be appreciated
if no command exists.
I would like to test a difference in difference of proportions.
-prtest- and -prtesti- do not work (easily) for my data, even for a
simple test of differences. I have data grouped such that, for N
states, I have the number of persons in state i with a condition (the
variable for that count is f) and the population of state i in year y
(pop). A "treatment" is applied and the pre-treatment period is t=0
and the post-treatment period is t=1. One can consider south=1 to be
the treated and south=0 to be the non-treated group.
For example, some observations may look like this:
state year pop f t south
For differences in proportions within, for example, the pre-treatment
period, for states in two regions (south==0 and south==1), I use,
egen f_north_0 = sum(f) if south==0 & t==0
egen pop_north_0 = sum(pop) if south==0 & t==0
egen f_south_0 = sum(f) if south==1 & t==0
egen pop_south_0 = sum(pop) if south==1 & t==0
gen phat_n_0 = f_north_0/pop_north_0 /* proportion in north pre-treatment */
gen phat_s_0 = f_south_0/pop_south_0 /* proportion in south pre-treatment */
gen sp_n_0 = sqrt(phat_n_0*(1 - phat_n_0)/pop_north_0) /* standard
error for phat_n_0 */
gen sp_s_0 = sqrt(phat_s_0*(1 - phat_s_0)/pop_south_0) /* standard
error for phat_s_0 */
egen fn_0 = mean(f_north_0)
egen fs_0 = mean(f_south_0)
egen pn_0 = mean(pop_north_0)
egen ps_0 = mean(pop_south_0)
gen phat_0 = (fn_0 + fs_0)/(pn_0 + ps_0) /* pooled proportion, pre-treatment */
gen qhat_0 = 1 - phat_0
gen sp_0 = sqrt(phat_0*qhat_0*(1/pn_0 + 1/ps_0)) /* standard error of
difference of proportions */
gen z_0 = (fs_0/ps_0 - fn_0/pn_0)/sp_0
(At this point I suppose I could use -prtesti- by summarizing the
relevant variables then typing the results into the prtesti
command...In any case, I think that neither -prtest- nor -prtesti-
will help me with testing a difference in differences.)
This, it would seem, allows me to test the difference in proportions
in the pre-treatment period. Similarly, if I generate similar values
for the post-treatment period, I can test the difference in
proportions in the post-treatment period.
egen f_north_1 = sum(f) if south==0 & t==1
egen pop_north_1 = sum(pop) if south==0 & t==1
egen f_south_1 = sum(f) if south==1 & t==1
egen pop_south_1 = sum(pop) if south==1 & t==1
gen phat_n_1 = f_north_1/pop_north_1
gen phat_s_1 = f_south_1/pop_south_1
gen sp_n_1 = sqrt(phat_n_1*(1 - phat_n_1)/pop_north_1)
gen sp_s_1 = sqrt(phat_s_1*(1 - phat_s_1)/pop_south_1)
egen fn_1 = mean(f_north_1)
egen fs_1 = mean(f_south_1)
egen pn_1 = mean(pop_north_1)
egen ps_1 = mean(pop_south_1)
gen phat_1 = (fn_1 + fs_1)/(pn_1 + ps_1)
gen qhat_1 = 1 - phat_1
gen sp_1 = sqrt(phat_1*qhat_1*(1/pn_1 + 1/ps_1))
gen z_1 = (fs_1/ps_1 - fn_1/pn_1)/sp_1
How can I test (p_hat_s_1 - p_hat_s_0) - (p_hat_n_1 - p_hat_n_0),
given that p_hat_* is a proportion?
My uninformed guess is that it might be ((p_hat_s_1 - p_hat_s_0) -
(p_hat_n_1 - p_hat_n_0)) / s,
where s = some weighted version of sp_0 and sp_1.
Many thanks,
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New Rules Explanation for HTX Copy Trading Profits
1. Calculation Method of Total PnL% (Updated)
Total PnL% = Carryover PnL% + PnL% in the current calculation period
PnL% in the current calculation period = PnL in the current calculation period / Assets at the start of the current calculation period * 100%
PnL in the current calculation period = Assets at the end of the current calculation period - Assets at the start of the current calculation period - Profits shared in the current calculation period
Assets at the start of the current calculation period = Assets at the end of the last calculation period + Incoming transfers in the current calculation period - Outgoing transfers in the current
calculation period
Assets at the end of the current calculation period = Total assets in the trader's Copy Trading account in the current calculation period
Profits shared in the current calculation period = Cumulative profits the trader received in the current calculation period
PnL% in the current calculation period: The amount of profit or loss in terms of percentage that has been incurred from the last transfer to the present moment.
Carryover PnL%: After a transfer occurs, the total PnL% from the previous calculation period is recorded as the carryover PnL%.
Calculation Period: The system automatically calculates the total PnL% every 15 minutes based on whether any transfers have been made by traders.
Note: Any assets below 50 USDT at the start of the calculation period will be considered equivalent to 50 USDT for the purpose of calculation.
2. Examples
Time Transferred Transferred Assets at Start of Assets at End of Profits Shared in Current PnL in Current Calculation PnL% in Current Calculation Carryover Total
In Out Calculation Period Calculation Period Calculation Period Period Period PnL% PnL%
T0 200 0 200 200 0 0 0% 0% 0%
T1 0 0 200 330 30 100 50% 0% 50%
T2 70 0 400 300 0 -100 -25% 50% 25%
T3 200 0 500 800 50 250 50% 25% 75%
T4 300 100 1000 1500 200 300 30% 75% 105%
If a trader's Copy Trading account has no assets and they make a transfer of 200 USDT in the current calculation period (T0), the trader would have initial assets of 200 USDT. Additionally, if no
further trades or profits/losses occur during the period, the assets at the end of the period would still be 200 USDT. As a result, the current PnL would be 0, and the total PnL percentage would also
be 0%.
If the trader's assets reach 330 USDT (from 200 USDT initially) at the end of the current calculation period (T1), with 30 USDT being the profits shared by their followers and the trader's net
profits being 100 USDT, the current PnL percentage would be 50%. However, since the carryover PnL percentage is 0% and there have been no transfers in the current period, the total PnL percentage
would also be 50%.
If the trader transfers in 70 USDT in the Copy Trading account, the assets at the start of the current calculation period (T2) would be 400 USDT. However, if the trader incurs a loss during the
period, resulting in assets of 300 USDT at the end of the period and no profits shared from followers, the current PnL and the PnL percentage for the period would be -100 USDT and -25%, respectively.
Since a transfer occurred during the period, the previous period's total PnL percentage is recorded as the carryover PnL percentage of 50%. Therefore, the total PnL percentage for the period would be
If the trader transfers in 200 USDT in the Copy Trading account, the assets at the start of the current calculation period (T3) would be 500 USDT. Assuming the trader gains profits during the period,
resulting in assets of 800 USDT at the end of the period and profits shared from followers of 50 USDT, the current PnL and the PnL percentage for the period would be 250 USDT and 50%, respectively.
Since a transfer occurred during the period, the previous period's total PnL percentage is recorded as the carryover PnL percentage of 25%. Therefore, the total PnL percentage for the period would be
If the trader transfers in 300 USDT and transfers out 100 USDT in the Copy Trading account, the assets at the start of the current calculation period (T4) would be 1,000 USDT. Assuming the trader
gains profits during the period, resulting in assets of 1,500 USDT at the end of the period and profits shared from followers of 200 USDT, the current PnL and the PnL percentage for the period would
be 300 USDT and 30%, respectively. Since a transfer occurred during the period, the previous period's total PnL percentage is recorded as the carryover PnL percentage of 75%. Therefore, the total PnL
percentage for the period would be 105%.
3. Data Display Under New PnL% Calculation Method
To mitigate the impact of the new PnL% calculation method on existing lead traders with HTX Copy Trading, adjustments are made for their data display.
For existing traders who were approved before December 7, 2023, their total PnL% at 00:00 (UTC+8) on December 7, 2023, will be used as the carryover PnL. After 00:00 (UTC+8) of the day, new total
PnL% will be calculated based on real-time PnL% and previous carryover PnL%.
For traders who applied and were approved after 00:00 (UTC+8) on December 7, 2023, their total PnL% will be calculated using the new calculation method. | {"url":"https://www.htx.com/support/94956171281397/","timestamp":"2024-11-09T14:33:09Z","content_type":"text/html","content_length":"249228","record_id":"<urn:uuid:12474c3f-1756-43cc-982f-f04079dd6f28>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00646.warc.gz"} |
Детайли за публикация от базата данни на ТУ - София (Publication Details)
Autors: Angelov, G. V.
Title: Note on an Generalized Solution of the Three-Conductor Transmission Line Equations
Keywords: electromagnetic compatibility, 3-conductor transmission line
Abstract: Here we present an abridged investigation on the electromagnetic compatibility aspects of three lossless transmission lines terminated by linear loads introduced by C. Paul. Taking into
account the mutual interaction between two lines we do not neglect the influence of the receptor line i.e. we do not apply the weak-coupling approximation. This leads to a more general mathematical
model than the model of C. Paul. We formulate a mixed problem for the hyperbolic system describing the three-conductor transmission line. It is proved that the mixed problem is equivalent to an
initial value problem for a functional system on the boundary of hyperbolic system’s domain. The unknown functions in this system are the lines’ voltages and currents. The obtained system of
functional equations can be solved by a fixed-point method that enables us to find an approximated but explicit solution.
2nd International Conference on Mathematics and Computers in Science and Engineering (MACISE 2020), pp. 278–283, 2020, Spain, DOI 10.1109/MACISE49704.2020.00058
Copyright IEEE Xplore
Full text of the publication | {"url":"http://e-university.tu-sofia.bg/e-publ/search-det.php?id=10229","timestamp":"2024-11-02T21:40:57Z","content_type":"text/html","content_length":"5126","record_id":"<urn:uuid:390bba0b-a933-4220-b9c4-e26ab4db377d>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00884.warc.gz"} |
Axis Deviation Chapter ppt video online download
2 Definition Electrical axis...The general direction in the frontal plane or toward which lead the QRS complex is predominately oriented ...the mean direction of depolarization through the frontal
plane of the heart
5 Mean QRS Axis CalculationGeneral rules the mean QRS axis points midway between any two leads that show tall R waves of equal height the mean QRS axis is oriented at right angles (90°) to any lead
showing a bi-phasic complex
11 Normal versus DeviationLeft 3 ? 1 ? 2 ? Right + 90∘
13 Axis Deviation CriteriaLEAD I LEAD II (or Lead aVF or III) Normal Positive LAD Negative RAD Intermediate axis
14 Axis Deviation RAD = If R wave in III > R wave in IILAD = If R wave in aVL > I; and deep S wave in III
24 Causes of Left Axis DeviationFYI • left anterior hemiblock • Q waves of inferior myocardial infarction • artificial cardiac pacing • emphysema • hyperkalaemia • Wolff-Parkinson-White syndrome -
right sided accessory pathway • tricuspid atresia • ostium primum ASD • injection of contrast into left coronary artery note: left ventricular hypertrophy is not a cause left axis deviation
25 Causes of Right Axis DeviationFYI • normal finding in children and tall thin adults • right ventricular hypertrophy • chronic lung disease even without pulmonary hypertension • anterolateral
myocardial infarction • left posterior hemiblock • pulmonary embolus • Wolff-Parkinson-White syndrome - left sided accessory pathway • atrial septal defect • ventricular septal defect | {"url":"https://slideplayer.com/slide/5055688/","timestamp":"2024-11-07T10:05:50Z","content_type":"text/html","content_length":"170143","record_id":"<urn:uuid:d299de49-7913-41a0-8818-334951f95072>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00436.warc.gz"} |
A simple but difficult arithmetic puzzle, and the rabbit hole it took me down
A while back, Mark Dominus proposed an arithmetic puzzle: combine the numbers 6, 6, 5, and 2 with arithmetic operations (addition, subtraction, multiplication, and division) to get 17. After fiddling
with the problem for a bit on my own and not being able to solve it, I decided to write a solver, and I ended up falling down an unexpected rabbit hole and dragging a few friends down with me.
(If you want to try to solve the puzzle on your own, or if you want to write a solver without having seen someone else’s, you may want to go do that before continuing to read this post.)
First draft
In the spirit of sharing process, here’s my first attempt at a solver. It’s a mess, but it works, sort of. It will find a way, if one exists, of combining four given integers using arithmetic
operations to get an expression that evaluates to a given target integer (assuming that the expression is parenthesized in a particular way; more on that later). I happened to hard-code 17 as the
target, but it would have been just as easy to have that be an argument. The approach I took is pretty boring: it first generates all permutations of the list of four inputs, then generates all the
arithmetic expressions that can be built by sticking +, -, *, or / in between the numbers in each of those permutations. Finally, it evaluates all the resulting expressions and sees which ones, if
any, evaluate to the target number.
I wrote it in Scheme because I had originally intended to use miniKanren, but at some point I changed my mind about that and just wrote vanilla Scheme. The less that’s said about my ugly first draft,
the better, probably, but I do want to make one process-related observation. I was having trouble writing the permutations function in Scheme; I knew that the output was wrong, but I couldn’t tell
where my code was wrong. I ported my Scheme permutations code to Haskell, tried to compile it and got a type error, and the problem became apparent: the Scheme version had been missing a concat. I
mentioned this to Mark – who had already written at least one solver, but had decided to try to do another one in Scheme when I told him that that’s what I had done – and he said, “I’m at exactly
that point in my Scheme implementation also! I have some function that is returning a [[[T]]] when it ought to be a [[T]] and I’m not sure yet where the fault is.” I think it’s interesting that we
both ran into more or less the same bug.
Mark also remarked, “I saw your first solution and said to myself ‘She used way too much code, I could write this much shorter’ and I tried and it exploded and now the walls and floor are covered
with dripping masses of Scheme code.” Well, we’ve all been there.
Second draft
Next, I wrote a Racket version that used the same strategy as the Scheme one, but was shorter and produced much easier-to-understand output. I found out that permutations was built into Racket, so I
didn’t even need to write it. Here’s my code:
#lang racket
;; A solver for the following puzzle:
;; Given 5 integers a, b, c, d, and e,
;; find an expression that combines a, b, c, and d with arithmetic operations (+, -, *, and /) to get e.
(require srfi/1)
(define ops '(+ - * /))
(define (combine4 n1 n2 n3 n4)
(map (lambda (op)
(map (lambda (e) `(,op ,n4 ,e)) (combine3 n1 n2 n3)))
(define (combine3 n1 n2 n3)
(map (lambda (op)
(map (lambda (e) `(,op ,n3 ,e)) (combine2 n1 n2)))
(define (combine2 n1 n2)
(map (lambda (op) `(,op ,n1 ,n2)) ops))
(define (eval-expr e)
(with-handlers ([exn:fail:contract:divide-by-zero?
(lambda (exn) +inf.0)])
(eval e)))
(define solve
(lambda (n1 n2 n3 n4 target)
(let* ([perms (permutations `(,n1 ,n2 ,n3 ,n4))]
[expr-lists (map (lambda (perm)
(combine4 (first perm)
(second perm)
(third perm)
(fourth perm)))
[val-lists (map (lambda (expr-list)
(map eval-expr expr-list)) expr-lists)]
;; For each perm, see if there's a val in its val-list that is equal to target.
;; If so, hold on to the corresponding expr from its expr-list.
[solutions (filter-map (lambda (perm expr-list val-list)
(let ([idx (list-index (lambda (elem)
(equal? elem target)) val-list)])
(if idx
(list-ref expr-list idx)
perms expr-lists val-lists)])
(delete-duplicates solutions))))
;; Example: combine 6, 6, 5, and 2 with arithmetic operations to get 17:
;; > (solve 6 6 5 2 17)
;; '((* 6 (+ 2 (/ 5 6))))
;; 5 / 6 = 5/6
;; + 2 = 17/6
;; * 6 = 17
I think the ugliest thing about my Racket solution is the combine2, combine3, and combine4 functions, especially all the repetition between combine4 and combine3. And, despite all that code, it can
still only produce solutions with the (op a (op b (op c d))) expression tree shape and therefore misses a lot of solutions.
Down the rabbit hole
I thought I was done thinking about this problem, but after I tweeted about my solver, a few other people shared their attempts, many of which do clever things. For instance, Darius Bacon’s Python
solution distinguishes between commutative and non-commutative operations, which I hadn’t thought to do. Then, Sebastian Fischer shared a cute solution in Haskell, specific to the “combine 6, 6, 5,
and 2 to get 17” problem. However, it looks like it’s choosing the three operations to be distinct, which overconstrains the problem.
But the real rabbit hole started with a now-deleted tweet in which someone offered an incredibly concise Haskell version that didn’t have the distinctness issue. It used replicateM 3 ["+","-","*","/
"] to create a list of combinations of operations, which looks like [["+","+","+"],["+","+","-"],...] and has length 64. So, there’s some list monad trickery going on there. The most surprising thing
about their solution, though, was that they wrote something like do { opList <- replicateM 3 ["+","-","*","/"]; exprs <- permutations ([6, 6, 5, 2] ++ opList); ... } to generate a massive list
containing all valid RPN programs written with those operators and operands, as well as many, many invalid ones. When I questioned this, the author was like, “It’s only 300K programs; it’s not a big
deal to evaluate them.” (!)^1
I wanted to come up with a nice way to refactor my Racket code to do what replicateM 3 ["+","-","*","/"] was doing, but then I got distracted just trying to figure out what the thing I wanted was
even called. Given a set of items (in this case, \(\lbrace \texttt{+}, \texttt{-}, \texttt{*}, \texttt{/} \rbrace\)), I wanted to enumerate all of the lists of a given length (in this case, 3) whose
elements are drawn from the set, with repetitions allowed. My first instinct was to call these things “ordered \(k\)-multisets”, where \(k\) is the length of the lists we’re producing, but that
terminology doesn’t seem to be much in use; there are only a handful of Google results for it. These lecture notes from someone’s 2013 discrete math course at TU Vienna, at least, seem to be using it
in the way I intended:
The number of ordered \(k\)-multisets over \(A\): \(n^{k}\). (Take a fixed number of positions \(k\) and for each position choose any element from \(A\)).
I wondered if there was a Racket library with a function that would enumerate the ordered \(k\)-multisets of a set. I asked some of the Racketeers I knew, and no one knew of such a library, but
Justin Slepak suggested a clever way to do it: for a set with \(X\) elements, convert each of \(0,\dots,X^{k}-1\) into base \(X\), and then convert each digit (or, uh, \(X\)-it?) of the resulting
base-\(X\) numbers back into an element of the original \(X\)-element set. I never got around to actually implementing that approach, but after Justin described it, I realized that it was in fact the
approach taken by this Mathematica code that I’d also come across and not really understood (I had seen things like Module and Thread in the Mathematica code and had given up trying to read it).
Then, a comment on that page led me to this diagram, which offers another name for “ordered \(k\)-multisets”: variations with repetition. Further investigation on Wikipedia revealed that there are
several competing names for this notion:
\(n\)-tuples whose entries come from a set of \(m\) elements are also called arrangements with repetition, permutations of a multiset and, in some non-English literature, variations with
Another Wikipedia page claims that “variations with repetition” is “an archaic term in combinatorics still commonly used by non-English authors”. In any case, it’s still a lot more popular than
“ordered \(k\)-multisets”!
At this point, I had satisfied my curiosity and was ready to move on from this problem, but my friend Michael “rntz” Arntzenius wasn’t quite done: he forked my Racket code and wrote a solver that can
produce answers with all of the possible expression tree shapes, which mine can’t do. Then, when I mentioned the Darius Bacon version that distinguishes between commutative and non-commutative
operations, he wrote a version that did that, too. Both rntz and Darius also used generators and other fancy stuff that my code doesn’t use.
Want another puzzle?
Mark mentioned that a couple of people have written to him to suggest an even harder instance of this problem: from 8, 8, 3, and 3, make 24. He said he puzzled over this one for several days before
giving up and asking his solver for help. I also had to give up and ask my own solver after a while, and I was pleased that despite its limitations, it coughed up a correct answer. So, that’s a happy
ending of sorts.
Update (January 2, 2017): On Twitter, Nada Amin pointed out the existence of a 2002 functional pearl paper by Graham Hutton about writing a Haskell solver for a similar problem. The version of the
problem in the paper restricts not only inputs but also intermediate results to being natural numbers, which changes things quite a bit; for instance, you need non-integral intermediate results to be
able to get 17 from 6, 6, 5, and 2, as shown above.
Update (April 9, 2017): Mark has written a follow-up blog post covering various people’s solution to this problem, and he says he would like to write “at least three or four” more articles on the
topic eventually, which perhaps gives a sense of just how deep this rabbit hole could go.
1. 332,560, to be precise. By contrast, my solver only needs to try 1536 possible solutions (24 permutations of the input integers, times 64 combinations of operations). Admittedly, though, there
are five possible expression tree shapes, and I can only produce solutions with one of those shapes. Five times 1536 is 7680, so 7680 of the 332,560 “RPN programs” would actually be valid RPN.
(These counts include duplicate solution candidates, which arise when the input numbers aren’t all distinct.) ↩ | {"url":"https://decomposition.al/blog/2016/12/31/a-simple-but-difficult-arithmetic-puzzle-and-the-rabbit-hole-it-took-me-down/","timestamp":"2024-11-05T03:03:26Z","content_type":"text/html","content_length":"34183","record_id":"<urn:uuid:56ca27fd-0752-402e-bb88-a4b0cebf3fe5>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00717.warc.gz"} |
Re: Removing trend and seasonality to create a regression and then adding them back
I have a weekly time series in the following format.
category Product date Sales Is_Discounted
a123 1224 12JUN2016 20 1
a123 1224 19JUN2016 10 0
a123 1224 26JUN2016 25 1
a123 1224 03JUL2016 19 0
a123 1224 10JUL2016 18 0
I need to predict weekly Sales for each unique combination of category and Product.
I want to remove the seasonality from this time series and then create forecasts using proc reg and then add the seasonality back on the forecasts. I have been able to create regression model (using
month number, week number and Is_Discounted as independent variables) without removing seasonality and its working fine, but I believe the seasonality in the data is impacting my accuracy with
regression. I checked proc X12 but I do not understand how to use it to add the seasonality back after regression. Thanks for the help!
09-10-2018 11:19 AM | {"url":"https://communities.sas.com/t5/SAS-Forecasting-and-Econometrics/Removing-trend-and-seasonality-to-create-a-regression-and-then/m-p/529810/highlight/true","timestamp":"2024-11-03T07:25:03Z","content_type":"text/html","content_length":"275346","record_id":"<urn:uuid:45196ef0-275d-4199-ab2e-256c9f0ce362>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00470.warc.gz"} |
Let’s say that a survey company would like to make a poll about the upcoming American election. How do they go about it? The goal for them would be to make the survey both cheaper and better. To make
the survey more cost efficient, it is important to know if it is possible to reduce the sample size in the survey without increasing the errors. Edgar Bueno, doctoral student, researches a method to
do that. | {"url":"https://www.samfak.su.se/cmlink/stockholms-universitet-samh%C3%A4llsvetenskapliga-fakulteten/statistiska-institutionen-nod/department-of-statistics/research/current-research?cache=1%3FentityUrl%3Dhttp%3A%2F%2Fsukat.su.se%2Fperson.jsp%3Fdn%3Duid%253Didol8879%252Cdc%253Dsocarb%252Cdc%253Dsu%252Cdc%253Dse%26targetFormat%3Datom%3FentityUrl%3Dhttp%3A%2F%2Fsukat.su.se%2Fperson.jsp%3Fdn%3Duid%253Drefa0212%252Cdc%253Dsocarb%252Cdc%253Dsu%252Cdc%253Dse%26targetFormat%3Datom","timestamp":"2024-11-14T16:55:45Z","content_type":"application/xhtml+xml","content_length":"76305","record_id":"<urn:uuid:4b953ca3-f344-4146-b9ba-b87a7076163b>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00408.warc.gz"} |
How Big is Two and a Half Acres of Land? | Spatiality Blog
Are you planning to invest in the land but unsure how much you need? Don’t worry; it happens to even the best of us. When you think about an investment as significant as land, it is only normal to
feel like standing in front of a giant buffet without knowing how hungry you are!
But if you are dreaming big – a mansion with a massive backyard or maybe a parcel of land where you can start a farm or even set up a little park for people to enjoy, then you need at least 2.5 acres
of land.
Knowing the exact size of a 2.5-acre property is super important when figuring out how much it’s worth on the market. Measuring the land helps ensure everything is up to code, gives a good estimate
of how much it’ll cost to build, helps plan out different areas, and ensures everyone knows where the property lines are for legal reasons.
Let’s see everything there is about this land size! But before that,
Also read: How big is 2 acres of Land?
1. How much is a two-and-a-half acre Exactly?
2.5 acres of land equals 108,900 square feet or approximately 10,117 square meters. But how much is its size in different units? Let’s find out!
Note that the size and dimensions of a two-and-a-half-acre parcel may vary depending on its specific shape and configuration.
1.1 How big is a two-and-a-half acre in square yards?
The measurement of land in square yards is commonly used for smaller parcels. A two-and-a-half acre parcel would be equivalent to 12,100 square yards.
If you were to draw a rectangular area with a length of 1 yard and a width of 1 yard, it would take 12,100 such squares placed side by side to cover an area of 2.5 acres.
When measuring smaller land areas like residential lots, gardens, or construction sites, square yards are commonly used units. This unit is widely utilized in industries such as real estate,
landscaping, and construction. Accurately assessing the land area and making informed decisions in these fields requires the ability to convert between acres and square yards.
Multiply the area value by 4840
2.5 acres x 4840 square yards/acre = 12,100 square yards
So, 2.5 acres is equivalent to 12,100 square yards.
1.2 How big is a two-and-a-half acre in square meters?
Land measurements are often expressed in square meters in countries that follow the metric system. To give an idea of size, 10,175 square meters is roughly equivalent to two-and-a-half acres. This
information can be beneficial when dealing with international land transactions or working with land in metric-based countries.
Square meters are commonly used in industries such as real estate, urban planning, construction, and environmental management. They offer precision and accuracy in measuring land area, which is
valuable for various applications such as project planning, property valuation, cost calculations, resource management, and regulatory compliance.
To calculate the size of 2.5 acres in square meters, we would have to multiply the area in acres by 4047.
So for 2.5 acres, the calculation would be:
Area in square meters = 2.5 acres x 4047
Area in square meters = 10,175
Therefore, 2.5 acres is approximately 10,175 square meters.
1.3 How big is a two-and-a-half acre in square feet?
In the United States, square feet is a commonly used unit of measurement for land. If you have 2.5 acres of land, that is equivalent to 108,900 square feet. Knowing this measurement can be useful in
different scenarios, like when buying or selling real estate or deciding how to use land for residential or commercial purposes.
Square feet provide a practical and familiar unit for measuring land area, especially for smaller areas such as residential lots, commercial properties, or construction sites. Square feet are
commonly used in various industries, including real estate, architecture, construction, interior design, and landscaping. They offer a practical and accessible way to measure land area.
To calculate the area of two and a half acres in square feet, we would have to multiply the number of acres by 43,560.
2.5 acres in square foot = 15 x 43,560 = 108,900 square feet
Therefore, 2.5 acres of land is equivalent to 108,900 square feet of land.
1.4 How big is a two-and-a-half acre in square inches?
Square inches are not typically used for land measurements, but there may be instances where a more precise measurement is needed. To estimate the size of a two-and-a-half acre parcel in square
inches, you would need to multiply the acreage by a large conversion factor of 6,273,000. This would result in an approximate measurement of 15,682,500 square inches.
Square inches are a precise unit of measurement used in industries like engineering, design, and manufacturing. Although not commonly used for measuring large areas of land, square inches are
valuable for applications that require accuracy, such as designing small components, calculating material requirements, or determining clearances in manufacturing processes.
Square inches provide a finer level of detail compared to larger units of area, making them useful in specific industries where precision is critical. To calculate the area of two and a half acres in
square inches, we would have to multiply the number of acres by 6,273,000.
2.5 acres in inches = 15 x 6,273,000 = 15,682,500 square inches
Therefore, 2.5 acres of land is equivalent to 15,682,500 square inches of land.
2. A Visual Comparison: How big is a two-and-a-half acre of Land?
Understanding the size of a two-and-a-half acre parcel of land can be challenging due to its large area. However, visual comparisons and relevant statistics, such as estimating the time it would take
to walk across it or the potential number of parking spaces it could accommodate, can help us comprehend its size.
These comparisons can be especially useful in industries like real estate, construction, and land usage planning. Visual comparisons and statistics aid in understanding the substantial size of a
two-and-a-half-acre parcel, which is essential for informed decision-making in various industries.
2.1 How big is a two-and-a-half acre compared to a football field?
2.5 acres of land is equal to 2.7 American football fields side by side 🤯!
The standard dimensions of an American football field, as regulated by the NFL (National Football League) and NCAA (National Collegiate Athletic Association), are 100 yards (300 feet) in length and
160 feet in width, including the two end zones.
This results in a total playing area of 300 feet x 160 feet = 48,000 square feet.
To put it into perspective, let’s start by comparing the size of a two-and-a-half acre area to that of an American football field, and then we can calculate how many football fields would fit into
two-and-a-half acres:
An acre is a unit of land measurement equivalent to 43,560 square feet. Therefore, two-and-a-half acres would equal 2.5 x 43,560 = 108,900 square feet. The area of an American football field is
48,000 square feet, significantly less than 2.5 acres.
Using these figures, we can calculate the number of football fields, equaling 2.5 acres.
108,900 square feet (size of two-and-a-half acres) ÷ 48,000 square feet (size of one football field) = 2.27 football fields.
So, a two-and-a-half acre area would be approximately equivalent to 2.27 American football fields.
2.2 How big is a two-and-a-half acre compared to a Tennis court?
Did you know you could fit nearly 39 standard tennis courts on a 2.5-acre land? That’s right, a 2.5-acre plot is over 14 times the size of a single tennis court, giving you plenty of room to dream
First, let’s talk about the size of a tennis court.
According to the International Tennis Federation (ITF), a standard tennis court measures 78 feet in length and 36 feet in width.
The playing area is = 78*36=2808 sq.ft.
That gives you a playing area of 2,808 square feet.
Now, let’s imagine you have a 2.5-acre piece of land.
An acre is equivalent to 43,560 square feet, so multiply that by 2.5, and you get 108,900 square feet (43560*2.5 = 108,900 sq.ft.).
When you divide the total square footage of your 2.5 acres (108,900 square feet) by the size of a standard tennis court (2,808 square feet), you find that you could fit roughly 38.79 (let’s round
that up to 39) tennis courts on your plot of land.
So, next time you’re standing on a 2.5-acre plot, just imagine 39 tennis matches happening all at once. That’s a lot of tennis! This sizeable piece of land gives you a world of possibilities, whether
you want to create a sports complex, develop properties, or even start a mini farm. The sky’s the limit!
2.3 How big is a two-and-a-half acre compared to a baseball field?⚾
A standard 400-foot fence surrounding a baseball field results in a size of approximately 4.5 acres, larger than a 2.5-acre land parcel.
To calculate how many baseball fields would fit in a two-and-a-half-acre land, we would have to divide the area of land being compared (2.5 acres) by the size of a regular 400-foot fence field which
is 4.5 acres.
Number of baseball fields that would fit = Total area of land / Area of a baseball field in acres
Number of baseball fields that would fit = 2.5 acres / 4.5 acres = 0.55 baseball fields (rounded to two decimal places)
Therefore, approximately 0.55 baseball fields would fit in a two-and-a-half-acre land, meaning that 2.5-acre land is almost half the size of an average baseball field, assuming we use the typical
dimensions for a regulation baseball field. It’s important to note that the actual number of baseball fields that could fit may vary depending on the shape and layout of the land, as well as any
local regulations or requirements.
2.4 How big is two and a half acres compared to a Soccer field?⚽
Imagine standing at the corner of a FIFA regulation soccer field, the crowd’s roar in your ears, the smell of fresh-cut grass in the air. You look across the field, which stretches 100 meters in
length and 68 meters in width – a total of 6,800 square meters of playing space. That’s a whole lot of room for epic goals and dramatic saves!
Now, let’s hop on over to your 2.5-acre plot of land. To compare it to the soccer field, we need to speak the same language, so let’s convert those acres into square meters.
Now, let’s convert the area of a soccer field from square meters to acres:
1 acre = 4046.86 square meters
Area of a soccer field in acres = 6800 square meters / 4046.86 square meters per acre = 1.68 acres (rounded to two decimal places)
Next, we divide the total area of the two and a half acres of land by the area of a soccer field in acres to determine how many soccer fields would fit:
Number of soccer fields that would fit = Total area of land / Area of a soccer field in acres
Number of soccer fields that would fit = 2.5 acres / 1.68 acres = 1.48 soccer fields (rounded to two decimal places)
That means you could fit almost 1.5 FIFA-regulation soccer fields on your 2.5-acre plot. Imagine hosting your own mini World Cup right in your backyard! Of course, this is a rough estimate, and you’d
need to consider the shape of your land, local rules, and how much space you’d want around the fields. But it gives you a fun way to envision the potential of your property!
2.5 How big is a two-and-a-half acre compared to a Swimming Pool?
The standard dimensions for an Olympic-sized swimming pool, as defined by the International Olympic Committee (IOC), are 50 meters in length, 25 meters in width, and a depth of at least 2 meters.
To calculate how many Olympic swimming pools would fit in a 2.5-acre land, we first need to determine the size of an Olympic swimming pool.
Area of an Olympic swimming pool = Length × Width
Area of an Olympic swimming pool = 50 meters × 25 meters = 1250 square meters
Now, let’s convert the area of an Olympic swimming pool from square meters to acres:
1 acre = 4046.86 square meters
Area of an Olympic swimming pool in acres = 1250 square meters / 4046.86 square meters per acre = 0.31 acres (rounded to two decimal places)
Next, we divide the total area of the 2.5-acre land by the area of an Olympic swimming pool in acres to determine how many Olympic swimming pools would fit:
Number of Olympic swimming pools that would fit = Total area of land / Area of an Olympic swimming pool in acres
Number of Olympic swimming pools that would fit = 2.5 acres / 0.31 acres = 8.06 Olympic swimming pools (rounded to two decimal places)
Therefore, approximately 8.06 Olympic-sized swimming pools would fit in a 2.5-acre land, assuming we use the standard dimensions for an Olympic swimming pool. It’s important to note that the actual
number of swimming pools that could fit may vary depending on the shape and layout of the land, as well as any local regulations or requirements related to pool construction and spacing.
2.6 How many average-size houses fit in a two-and-a-half acre of Land?
Taking 2,480 square feet as the average size of a house in the US. With a two-and-a-half acre parcel of land measuring approximately 108,900 square feet, it can accommodate approximately 43.9 houses.
However, it’s important to note that the number of houses that can be built on the land may vary due to setback requirements, zoning regulations, and other land use considerations.
But if we take,
The average size of houses = 2,480 square feet
Now we can calculate the number of houses that can fit the given land area.
We need to convert the land area from acres to square feet and then divide that by the average size of the house.
1 acre = 43,560 square feet
2.5 acres = 2.5 * 43,560 = 108,900 square feet
Land area / Average size of apartments = Number of apartments that can fit
108,900 square feet ÷ 2,480 square feet (rounded to the nearest whole number) = 43.91
Since we cannot have a fraction of a house, we round down to the nearest whole number. Therefore, approximately 43 average-size houses can fit in a two-and-a-half acre of land.
2.7 How many average-size apartments fit in a two-and-a-half acre of Land?
The number of apartments accommodated on a two-and-a-half-acre parcel of land can vary significantly depending on various factors. However, the average size of the apartments across the US is 882
square feet.
To calculate how many average-size apartments can fit in a two-and-a-half acre of land, we need to know the size of the average apartment and the units of measurement being used.
First, we need to convert the two-and-a-half acres of land to square feet. Since 1 acre is equal to 43,560 square feet, two-and-a-half acres would be:
2.5 acres * 43,560 square feet per acre = 108,900 square feet
Next, we divide the total square footage of the land by the size of the average apartment:
108,900 square feet / 882 square feet per apartment = 123.46 apartments
So, approximately 123.46 average-size apartments can fit in a two-and-a-half acre of land. Since we cannot have a fractional number of apartments, we would round down to the nearest whole number,
which means that approximately 123 average-size apartments can fit in the given land.
However, please note that this is a rough estimate. Other factors, such as setbacks, parking space, and common areas, may affect the number of apartments that can be accommodated on the land.
2.8 How many iPhone 14 fit in a two-and-a-half acre of Land?
Picture this: you’re standing on a vast, open expanse of 2.5-acre land. In your hand, you’re holding the sleek and shiny iPhone 14.
Now, here’s a wild thought – have you ever wondered how many of these iPhones it would take to cover your entire plot of land? We’re not talking about a stack of phones here, but laying them flat,
side by side.
Sounds crazy, right? But let’s dive into it! Grab your calculators and put on your thinking caps because we’re about to embark on a fun mathematical journey that will give you a whole new perspective
on your iPhone and your land.
To calculate:
First, we need to convert two-and-a-half acres of land to square inches. Since 1 acre is equal to 43,560 square feet, and 1 square foot is equal to 144 square inches, two-and-a-half acres would be:
2.5 acres * 43,560 square feet per acre * 144 square inches per square foot = 15,681,600 square inches
Next, we calculate the area occupied by a single iPhone 14 by multiplying its length and width:
Length: 5.78 inches
Width: 2.82 inches
Area of a single iPhone 14 = Length * Width = 5.78 inches * 2.82 inches = 16.3236 square inches (rounded to four decimal places)
Finally, we divide the total square inches of the land by the area of a single iPhone 14 to determine the number of iPhones that can fit:
15,681,600 square inches / 16.3236 square inches per iPhone 14 = 960,670.44 iPhones
So, approximately 960,670.44 iPhone 14 devices can fit in a two-and-a-half acre of land. However, since we cannot have a fractional number of iPhones, we would round down to the nearest whole number,
which means that approximately 960,670 iPhone 14 devices can fit in the given land.
2.9 How many Parking Lots are in a two-and-a-half acre of Land?
To calculate how many parking lots would fit in a 2.5-acre land, we need to know the size of the parking space and the units of measurement being used.
Parking space sizes can vary depending on the design, layout, and regulations in a particular area. However, a common standard for parking space size is about 180 square feet per parking space.
First, we need to convert 2.5 acres of land to square feet. Since 1 acre is equal to 43,560 square feet, 2.5 acres would be:
2.5 acres * 43,560 square feet per acre = 108,900 square feet
Next, we divide the total square footage of the land by the size of the parking space to determine the number of parking spaces that can fit:
108,900 square feet ÷ 180 square feet per parking space = 605 parking spaces
We’ve calculated that a 2.5-acre plot of land could potentially fit 605 parking spaces. However, it’s important to keep in mind that this estimation is rough and other factors such as setbacks,
access points, and local regulations may have an impact on the actual number of parking spaces that can be accommodated on the land.
2.10 2.5 acres is Just a little under one-tenth as big as Ellis Island
Ellis Island is a historic island located in the Upper New York Bay, USA, known for its significance as an immigration processing center from 1892 to 1954. The total land area of Ellis Island,
including both the main island and adjacent landfills is approximately 27.5 acres or 0.1113 square kilometers.
As the Ellis Island is bigger than 2.5 acres of land, we would have to divide the area of land we are comparing with the size of Ellis Island.
Area of Land we are comparing = 2.5 acres
Area of Ellis Island = 27.5 acres
Size of land compared to Ellis Island = Size of Ellis Island ÷ Size of land being compared
= 2.5 acres ÷ 27.5 acres
= 0.909090 or 1/11
According to the calculation, 1/11 of an Ellis Island (main island only) would fit in a 2.5-acre land area. Or in other words, 2.5 acres of land is 11 times smaller than Ellis Island. It’s important
to note that this calculation assumes that the shape and dimensions of the land area are compatible with those of Ellis Island without considering any other features or obstacles on the land.
2.11 How long does it take to walk across a two-and-a-half acre?
To estimate the time it would take to walk across a two-and-a-half acre parcel of land, we can consider the average walking speeds according to the National Center for Biotechnology Information
(NCBI). For adults, the average walking speed is approximately 3 to 4 miles per hour, equivalent to about 4.4 to 5.9 feet per second or 1.34 to 1.79 meters per second.
First, we need to convert the acre land area to a distance that can be covered by walking. The conversion factor depends on the shape and dimensions of the land, as acres are units of area, not
Let’s assume that the two-and-a-half acre land is square, with sides measuring approximately 208.71 feet (64 meters) each.
Now, we can calculate the distance across the land by multiplying the side length by the square root of 2, as the diagonal of a square is equal to the side length multiplied by the square root of 2.
Distance across the land = Side length × √2
= 208.71 feet × 1.41421356 (approximate value of √2)
= 294.41 feet (rounded to two decimal places)
Next, we can convert the distance from feet to miles by dividing by 5280 (the number of feet in a mile):
Distance across the land in miles = 294.41 feet / 5280 feet per mile = 0.056 miles (rounded to three decimal places)
Finally, we can calculate the time it would take to walk across the land at a speed of 3 miles per hour:
Time to walk across the land = Distance across the land / Walking speed
= 0.056 miles / 3 miles per hour
= 0.01867 hours (or approximately 1.12 minutes)
It would take approximately 1.12 minutes to walk across a two-and-a-half acre land at a walking speed of 3 miles per hour, assuming it is a square shape with sides measuring approximately 208.71 feet
each. Please note that the time taken may vary depending on terrain, walking speed, and individual fitness levels.
3. How to Use 2.5 acres of land?
Utilizing a 2.5-acre parcel of land for dairy farming can be a profitable and rewarding venture with proper planning and management. We will explore the potential of starting a dairy farm on 2.5
acres, discussing the benefits, challenges, and considerations involved. Dairy farming offers high-profit potential, sustainable farming practices, diversification of income, and a close connection
with nature and animals.
However, challenges such as limited grazing space, proper management and planning, compliance with regulations, and labour intensity need to be considered. Before starting a dairy farm, a feasibility
study, a comprehensive business plan, and proper farm infrastructure should be developed. With careful planning and execution, dairy farming on 2.5 acres of land can be a viable and fulfilling
3.1 For Farming
Farming on a 2.5-acre plot of land offers numerous benefits, including self-sufficiency, improved health, and positive environmental impact. By cultivating fresh, organic produce, reducing reliance
on store-bought goods, and promoting sustainable practices, farmers can contribute to the local food system.
However, successful farming requires thorough research, meticulous planning, and physical labor. Essential steps to get started involve researching suitable crops, creating a detailed plan, preparing
the land, planting, maintaining the crops, and harvesting and marketing the produce. Despite challenges such as the need for knowledge and resources, farming on a small parcel of land can be highly
Farming provides opportunities for community engagement, promotes sustainable practices, and offers the advantages of fresh and nutritious produce. Whether an aspiring farmer or an experienced one,
utilizing 2.5 acres for farming can be a fulfilling way to cultivate the land for food production while embracing a healthy and sustainable lifestyle.
3.2 Start producing dairy farms
Dairy farming on a small piece of land, such as 2.5 acres, has both advantages and challenges. The benefits include the potential for high profits, sustainable farming practices, diversification of
income, and a connection with nature and animals. However, challenges may arise from limited space for grazing, the need for proper management and planning, compliance with regulations, and
labour-intensive work.
Dairy farming can be financially rewarding, as dairy products are always in demand. It also promotes sustainable farming practices by utilizing natural resources and allows for income diversification
through various avenues. Additionally, it offers a fulfilling connection with nature and animals for those who enjoy working with cows and being in a rural environment.
Before starting a dairy farm on a 2.5-acre land, conducting a feasibility study, developing a comprehensive business plan, and planning farm infrastructure is crucial. Managing resources effectively,
complying with regulations related to milk quality, animal welfare, and environmental standards, and handling daily chores can be demanding along with this, considering factors such as soil
fertility, water availability, climate, and market demand, and addressing challenges proactively can lead to a successful dairy farming operation on a small piece of land.
Bottom Line
Understanding the size of a two-and-a-half-acre plot can open up a world of possibilities for its use, whether for construction, agriculture, or recreation.
2.5 acres are big enough for 39 tennis courts or nearly one and a half FIFA standard soccer fields, and over 900,000 iPhones could lie flat on it! But remember, owning land also means considering
ongoing costs and responsibilities. So, whether you’re a potential buyer or just someone curious about land sizes, we hope this guide has provided you with a clear, relatable understanding of just
how vast two and a half acres truly is.
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Fractions and Binomials
This article explains how to typeset fractions and binomial coefficients, starting with the following example which uses the amsmath package:
The binomial coefficient, \(\binom{n}{k}\), is defined by the expression:
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!}
Open this example in Overleaf.
The amsmath package is loaded by adding the following line to the document preamble:
Here is the output produced:
Displaying fractions
The visual appearance of fractions will change depending on whether they appear inline, as part of a paragraph, or typeset as standalone material displayed on their own line. The next example
demonstrates those changes to visual appearance:
% Using the geometry package to reduce
% the width of help article graphics
Fractions can be used inline within the paragraph text, for
example \(\frac{1}{2}\), or displayed on their own line,
such as this:
Open this example in Overleaf.
This example produces the following output:
• Note: More information on inline and display versions of mathematics can be found in the Overleaf article Display style in math mode.
Our example fraction is typeset using the \frac command (\frac{1}{2}) which has the general form \frac{numerator}{denominator}.
Text-style fractions
The following example demonstrates typesetting text-only fractions by using the \text{...} command provided by the amsmath package. The \text{...} command is used to prevent LaTeX typesetting the
text as regular mathematical content.
% Using the geometry package to reduce
% the width of help article graphics
\usepackage{amsmath}% For the \text{...} command
We use the \texttt{amsmath} package command
\verb|\text{...}| to create text-only fractions
Without the \verb|\text{...}| command the result
looks like this:
Open this example in Overleaf.
This example produces the following output:
Size and spacing within typeset mathematics
The size and spacing of mathematical material typeset by LaTeX is determined by algorithms which apply size and positioning data contained inside the fonts used to typeset mathematics.
Occasionally, it may be necessary, or desirable, to override the default mathematical styles—size and spacing of math elements—chosen by LaTeX, a topic discussed in the Overleaf help article Display
style in math mode.
To summarize, the default style(s) used to typeset mathematics can be changed by the following commands:
• \textstyle: apply the style used for mathematics typeset in paragraphs;
• \displaystyle: apply the style used for mathematics typeset on lines by themselves;
• \scriptstyle: apply the style used for subscripts or superscripts;
• \scriptscriptstyle: apply the style used for second-order subscripts or superscripts;
which are demonstrated in the next example.
% Using the geometry package to reduce
% the width of help article graphics
Fractions typeset within a paragraph typically look like this: \(\frac{3x}{2}\). You can force \LaTeX{} to use the larger display style, such as \( \displaystyle \frac{3x}{2} \), which also has an effect on line spacing. The size of maths in a paragraph can also be reduced: \(\scriptstyle \frac{3x}{2}\) or \(\scriptscriptstyle \frac{3x}{2}\). For the \verb|\scriptscriptstyle| example note the reduction in spacing: characters are moved closer to the \textit{vinculum} (the line separating numerator and denominator).
Equally, you can change the style of mathematics normally typeset in display style:
\[f(x)=\frac{P(x)}{Q(x)}\quad \textrm{and}\quad \textstyle f(x)=\frac{P(x)}{Q(x)}\quad \textrm{and}\quad \scriptstyle f(x)=\frac{P(x)}{Q(x)}\]
This example produces the following output:
Continued fractions
Fractions can be nested to obtain more complex expressions. The second pair of fractions displayed in the following example both use the \cfrac command, designed specifically to produce continued
fractions. To use \cfrac you must load the amsmath package in the document preamble.
% Using the geometry package to reduce
% the width of help article graphics
% Load amsmath to access the \cfrac{...}{...} command
Fractions can be nested but, in this example, note how the default math styles, as used in the denominator, don't produce ideal results...
\[ \frac{1+\frac{a}{b}}{1+\frac{1}{1+\frac{1}{a}}} \]
\noindent ...so we use \verb|\displaystyle| to improve typesetting:
\[ \frac{1+\frac{a}{b}} {\displaystyle 1+\frac{1}{1+\frac{1}{a}}} \]
Here is an example which uses the \texttt{amsmath} \verb|\cfrac| command:
\[ a_0+\cfrac{1}{a_1+\cfrac{1}{a_2+\cfrac{1}{a_3+\cdots}}}
Here is another example, derived from the \texttt{amsmath} documentation, which demonstrates left
and right placement of the numerator using \verb|\cfrac[l]| and \verb|\cfrac[r]| respectively:
Open this example in Overleaf.
This example produces the following output:
A final example
This example demonstrates a more complex continued fraction:
\[ a_0 + \contfrac{a_1}{
Open this example in Overleaf.
This example produces the following output:
Further reading
For more information see:
Overleaf guides
LaTeX Basics
Figures and tables
References and Citations
Document structure
Field specific
Class files
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nep-ecm 2024-02-26 papers
Abstract: During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1 or
H2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1 and H2). For
example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 when testing H1 and H2, find a significant result for H1 (p < 0.025)
and not for H2 (p > .0.025), and so claim support for H1 and not for H2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union
alternative hypothesis “H1 or H2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it depends on the familywise error rate. When a
researcher corrects their alpha level during multiple testing but does not make an inference about the union alternative hypothesis, their correction is redundant. In the present article, I discuss
this redundant correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment
ritual. I also provide three illustrations of redundant corrections from recent psychology studies. I conclude that redundant corrections represent a symptom of statisticism, and I call for a more
nuanced inference-based approach to multiple testing corrections. | {"url":"https://nep.repec.org/nep-ecm/2024-02-26","timestamp":"2024-11-04T23:27:22Z","content_type":"application/xhtml+xml","content_length":"67396","record_id":"<urn:uuid:a2c63cd0-befd-4d54-9811-ff839c029f79>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00405.warc.gz"} |
Finding the greatest common divisor in TypeScript
First described in the classic geometry book Elements, by the ancient Greek mathematician Euclid (ca. 300 BC, at the book VII, proposition 2), the method of finding de greatest common divisor between
the positive numbers a and b, being a > b consists on the knowledge that the common divisors of a and b are the same of a - b and b. Therefore, we can find this greatest common divisor by replacing
the largest number (a) by the different between the two numbers (a - b), repeatedly, until the two numbers are equal. In TypeScript, we can do that like this:
const gcd = (a: number, b: number): number => {
// When `a` is equal to `b`, return the result
if (a === b) {
return a
// When `a` is bigger than b, calculate the the GCD again
// with the new `a` being `a - b`.
if (a > b) {
return gcd(a - b, b)
// If the new `b` is bigger than `a`,
// subtract a from it.
return gcd(a, b - a)
This method can be very slow if the difference between a and b is too large. Thankfully, there's another method to find the greatest common divisor between two numbers, that can be described as
1. In order to find the greatest common divisor between a and b, being a > b, perform the division between the two numbers. This operation will give a quotient and a remainder (that we will call q
and r, respectively). Thus, a can be described as a = q × b + r;
2. If r is equal to 0, we stop, because we found that the greatest common divisor of a and b is b. Otherwise, we go back to step 1, making b the new a and r will be the new b.
Now, we can start with the implementation of the algorithm above:
const gcd = (a: number, b: number): number => {
// First, we take the remainder between the division of a and b:
const r = a % b
// If the remainder is equal to zero, it means that we already found the
// greatest common divisor, therefore, we return b:
if (r === 0) {
return b
// If the remainder is not equal to 0, we call the function again
// with the new values for a and b:
return gcd(b, a % b)
The implementation is very straightforward and can be read exactly as is described in steps 1 and 2. We can make the function simpler, by checking, directly, if b is equal to zero and only doing the
remainder operation afterwards. Therefore, if the function receive a b that is equal to zero, we will know that a is the greatest common divisor:
const gcd = (a: number, b: number): number => {
if (b === 0) {
return a
return gcd(b, a % b)
This variant is called Euclidean algorithm (in contrast of the first one, which is the Euclid's algorithm) and it significantly faster than the first implementation.
Alternative implementations
We can also take a different approach. Instead of calling our gcd function recursively, we can implement our function using a while loop (analogous to our first implementation above):
const gcd = (a: number, b: number): number => {
// Run this loop while a is different of b
while (a !== b) {
if (a > b) {
// Subtracts b from a while a is bigger than b
a = a - b
// Go to the next loop
// Subtracts a from b when a <= b
b = b - a
// Returns the greatest common divisor between a and b
return a
And this is another way (analogous to our second implementation above):
const gcd = (a: number, b: number): number => {
// Run this loop while `b` is different from 0
while (b !== 0) {
// Save the new value for a in a temporary variable
const newA = b
// Set b to the modulo of a and b (the remainder of the division between a and b)
b = a % b
// Set a to its new value before the next loop
a = newA
// Now that b is equal to 0, we know that a is the greatest common divisor
return a
Finding the greatest common between three or more numbers
The greatest of three or more numbers is equal the product of the prime factors common to all the numbers (we will explore more of that in a future article), but, you can also calculate the greatest
common divisor between pairs of this list of numbers with the same functions we have showed already. So, let's refactor our gcd function to receive multiple parameters:
const gcd = (...numbers: number[]): number => {
const calculateGcd = (a: number, b: number): number => {
if (b === 0) {
return a
return calculateGcd(b, a % b)
return (
// Just to be sure, sort numbers in descendant order:
.sort((a, b) => b - a)
// Call `calculateGcd` for each pair in the numbers array:
.reduce((a, b) => calculateGcd(a, b))
Validating our input
Let's guarantee that our functions should always receive, at least, two numbers and that all numbers must not be negative:
const gcd = (...numbers: number[]): number => {
if (numbers.length < 2) {
throw new Error("You must pass, at least, 2 numbers")
if (numbers.some((number) => number < 0)) {
throw new Error("The numbers must be >= 0")
const calculateGcd = (a: number, b: number): number => {
if (b === 0) {
return a
return calculateGcd(b, a % b);
return (
// Just to be sure, sort numbers in descendant order:
.sort((a, b) => b - a)
// Call `calculateGcd` for each pair in the numbers array:
.reduce((a, b) => calculateGcd(a, b))
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Lineae ex punctis
Blog entries
Real time abstract art generation using a neural net
A simple artificial neural net can be leveraged to produce a variety of visually appealing abstract patterns. For a static image, all that's needed is a random mapping from pixel coordinates to RGB
values. Add a cyclical temporal input, and you'll have evolving patterns. For interactivity, just add mouse coordinates as inputs.
How random can you be?
Suppose I asked you to generate a random sequence of ones and zeroes. Every time you add another 1 or 0 to the sequence, I am going to predict your next choice. Do you think you can make your
sequence random enough that I fail to guess more than ~50% correct? Read this post to find out. Spoiler — you are not so random.
Covariance matrix and principal component analysis — an intuitive linear algebra approach
Let's take a close look at the covariance matrix using basic (unrigorous) linear algebra and investigate the connection between its eigen-vectors and a particular rotation tranformation. We can then
have fun with an interactive visualisation of principal component analysis.
Power iteration algorithm — a visualization
The power method is a simple iterative algorithm used to find eigenvectors of a matrix. I used vtvt to create a visualization of this algorithm.
Popularity of car colours in the Greater Toronto Area
According to a survey conducted in 2012 by PPG Industries, white (21%) and black (19%) were the two most popular colours in North America followed closely by silver and grey (16% each). Red and blue
accounted for 10 and 8% respectively. I decided to test this data by taking photographs of an intersection in Mississauga, Ontario and analyzing them with the help of YOLOv3 as well as OpenCV and
scikit-learn libraries.
Visualization of E, V, B fields
Most physics textbooks illustrate electric and magnetic fields with field lines which are sets of parametrized curves with tangents defined by field vectors. Field lines are great for emphasizing the
directional nature of E and B fields, however they fail to convey the magnitude of forces acting on charges by such fields. One way to overcome this issue is to add level curves indicating vector | {"url":"https://www.expunctis.com/tags/visualisation.html","timestamp":"2024-11-05T13:08:15Z","content_type":"text/html","content_length":"14423","record_id":"<urn:uuid:627eac38-10b9-4b21-92f3-0c23b194686e>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00714.warc.gz"} |
4.2 Non-hierarchical clustering
Pierre Denelle, Boris Leroy and Maxime Lenormand
Non-hierarchical clustering consists in creating groups of objects (called clusters) while maximizing (or minimizing) an evaluating metric. Contrarily to hierarchical clustering, the partition
obtained is not nested. All functions in bioregion relying on non-hierarchical clustering start with the prefix nhclu_.
In biogeography, non-hierarchical clustering is usually applied to identify clusters of sites having similar species compositions. These clusters are then called bioregions.
Non-hierarchical clustering takes place on the very right-hand size part of the bioregion conceptual diagram:
Although these methods are conceptually simple, their implementation can be complex and requires important choices on the part of the user. In the following, we provide a step-by-step guide on how to
do non-hierarchical clustering analyses with bioregion. Such analysis usually has the following steps.
1. Construct a dissimilarity matrix
To initiate the non-hierarchical clustering procedure, we first need to provide pairwise distances between sites.
2. Clustering Non-hierarchical algorithms rely on a user-defined number of clusters. Once this number is defined, users can chose among the 3 functions provided in bioregion to perform
non-hierarchical clustering. These functions are based on centroid-based algorithms (Kmeans and PAM ) or density-based algorithms (DBSCAN).
3. Determining the optimal number of clusters
The two functions partition_metrics() and find_optimal_n() help determining what the optimal number of clusters would be (see Section 4 of this vignette).
1. Dissimilarity indices
Pairwise distances between sites can be obtained by running dissimilarity() on a site-species matrix.
In the example below, we use the fish dataset from the package to compute distance metrics.
# It is a presence/absence matrix with sites in rows and species in columns
fishmat[1:3, 1:3]
## Abramis brama Alburnus alburnus Barbatula barbatula
## Aa 1 1 1
## Abula 0 0 0
## Acheloos 0 0 0
We are going to compute the $\beta_{sim}$ diversity metric, which is a presence-absence dissimilarity index. The formula is as follows:
$\beta_{sim} = min(b, c) / (a+min(b, c))$
Where a is the number of species shared by both sites; b is the number of species occurring only in the first site; and c is the number of species only occurring only in the second site.
We typically choose this metric for bioregionalisation, because it is the turnover component of the Sorensen index (Baselga, 2012) (in a nutshell, it tells us how sites are different because they
have distinct species), and because it has less dependence on species richness than the Jaccard turnover (Leprieur & Oikonomou, 2014).
The choice of the distance metric is very important for the outcome of the clustering procedure, so we recommend that you choose carefully depending on your research question.
dissim <- dissimilarity(fishmat, metric = "Simpson")
dissim[1:3, ]
## Data.frame of dissimilarity between sites
## - Total number of sites: 338
## - Total number of species: 195
## - Number of rows: 56953
## - Number of dissimilarity metrics: 1
## Site1 Site2 Simpson
## 2 Aa Abula 0.3333333
## 3 Aa Acheloos 1.0000000
## 4 Aa Adige 0.7692308
By default, only the Simpson index is computed, but other options are available in the metric argument of dissimilarity(). Furthermore, users can also write down their own formula to compute any
index they wish for in the argument formula, see ?dissimilarity().
We are now ready to start the non-hierarchical clustering procedure with the object dissim we have just created. Alternatively, you can also use other types of objects such as a distance matrix
object (class dist) or a data.frame of your own crafting (make sure to read the required format carefully as explained in the help of each function).
2. Centroid-based clustering
The core idea of these algorithms is to place points into the cluster for which a central-point is the closest. This central-point can either be the centroid of the cluster, i.e. the mean of the x
and y coordinates of all the points belonging to the cluster, or the medoid. The medoid is the most centrally located data point in the cluster, or in other words the least dissimilar point to all
points in the cluster.
The objective is then to minimize the sum of squared distances between points and the assigned centroids/medoids.
2.1. Kmeans
K-means clustering is perhaps the most famous method of non-hierarchical clustering. It uses centroids of clusters.
This algorithm usually follows an iterative framework such as:
1. An initialization step creates k centroids with random placements.
2. For every point, its Euclidean distance with all the centroids is calculated. Each point is then assigned to its nearest centroid. The points assigned to the same centroid form a cluster.
3. Once clusters are formed, new centroids for each cluster are calculated by taking the mean of the x and y coordinates of all the points belonging to the cluster.
4. A re-assignment step then calculates new centroids based on the membership of each cluster. Steps 2 and 3 are repeated until the solution converges, i.e. when the centroid positions no longer
Finding an optimal solution to K-means is computationally intensive and their implementation rely on efficient heuristic algorithms to quickly converge to a local optimum.
The k-means algorithm can become ‘stuck’ in local optima. Repeating the clustering algorithm and adding noise to the data can help evaluate the robustness of the solution.
The function to compute K-means clustering in bioregion is nhclu_kmeans(). We here illustrate how the functions works with an example applied on the dissimilarity matrix calculated above.
We chose 3 clusters.
All the above steps come with arguments that can be tweaked. Specifically, iter_max determines the maximum number of iterations allowed (i.e. how many times the steps described above are run) and
nstart specifies how many random sets of n_clust should be selected as starting points.
Several heuristic algorithms can also be used along with the K-means method and this can be parameterized using the algorithm argument. By default, the algorithm of Hartigan-Wong (Hartigan & Wong
(1979)) is used.
Let’s start by setting both iter_max and nstart to 1.
ex_kmeans <- nhclu_kmeans(dissim, index = "Simpson", n_clust = 3, iter_max = 1,
nstart = 1, algorithm = "Hartigan-Wong")
When asking for one iteration only, the function displays a message saying that the algorithm did not converge.
We therefore need to increase the value of iter_max.
ex_kmeans <- nhclu_kmeans(dissim, index = "Simpson", n_clust = 3, iter_max = 3,
nstart = 1, algorithm = "Hartigan-Wong")
Like for all other functions of the bioregion package, the class of the object is specific for the package (here bioregion.clusters) and it contains several parts. The clusters assigned to each site
are accessible in the $clusters part of the output:
ex_kmeans$clusters[1:3, ]
## ID K_3
## Aa Aa 3
## Abula Abula 1
## Acheloos Acheloos 2
## 1 2 3
## 142 93 103
Here, we see that 142 sites are assigned to cluster 1, 93 to cluster 2 and 103 to cluster 3.
This assignment can change depending on the two other main arguments of the functions, iter_max and nstart.
ex_kmeans2 <- nhclu_kmeans(dissim, index = "Simpson", n_clust = 3,
iter_max = 100, nstart = 1,
algorithm = "Hartigan-Wong")
ex_kmeans3 <- nhclu_kmeans(dissim, index = "Simpson", n_clust = 3,
iter_max = 3, nstart = 100,
algorithm = "Hartigan-Wong")
As shown below, the distribution of sites among the three clusters appears quite homogeneous with our three examples but some discrepancies emerge.
table(ex_kmeans$clusters$K_3, ex_kmeans2$clusters$K_3)
## 1 2 3
## 1 1 12 129
## 2 77 16 0
## 3 0 9 94
table(ex_kmeans$clusters$K_3, ex_kmeans3$clusters$K_3)
## 1 2 3
## 1 111 29 2
## 2 0 0 93
## 3 0 102 1
Overall, increasing iter_max and nstart increases the chances of convergence of the algorithm but also increases the computation time.
2.2. K-medoids
Instead of using the mean of the cluster, the medoid can also be used to partition the data points.
In comparison with the centroid used for K-means, the medoid is less sensitive to outliers in the data. These partitions can also use other types of distances and do not have to rely on the Euclidean
distance only.
Several heuristics exist to solve the K-medoids problem, the most famous ones being the Partition Around Medoids (PAM), and its extensions CLARA and CLARANS.
2.2.1. Partitioning Around Medoids (PAM)
PAM is a fast heuristic to find a solution to the k-medoids problem. With k clusters, it decomposes following these steps:
1. Randomly pick k points as initial medoids
2. Assign each point to the nearest medoid x
3. Calculate the objective function (the sum of dissimilarities of all points to their nearest medoids)
4. Randomly select a point y
5. Swap x by y if the swap reduces the objective function
6. Repeat 3-6 until no change
In the nhclu_pam() function, there are several arguments to tweak. The number of clusters n_clust has to be defined as well as the number of starting positions for the medoids nstart.
Several variants of the PAM algorithm are available and can be changed with the argument variant (see cluster::pam() for more details).
ex_pam <- nhclu_pam(dissim, index = "Simpson", n_clust = 2:25, nstart = 1,
variant = "faster", cluster_only = FALSE)
## 1 2
## 258 80
With 2 clusters, we see that 258 sites are assigned to cluster 1 and 80 to cluster 2.
2.2.2. Clustering Large Applications (CLARA)
CLARA (Clustering Large Applications, (Kaufman and Rousseeuw 1990)) is an extension of the k-medoids (PAM) methods to deal with data containing a large number of objects (more than several thousand
observations) in order to reduce the computational time and the RAM storage problem. This is achieved by using the sampling approach.
ex_clara <- nhclu_clara(dissim, index = "Simpson",
n_clust = 5,
maxiter = 0L, initializer = "LAB", fasttol = 1,
numsamples = 5L, sampling = 0.25, independent = FALSE,
seed = 123456789L)
## 1 2 3 4 5
## 241 21 16 50 10
2.2.3. Clustering Large Applications based on RANdomized Search (CLARANS)
CLARANS (Clustering Large Applications based on RANdomized Search, (Ng and Han 2002)) is an extension of the k-medoids (PAM) methods combined with the CLARA algorithm.
ex_clarans <- nhclu_clarans(dissim, index = "Simpson",
n_clust = 5,
numlocal = 2L, maxneighbor = 0.025,
seed = 123456789L)
## 1 2 3 4 5
## 241 21 16 50 10
3. Density-based clustering
Density-based clustering is another type of non-hierarchical clustering. It connects areas of high density into clusters. This allows for arbitrary-shaped distributions as long as dense areas can be
connected. These algorithms can however have difficulty with data of varying densities and high dimensions.
3.1. DBSCAN
Density-based Spatial Clustering of Applications with Noise (DBSCAN) (Hahsler et al. (2019)) is the most famous density-based clustering approach.
It operates by locating points in the dataset that are surrounded by a significant number of other points. These points are regarded to be part of a dense zone, and the algorithm will next attempt to
extend this region to encompass all of the cluster’s points.
DBSCAN uses the two following parameters:
Epsilon (eps): the maximum distance between two points to be considered as neighboring points (belonging to the same cluster).
Minimum Points (minPts): The minimum number of neighboring points that a given point needs to be considered a core data point. This includes the point itself. For example, if minimum number of points
is set to 4, then a given point needs to have 3 or more neighboring data points to be considered a core data point.
If minimum number of points meet the epsilon distance requirement then they are considered as a cluster.
Having set these two parameters, the algorithm works like this:
1. Decide the value of eps and minPts.
2. For each point: Calculate its distance from all other points. If the distance is less than or equal to eps then mark that point as a neighbor of x. If the point gets a neighboring count greater
than or equal to minPts, then mark it as a core point or visited.
3. For each core point, if it not already assigned to a cluster than create a new cluster. Recursively find all its neighboring points and assign them the same cluster as the core point.
4. Continue these steps until all the unvisited points are covered.
This algorithm can be called with the function nhclu_dbscan(). If the user does not define the two arguments presented above, minPts and eps, then the function will provide a knee curve helping the
search of an optimal eps value.
ex_dbscan <- nhclu_dbscan(dissim, index = "Simpson", minPts = NULL, eps = NULL,
plot = TRUE)
## Trying to find a knee in the curve to search for an optimal eps value...
## NOTE: this automatic identification of the knee may not work properly
## if the curve has knees and elbows. Please adjust eps manually by
## inspecting the curve, identifying a knee as follows:
## /
## curve /
## ___________/ <- knee
## elbow -> /
## /
## /
Here, we see that we can set eps to 1.
ex_dbscan2 <- nhclu_dbscan(dissim, index = "Simpson", minPts = NULL, eps = 1,
plot = FALSE)
With this set of parameters, we only get one cluster.
## 1
## 338
If we decrease the eps value and increase minPts, we can get more clusters.
ex_dbscan3 <- nhclu_dbscan(dissim, index = "Simpson", minPts = 4, eps = 0.5,
plot = FALSE)
## < table of extent 0 >
4. Affinity propagation
This algorithm is based on the paper of Frey & Dueck (2007) and relies on the R package apcluster
Unlike the previous algorithms in this vignette, this algorithm and its associated function use a similarity matrix.
5. Optimal number of clusters
Previous methods did not help in determining the optimal number of bioregions structuring the site-species matrix.
For this purpose, we can combine both functions partition_metrics() and find_optimal().
partition_metrics() calcultes several metrics based on the previous clustering attempts.
## Partition metrics:
## - 24 partition(s) evaluated
## - Range of clusters explored: from 2 to 25
## - Requested metric(s): pc_distance
## - Metric summary:
## pc_distance
## Min 0.5464742
## Mean 0.8022971
## Max 0.8949633
## Access the data.frame of metrics with your_object$evaluation_df
*Note For the two metrics tot_endemism and avg_endemism, you also need to provide the site-species matrix.
a <- partition_metrics(ex_pam, dissimilarity = dissim, net = fishdf,
species_col = "Species", site_col = "Site",
eval_metric = c("tot_endemism", "avg_endemism",
"pc_distance", "anosim"))
Once the partition_metrics() function has calculated the partitioning metrics, we can call find_optimal() to get the optimal number of clusters.
## [1] "tot_endemism" "avg_endemism" "pc_distance" "anosim"
## Number of partitions: 24
## Searching for potential optimal number(s) of clusters based on the elbow method
## * elbow found at:
## tot_endemism 4
## avg_endemism 4
## pc_distance 7
## anosim 2
## Plotting results...
## Search for an optimal number of clusters:
## - 24 partition(s) evaluated
## - Range of clusters explored: from 2 to 25
## - Evaluated metric(s): tot_endemism avg_endemism pc_distance anosim
## Potential optimal partition(s):
## - Criterion chosen to optimise the number of clusters: elbow
## - Optimal partition(s) of clusters for each metric:
## tot_endemism - 4
## avg_endemism - 4
## pc_distance - 7
## anosim - 2
Based on the metric selected, the optimal number of clusters can vary.
Baselga, A. (2012). The relationship between species replacement, dissimilarity derived from nestedness, and nestedness. Global Ecology and Biogeography, 21(12), 1223–1232.
Frey, B., & Dueck, D. (2007). Clustering by passing messages between data points. Science, 315, 972–976.
Hahsler, M., Piekenbrock, M., & Doran, D. (2019). Dbscan: Fast density-based clustering with r. Journal of Statistical Software, 91(1).
Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the Royal Statistical Society. Series c (Applied Statistics), 28(1), 100–108.
Leprieur, F., & Oikonomou, A. (2014). The need for richness-independent measures of turnover when delineating biogeographical regions. Journal of Biogeography, 41, 417–420. | {"url":"https://biorgeo.github.io/bioregion/articles/a4_2_non_hierarchical_clustering.html","timestamp":"2024-11-04T19:49:21Z","content_type":"text/html","content_length":"48182","record_id":"<urn:uuid:b8cba771-2511-4c6b-9b8d-f8397ccddec9>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00660.warc.gz"} |
How to Calculate Annualized Rate of Return in Excel?
How to Calculate Annualized Rate of Return in Excel?
If you’re looking for a way to easily calculate the annualized rate of return in Excel, look no further. With the help of this article, you will learn the simple steps necessary to accurately
calculate the annualized rate of return in Excel. By the end of this article, you will have the knowledge and confidence to calculate your own annualized rate of return in Excel. So let’s dive right
in and learn how to calculate your annualized rate of return in Excel.
To calculate Annualized Rate of Return in Excel, follow the steps below:
• Open a new Excel Spreadsheet.
• Enter the data into the spreadsheet.
• Calculate the initial investment’s return by subtracting the initial investment amount from the total investment value.
• Divide the return by the initial investment amount.
• Multiply the result by 100 to calculate the rate of return.
• Multiply the rate of return by the number of years the investment was held.
• Add 1 to the result, then divide by the number of years the investment was held.
• Subtract 1 from the result to calculate the Annualized Rate of Return.
Calculating the Annualized Rate of Return in Excel
The annualized rate of return is a measure of the gain or loss generated by an investment over a certain period of time. It is typically used to compare different investments, such as stocks, bonds,
and mutual funds. By calculating the annualized rate of return, investors can determine which investments are more profitable and which are less so. Fortunately, calculating the annualized rate of
return in Excel is relatively straightforward.
Step 1: Gather Data
The first step in calculating the annualized rate of return in Excel is to gather the necessary data. This includes the initial investment amount, the ending value of the investment, and the length
of time the investment was held. This data can be found in financial statements, such as brokerage statements or mutual fund statements. Once the data has been gathered, it can be entered into Excel.
Step 2: Enter Data into Excel
Once the data has been gathered, it can be entered into Excel. The data should be entered into separate columns, with the initial investment amount in one column, the ending value of the investment
in another column, and the length of time the investment was held in a third column.
Step 3: Calculate Rate of Return
Once the data has been entered into Excel, the rate of return can be calculated using the XIRR function. This function takes the initial investment amount, the ending value of the investment, and the
length of time the investment was held and calculates the annualized rate of return.
Calculating the Internal Rate of Return
The internal rate of return (IRR) is a measure of the return generated by an investment over a certain period of time. It is typically used to compare different investments, such as stocks, bonds,
and mutual funds. By calculating the internal rate of return, investors can determine which investments are more profitable and which are less so. Fortunately, calculating the internal rate of return
in Excel is relatively straightforward.
Step 1: Gather Data
The first step in calculating the internal rate of return in Excel is to gather the necessary data. This includes the initial investment amount, the ending value of the investment, and any cash flows
that may have occurred during the period the investment was held. This data can be found in financial statements, such as brokerage statements or mutual fund statements. Once the data has been
gathered, it can be entered into Excel.
Step 2: Enter Data into Excel
Once the data has been gathered, it can be entered into Excel. The data should be entered into separate columns, with the initial investment amount in one column, the ending value of the investment
in another column, and any cash flows that may have occurred during the period the investment was held in a third column.
Step 3: Calculate Internal Rate of Return
Once the data has been entered into Excel, the internal rate of return can be calculated using the XIRR function. This function takes the initial investment amount, the ending value of the
investment, and any cash flows that may have occurred during the period the investment was held and calculates the internal rate of return.
Related FAQ
What is the Annualized Rate of Return?
The Annualized Rate of Return, or ARR, is a measure of the annual rate of return on an investment. It is calculated by taking the rate of return over a specific period of time, such as a year, and
multiplying it by the number of periods in a year. It is often used to compare different investments or to measure the performance of a portfolio over time.
What is the Formula for Calculating the Annualized Rate of Return in Excel?
The formula for calculating the Annualized Rate of Return in Excel is: ARR = ((Investment Value at the End of the Year – Investment Value at the Beginning of the Year) + Dividends)/Investment Value
at the Beginning of the Year.
How Do I Input Data for Calculating the Annualized Rate of Return in Excel?
In order to calculate the Annualized Rate of Return in Excel, you will need to input the data for the beginning and end of year values for the investment, as well as any dividends that have been
earned. This data should be entered into cells in the spreadsheet, with one column for the beginning of year value, one column for the end of year value, and one column for the dividends.
How Do I Calculate the Annualized Rate of Return in Excel?
Once the data has been entered into the spreadsheet, the Annualized Rate of Return can be calculated by using the ARR formula. To do this, select the cell where the ARR formula should be entered and
enter =((end of year value – beginning of year value) + dividends)/beginning of year value. This will calculate the Annualized Rate of Return for the investment.
How Can I Use the Calculated Annualized Rate of Return in Excel?
The calculated Annualized Rate of Return can be used to compare different investments, measure the performance of a portfolio over time, or to assess the return on an individual investment. This
information can be used to make decisions about where to invest money and which investments are more likely to generate a higher return.
What Other Factors Should I Consider When Calculating the Annualized Rate of Return in Excel?
When calculating the Annualized Rate of Return in Excel, it is important to consider other factors that could affect the rate of return, such as taxes, inflation, and fees. Additionally, it is
important to consider the time horizon of the investment, as different investments may have different rates of return over different periods of time.
Calculate Annualized Returns for Investments in Excel
In conclusion, calculating the annualized rate of return in Excel is a simple and straightforward process. With the help of basic Excel formulas and functions, anyone can quickly and accurately
calculate their annualized rate of return. With this knowledge, investors can make the most informed decisions when it comes to making investments and managing their portfolios. | {"url":"https://keys.direct/blogs/blog/how-to-calculate-annualized-rate-of-return-in-excel","timestamp":"2024-11-13T15:05:12Z","content_type":"text/html","content_length":"355436","record_id":"<urn:uuid:1bbd6d78-f9fa-41b5-bce1-c58d82ef4b88>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00318.warc.gz"} |
Stochastic optimal feedforward-feedback control determines timing and variability of arm movements with or without vision
Human movements with or without vision exhibit timing (i.e. speed and duration) and variability characteristics which are not well captured by existing computational models. Here, we introduce a
stochastic optimal feedforward-feedback control (SFFC) model that can predict the nominal timing and trial-by-trial variability of self-paced arm reaching movements carried out with or without online
visual feedback of the hand. In SFFC, movement timing results from the minimization of the intrinsic factors of effort and variance due to constant and signal-dependent motor noise, and movement
variability depends on the integration of visual feedback. Reaching arm movements data are used to examine the effect of online vision on movement timing and variability, and test the model. This
modelling suggests that the central nervous system predicts the effects of sensorimotor noise to generate an optimal feedforward motor command, and triggers optimal feedback corrections to
task-related errors based on the available limb state estimate.
Author summary
Stochastic optimal feedback control, which has been extensively used to model human motor control in the last two decades, proposes to compute an optimal motor command online based on an estimation
of the current system state using sensory feedback. However, this modelling approach underestimates the role of motor plans to generate appropriate feedforward motor command before the movement
starts, which is emphasized in conditions with large uncertainty about current limb state estimates such as when visual feedback is lacking. Here we propose a model combining stochastic feedforward
and feedback control to address this issue. The new stochastic feedforward-feedback (SFFC) model considers effort and variance minimization as well as the effects of motor and sensory noise both on
planning and execution of arm movements. By combining the feedforward and feedback aspects of stochastically optimal control in an elegant way, SFFC can predict the timing and variability of
movements carried out with or without visual feedback, while previous models would fail in one or another aspect, or have to use ad hoc fixes.
Citation: Berret B, Conessa A, Schweighofer N, Burdet E (2021) Stochastic optimal feedforward-feedback control determines timing and variability of arm movements with or without vision. PLoS Comput
Biol 17(6): e1009047. https://doi.org/10.1371/journal.pcbi.1009047
Editor: Ulrik R. Beierholm, Durham University, UNITED KINGDOM
Received: November 26, 2020; Accepted: May 5, 2021; Published: June 11, 2021
Copyright: © 2021 Berret et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction
in any medium, provided the original author and source are credited.
Data Availability: All relevant experimental data are within the manuscript and its Supporting information files.
Funding: This work was in part funded by the EC under grants H2020 PH-CODING (FETOPEN 829186), INTUITIVE (ITN 861166), REHYB (ICT 871767) [EB], by NIH NINDS 1R56NS100528, NIH NINDS R21NS120274 grants
[NS], and by the French National Agency for Research (grant ANR-19-CE33-0009) [BB]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the
Competing interests: The authors have declared that no competing interests exist.
Spatial and temporal regularities in human motion suggest that the neural control of movement involves a planning stage [1, 2]. Evidence for motor planning has been provided in behavioural
experiments [3, 4] and through the observation of neural processes prior to movement generation [5–7]. Among the planned aspects of movement, the timing (i.e. speed and duration) and trial-by-trial
variability are important determinants of successful actions [8]. However, the principles according to which the central nervous system (CNS) may determine these critical features is not well
explained by existing models.
The currently dominating theory of motor control, stochastic optimal (feedback) control (SOC) [9–12], can explain the coordination of the degrees-of-freedom of the sensorimotor system, the structure
of trial-by-trial variability or the reactive behavior to external perturbations [13–16]. However, SOC does not account well for the timing of self-paced reaching movements. As with deterministic
optimal control (DOC) models (e.g. [17, 18]) the costs minimised in SOC models, effort and error, decrease monotonically with increasing movement duration, thereby predicting infinitely slow
visually-guided movements. Fig 1A illustrates this issue for the SOC model of [19] where both motor and observation noise are considered. Interestingly, when SOC is used to model movements without
vision by increasing observation noise to reflect a degraded hand state estimate, a finite optimal duration can be obtained because endpoint variance now increases with duration. Therefore, SOC with
large enough observation noise may determine the timing and variability of movements without vision (Fig 1B), but the same principle cannot be used directly for visually-guided movements.
A 10-cm long reaching movement of a point mass model of an arm is simulated. These simulations rely on the extended linear-quadratic-Gaussian framework considering multiplicative (signal-dependent)
and additive (constant) motor noise as well as additive observation noise. A. Simulations with a standard observation noise corresponding to a visually-guided movement, as proposed in the original
model of [19]. The expected costs for different movement durations were estimated using the Monte Carlo method (100,000 samples). This model fails to predict a finite movement duration because the
optimal expected effort and total cost (sum of effort and terminal error costs) monotonically decrease with duration and plateau. The positional endpoint variance (gray trace) can also be seen to
decrease and plateau to a value which mainly corresponds to that of visually-guided movements. B. Simulations with a large observation noise (noise in A multiplied by 10), corresponding to movements
without vision. In this case, an optimal duration can be determined as the minimum of the total cost (indicated by a black vertical dotted line).
Several ad hoc solutions have been proposed to circumvent this issue. In several models considering sensorimotor noise, duration was selected as the minimum time to match a desired endpoint variance
related to target’s width, based on the speed-accuracy trade-off underlying visually-guided movements [8, 20–22]. Alternatively, a number of studies have assumed a “cost of time” (reflecting
neuroeconomical processes related to decision-making and explicitly penalizing duration) to explain the preferred timing of movement [23–30].
However, the preferred movement timing may be predicted without requiring an ad hoc solution. In particular, the results of [31] suggest that the motor noise, with its constant and signal dependent
components, is a relevant factor to determine this characteristic of motion planning. Specifically, the preferred duration of movements performed without vision was found to be longer than the
minimum variance duration, thereby suggesting that movement timing was determined from a neuromechanical principle based on a trade-off between effort and variance in the presence of signal-dependent
and constant motor noise. Such optimality principle could explain the stereotyped durations and trajectories of saccades [32], but its relevance for arm reaching has not been tested in particular for
visually-guided movements.
Because SOC cannot be used for this purpose (see Fig 1A), here we develop a new computational model to predict the timing and variability of arm pointing movements carried out with complete or
degraded sensory feedback (e.g. when vision of the hand is prevented) from neuromechanical factors only. This stochastic feedforward-feedback control (SFFC) model assumes that the motor command
comprises a feedforward and a feedback components. The feedforward component is computed using the stochastic optimal open-loop control (SOOC) framework, which was initially developed to account for
the planning of mechanical impedance via muscle co-contraction [33, 34]. This feedforward command yields an expectation about a timed trajectory. The feedback component is then computed using the
linear SOC framework from a local approximation of the task dynamics, which allows triggering motor corrections in reaction to deviations from the goal, based on an estimation of the system’s state
from the available sensory information and internal predictions. As a result, the proposed model merges the main precepts of influential models highlighting either the role of feedforward-only or
feedback-only control [8–10, 13, 17–19].
Predictions from the SFFC model are first tested by simulating arm reaching movements carried out without visual feedback and comparing the results with the available experimental results of [31, 35
], and [36]. Second, an experiment was conducted to analyse the timing and variability of movements performed with and without online visual feedback of the hand. The SFFC predictions for movements
in these two conditions are then compared to these new experimental data.
Stochastic feedforward-feedback control model
In the proposed model, the actual motor command is made of a feedforward component (i.e. determined prior to movement execution) and a feedback component (i.e. determined throughout movement
execution based on an estimation of the current state) to correct task-related errors as illustrated in Fig 2. This is a classical approach in optimal control theory (e.g. see [37, 38]). However,
feedforward control is usually associated with deterministic systems and feedback control with stochastic systems. In the approach presented here, the feedforward command is optimized for the
system’s stochasticity (i.e. presence of both signal-dependent and constant motor noise) as in [8] and [33].
A feedforward command u(t) is formed by the CNS based on prior knowledge about the task dynamics represented by f and G. A representation of the associated expected system’s trajectory is also
established, which allows building a local approximation of the task dynamics and working in terms of state/control deviations (z[t] and v[t] respectively) during movement execution. This is done by
setting the matrices and . An estimate of the current state deviation is computed from multisensory information y[t]. This allows triggering a feedback command online to correct task-relevant errors
caused by unexpected internal and external perturbations due e.g. to motor noise or external forces. In this scheme, the actual motor command u(t) + v[t] is the sum of the feedforward and feedback
commands. The matrices L(t) and K(t) denote the optimal filter and feedback gains respectively, g is the output function and in the local approximation. The random processes ω[t] and η[t] are
implemented here as Brownian. D(t) is an observation noise matrix, the magnitude of which can be increased to simulate the absence of vision. The vector h[t] denotes the deviation from the sensory
prediction. The terms C[ff] and C[fb] refer to the cost functions that determine the optimal signature of the feedforward and feedback commands. The definition and meaning of all the variables are
given in the Results section.
As we shall see, considering a feedforward command for a stochastic plant allows predicting an optimal movement duration because this command considers the effects of additive noise in the temporal
evolution of the state covariance. The actual movement timing and variability may however be affected by sensory-based motor corrections issued online to handle unexpected perturbations and critical
deviations from the task’s goal. This is the role of the high-level feedback command. In SFFC, the motor plan is thus primarily composed of a feedforward motor command (i.e. an optimal open-loop
control) and an expectation about the upcoming state trajectory. It is complemented by a locally-optimal feedback gain that combines with a limb state estimate throughout movement execution to
determine a task-relevant corrective motor command. This estimate is based on both internal predictions and relevant sensory information (e.g. proprioception or vision). We describe below how the
feedforward and feedback components of the model are computed.
Determining the feedforward motor command via nonlinear stochastic optimal open-loop control.
Here we consider a minimum effort-variance model of motor planning with additive and multiplicative motor noise to determine the feedforward motor command. The expectation and covariance of a nominal
state trajectory can be obtained from this sub-problem.
Let us consider a general rigid body dynamics with n degrees of freedom such as to model human arm movements: (1) where is the joint coordinates vector, the net joint torque vector produced by
muscles, the inertia matrix, the Coriolis/centripetal, the viscosity, and the gravity terms. This dynamical system is nonlinear due to the mechanical coupling between the different body segments and
gravity. Let us assume that the torque change is the control variable as in [18]: (2)
In a standard SOC model the motor command would be a stochastic variable u[t] that depends on the random fluctuations arising from motor and measurement noise as well as from any environmental
perturbations. As stressed before and in Fig 2, here we rather assume that motor planning primarily builds a feedforward motor command. This enables the feedforward component of the motor command to
consider all the internal and external dynamic effects that can be learnt (including the consequences of noise, the sensory delays, the instability due to the interaction with the environment etc.)
during the planning stage. To derive such a feedforward motor command, we restrict the control to be open-loop (denoted by u(t) to stress its deterministic nature) while retaining the stochastic
aspect of the system’s dynamics.
To this aim, let us assume that the arm movements are affected by multiplicative motor noise (i.e. with signal-dependent variance) and additive motor noise (i.e. with constant variance), modeled as a
M-dimensional standard Brownian motion, ω[t]. The corresponding stochastic dynamics of the arm can be described by (3) where x[t] is the stochastic state vector and and are respectively the drift and
diffusion terms (here N = 3n). The matrix G includes both the constant and the signal-dependent noise terms.
For the reaching task under consideration, the control objective is to move the arm from an initial position x[0] to a given target in time T with minimum effort and minimum variance, that is, by
minimizing an expected cost of the form (4) where ϕ is a quadratic function penalizing the final state of the process (typically related to its covariance here), and l is a cost depending on and the
open-loop control u(t). The cost l can be thought as a measure of effort but it can also include terms like trajectory smoothness. The parameter r is a weighting factor to trade-off the variance and
effort/trajectory costs.
This stochastic optimal open-loop control problem can be solved using approximate solutions based on stochastic linearization techniques (see [33]).
Let us denote the covariance of the process x[t] by (5)
It can be shown (e.g. [39], Chap. 12) that propagation of the mean m(t) and covariance P(t) can be approximated using a second order Taylor’s expansion for f by the following ordinary differential
equations: (6)
These ordinary differential equations are important to reformulate the initial problem as a deterministic optimal control problem involving only the mean and covariance of the original stochastic
state process x[t].
To do so, it must be noted that the expected cost function can also be rewritten in terms of the mean and covariance of x[t] only as (7) where Φ is a function of the terminal mean and covariance of
the random variable x[T]. Note that the trajectory cost l can be taken outside of the expectation because the control and mean are deterministic variables (by hypothesis and definition,
We thus obtain a deterministic optimal control problem (approximately equivalent to the stochastic problem defined by Eqs 3 and 4) to solve for the augmented state (m, P). This problem is summarized
as: (8)
Interestingly, the efficient theoretical and numerical tools developed for DOC can be used to solve the above problem (e.g. [40]). Note that hard constraints for the final mean or covariance of the
state can also be added in this formulation. We did so for the final mean state to ensure that the arm exactly reaches the desired target on average even though we could have modelled this constraint
in the cost itself. The latter choice has the disadvantage of introducing additional tuning weights in the cost but could allow accounting for a terminal bias. Here we rather left the final
covariance free because it was penalized in the cost function and was needed to determine an optimal movement duration without having to preset a desired amount of endpoint variance. The above
optimal control problem can be run in free time, which means that the duration T can be found automatically from the necessary optimality conditions of Pontryagin’s maximum principle (instead of a
laborious trial-and-error search process as it has been done in previous approaches such as [8] or [41]). The problem can also be run in fixed time, which means that the duration is preset by the
researcher. We did so when investigating the evolution of optimal costs with respect to various movement durations and to adjust noise magnitudes for fast or slow movements performed without vision
(see Materials and methods section).
Determining the feedback motor command via linear stochastic optimal feedback control.
During their execution, movements can be modified with incoming sensory information. This information can be exploited to form an optimal estimate of the current limb state, which can be used online
through a linear locally-optimal feedback control scheme. Here, by linearizing the dynamics around the nominal expected state/control trajectories coming from SOOC, we will use the standard
linear-quadratic-Gaussian framework [19, 37]. We shall also consider that, besides motor noise, there is some observation noise, the magnitude of which will depend on the available sensory modalities
(e.g. with or without vision).
At this stage, we have access to a nominal open-loop control and an expected state trajectory, denoted by u(t) and m(t) respectively, for t ∈ [0, T]. We next extended the time horizon T′ > T in order
to consider that executed movements have a longer duration than initially planned, assuming that the system is at rest for t ≥ T.
To compute a locally-optimal feedback control, the dynamics is linearized around m(t) and u(t) using Taylor’s expansions to obtain a linear-quadratic-Gaussian approximation in terms of state/control
deviations (e.g. [42]) as follows: (9) where (10) and (11)
We further assume that the noisy sensory feedback y[t] is obtained during motion execution from the following output equation: (12) where and is the output function. The matrix specifies how
observation noise affects sensory feedback, where η[t] is a L-dimensional standard Brownian motion process.
Using again a Taylor’s expansion and defining , the output equation can be approximated locally in terms of state deviations z[t] as (13) where h[t] = y[t] − y(t) with y(t) = ∫g(m(t))dt.
For this sub-problem, a quadratic cost function to ensure task achievement with minimal effort is defined as follows: (14)
The locally-optimal feedback control law can be written as where K(t) is the feedback gain matrix and is the optimal estimate of the state deviation z[t] obtained from the Kalman filter equation:
(15) where L(t) is the optimal filter gain.
The problem defined by Eqs 9, 13 and 14 is a linear-quadratic-Gaussian problem, which can be solved using standard algorithms (e.g. [19]).
An overview of the SFFC model is given in Fig 2.
While the cost functions for the feedforward and feedback components both minimize error and effort terms (see Eqs (4) and (14)), they differ in several fundamental aspects. On the one hand, the
feedforward cost function relies on deterministic variables that can be computed or estimated prior to the movement start. It aims at determining an optimal feedforward motor command, from which an
expectation about the upcoming trajectory can be obtained. This cost minimizes effort (and possibly other terms such as smoothness) and endpoint variance, which in turn allows to specify the shape
and characteristics of mean arm trajectories as well as the state covariance that would result from feedforward control (i.e. without online sensory feedback). Critically, this knowledge allows
linearizing the arm’s dynamics in order to apply the linear SOC framework subsequently. On the other hand, the feedback cost function depends on the stochastic deviations from the above expected
control/state trajectories which will arise during movement execution. It ensures that the task will be achieved with a minimal amount of motor correction, in accordance with the minimal intervention
principle [13]. This is done here by minimizing errors at the end of the movement (i.e. for times longer than the planned movement duration). The R term can be adjusted depending on the task, which
will in turn determine the magnitude of the planned feedback gain K(t). To compute the feedback component of the motor command, related to online corrections, the system requires sensory information
to update the estimate of the limb state throughout movement execution. Hence, internal or external perturbations inducing a deviation from the expected trajectory will be corrected via a
task-dependent feedback mechanism. While SFFC assumes that the brain has some knowledge of the upcoming reach trajectory and feedforward command to reformulate the task in terms of state/control
deviations, it must be noted that the feedback cost does not assume that a reference trajectory is tracked. If the task does involve trajectory tracking this can be handled by minimizing errors
throughout the whole movement in the feedback cost or modelled by considering muscle viscoelasticity and mechanical impedance as in [33].
Simulation results and comparison to experimental data
To test the SFFC model we consider a pointing task with a two-link arm moving in the horizontal plane from an initial posture to a target in Cartesian space (e.g. [31, 35, 36]). More details about
the task, model of the arm and choice of parameters can be found in the Materials and methods section.
Comparison to previous data of reaching movements without vision.
We first tested if SOOC can determine an optimal movement timing from the principle illustrated in Fig 1B. As SOOC does not consider the influence of online sensory feedback, its prediction would
mainly correspond to the behavior of deafferented patients without vision of the moving hand (e.g. [43, 44]). It must be noted that SOOC at least requires an estimate of the initial arm’s state to
build the optimal feedforward motor command, in agreement with [43] who showed that prior vision of the arm improved movement precision in these patients.
Fig 3A illustrates that the evolution of the optimal expected cost with respect to movement duration. This U-shape cost function yields an optimal duration, which can be thought as the limit case of
Fig 1B when observation noise is infinite. Remarkably, the resulting optimal duration is longer than the duration of minimum variance, which is in agreement with the observation of [31]. Fig 3B and
3C show the corresponding mean hand trajectory, the path of which is approximately straight with bell-shaped velocity profile. This agrees with typical findings in healthy subjects and also with the
overall strategy of deafferented patients without online vision [44]. Interestingly, SOOC also provides information about the final variability of the pointing under pure feedforward control (i.e.
without feedback component; represented as a confidence ellipse in Fig 3B). The large final variability (compared to target size) is compatible with the relatively large endpoint variability
exhibited by deafferented patients [44].
A. Evolution of the optimal costs with respect to the movement duration. The total cost function exhibits a U-shape, i.e. additive motor noise yields a minimal movement duration. The minimal duration
(minimum of the black solid trace) is larger than the duration of minimum variance (the gray curve). B. Mean hand path and predicted endpoint variability (here depicted as a 90% confidence ellipse).
These data can be computed from m(t) and P(t) respectively (converted from joint space to Cartesian space). The black circle depicts the target. C. Corresponding mean velocity profile. The dashed
horizontal line indicates the threshold at which velocity profiles are cut in the experimental data. This figure is generated using simulation data of free-time optimal control computed with SOOC.
Next, we focus on previous experimental observations in healthy subjects performing movements without online visual feedback of the hand [31, 35, 36]. Healthy subjects typically have a smaller
endpoint variability than deafferented patients without vision. In healthy subjects, proprioceptive feedback is indeed available and this sensory information can be used by the brain to build an
estimate of the limb state. However, the absence of vision (and thus of multisensory integration) may degrade the hand state estimate [45], which can be accounted for in our model by assuming a
relatively large observation noise in this case.
Fig 4A and 4B show the path of trials in the N-W and N-E directions when simulating the experiment of [31], where parameters were selected to reproduce the data in the N-W direction. The trajectories
predicted by the model are similar to the trajectories experimentally measured in this task, with relatively straight hand path and bell-shaped velocity profile. The duration determined by the SFFC
model was also in good agreement with the data. Interestingly, as in the experimental data of [31], the predicted duration was slightly longer for movements in the N-W than in the N-E direction, and
the variance was also slightly larger in the N-W direction. It can also be noted that the endpoint variability is smaller with SFFC than with SOOC, thereby illustrating the improvement with
proprioceptive feedback.
A-B. Simulation of the data of [31]. Hand paths of 20 trials are shown in panels A and B for the N-W and N-E directions, respectively. 90% confidence ellipses of the end points are depicted in blue,
which were computed from 1,000 samples. Dotted ellipses, corresponding to the endpoint variance of SOOC solutions, are depicted for comparison. The corresponding mean velocity profiles are also
depicted as insets. The target is depicted as a black circle. Movement duration and endpoint variance are reported for each direction. C-F. Simulation of the data of [35, 36]. Hand paths of 20 trials
are shown in panels C and E for the different directions and different distances for the N-E direction. 90% confidence ellipses of the end point are depicted (estimated from 1,000 samples). The
corresponding durations are reported in panels D and F. In panel D, the acceleration predicted from the hand mobility matrix is depicted (and calculated as in [36]). The direction-dependent and
distance-dependent modulation of duration can be noticed.
We then analyzed how the optimal movement duration depends on its direction and amplitude by using the same model parameters and still focusing on movements carried out without online visual feedback
of the hand. Fig 4C–4F show how movements vary with the direction and with the distance. As in the experimental results of [35] and [36], movements in directions requiring more effort are slower. Fig
4F further shows that the predicted movement duration increases monotonically with the target distance as in experimental data [36].
These simulations suggest that the model can reproduce the basic characteristics of planar arm reaching movements without visual feedback, showing typical dependencies on distance and direction.
Next, we compare movements carried out with and without vision. In particular, movements with vision are known to exhibit a smaller endpoint variability than analog movements without vision [45, 46].
Comparison to data of reaching movements with and without vision.
We asked healthy participants to perform arm pointing movements to test the impact of online visual feedback of the hand on the preferred timing and variance of goal-directed movements. We wanted to
estimate the extent to which movements with and without visual feedback differed in terms of timing and trial-by-trial variability, and whether these data could be replicated by the proposed SFFC
model. Horizontal arm pointing movements of various directions {E, N-E, N-W, W} and amplitudes {0.06, 0.12, 0.18, 0.24} m both with and without vision of the moving hand (represented as a cursor on
the screen, the actual arm being hidden) were recorded. Details about the task can be found in the Materials and methods section.
Fig 5A illustrates the experimental hand paths in all the directions and amplitudes in one participant. As expected, movements without vision were clearly less precise than movements with vision.
This was confirmed by the group analysis reported in Fig 6A where the endpoint variance was computed for each distance and direction.
Movements with vision and without vision are depicted in red and blue respectively. Panels A and B show experimental trajectories in the N-W and N-E directions respectively. The four distances {0.6,
0.12, 0.18, 0.24} m are represented by shifting the starting point for visibility. The real starting point was the same as described in Fig 8B. Targets are represented as 90% confidence ellipses for
the endpoints, which were estimated from the five experiment’s trials. Corresponding mean speed profiles over the five trials are computed after cutting the start and end using a 1.0 cm/s threshold
and a time normalization. The same information is shown in panels C and D for 1,000 simulated movements with SFFC, where only 5 trajectories are depicted for clarity. The blue traces correspond to
large observation noise and red traces to normal observation noise when vision is available. The simulation parameters were chosen to reproduce the average behavior of the participants, and not the
plotted data of a specific participant.
A. Mean experimental endpoint variance (across participants) for each direction and distance. Error bars indicate standard deviations across the 16 conditions (distance-direction pairs). Movement
with and without vision are reported in red and blue, respectively. Circles, diamonds, squares and triangles represent the E, N-E, N-W and W directions, respectively. B. Same information for
simulated movements. C. Root mean squared deviation (RMSD) between the real and simulated endpoint variance, (in log(mm^2)). D-I. Same by reporting duration (in s) and peak velocity (in cm/s) instead
of endpoint variance.
Two-way repeated measures ANOVAs confirmed a main effect of the visual condition (F[1,20] = 426.83, p < 0.001) with movements without vision exhibiting much more endpoint variance. A main effect of
distance was also found (F[3,60] = 12.55, p < 0.001) and there was a significant interaction (F[3,60] = 46.59, p < 0.001) revealing that, without vision, participants were less and less precise as
movement amplitude increased. A main effect of the direction was also detected on the variance (F[3,60] = 3.73, p < 0.05), and there was no interaction effect between direction and condition (p =
These empirical observations were well replicated by our model (Figs 5B and 6B). In particular, the increase of endpoint variance with distance is well predicted by the model with large observation
noise and the gain of precision is also clear when vision is present and observation noise is thus reduced. To quantify the errors between the model predictions and the empirical data, we computed
root mean squared deviations (RMSD). Fig 6C reports RMSD values averaged across all directions and distances for endpoint variance. The average RMSD was 0.40 and 0.28 log(mm^2) for the without and
with vision conditions respectively, which corresponded to 6.9% and 11.6% of the respective experimental mean values.
We next analyzed the timing of movements performed with and without vision (Fig 6D). A visual inspection reveals that the durations of movements with and without visual feedback of the hand exhibit
similar trends, although movements with vision may tend to have slightly longer durations.
A two-way repeated measures ANOVA revealed no main effect of the visual condition on movement duration (p = 0.055). We found a main effect of distance (F[3,60] = 242.40, p < 0.001) on movement
duration (i.e. duration clearly increases with distance). A significant interaction effect between the visual condition and the distance was found (F[3,60] = 10.06, p < 0.001). Post-hoc analyses
revealed that only the 24 cm distance had significantly longer duration with vision compared to without vision (p = 0.014). Regarding the effect of direction on duration, a significant interaction
effect between the visual condition and direction was found (F[3,60] = 5.66, p = 0.002). Post-hoc analyses mainly revealed that N-W movements with vision lasted longer than the other directions of
movement (p < 0.001). The model replicated the increase of movement duration with distance relatively well, although some variations with respect to direction were less clear in these data (see Fig
6E). Quantitative comparisons are reported in Fig 6F and reveal that, on average across distance and direction conditions, RMSD for duration was 70 and 113 ms for the without and with vision
conditions respectively, which corresponded to 7.1 and 11.8% of the respective experimental mean values.
To analyze the differences in movement timing with a variable less sensitive to terminal adjustments, we repeated the above analyses using peak velocity instead of duration (Fig 6G). We found neither
a main effect of the visual condition (p = 0.052) nor an interaction effect (p = 0.262) with distance. Although there was a trend to have slightly lower peak velocities with vision, no statistical
difference was observed on peak velocity for movements with and without vision (even for the largest distance, 24 cm, in contrast to the results found for duration). A main effect of distance on peak
velocity was found as expected since peak velocity clearly increases with movement distance (F[3,60] = 253.72, p < 0.001). Regarding the effect of direction, we found a significant interaction (F
[3,60] = 2.83, p < 0.05). Post-hoc tests mainly indicated that N-W movements were slower than those in other directions with and without vision (p < 0.01). The model replicated well the increase of
peak velocity with distance (Fig 6H) and the dependence of peak velocity on direction was again less clear in these data. RMSD for peak velocity was on average 3.8 and 2.7 cm/s for the without and
with vision conditions respectively, which corresponded to 13.4 and 10.0% of the respective experimental values (Fig 6I).
Finally, a correlation analysis was carried out to analyse the extent to which the timing properties of movements performed with and without vision were related (Fig 7A for durations and Fig 7B for
peak velocities). We found strong correlations in experimental data (R^2 > 0.96), thereby confirming the consistency of movement timing with and without visual feedback. Similarly strong correlations
were found in simulated data based on the proposed model. The main reason is that, in the model, movements with or without vision are both based on the same feedforward motor command and just differ
here in the magnitude of observation noise (which was assumed to be ×10 larger for movements without vision than for movements with vision).
A. Correlations for durations. Each data point represents one condition of distance and direction (averaged across participants). Experimental and simulated data are plotted respectively in black and
grey. B. Correlations for peak velocities. Regression lines are plotted for the illustration.
This paper introduced the stochastic optimal feedforward-feedback control model (SFFC) of learned goal-directed arm movements unifying previous optimal control models that focused either on
deterministic or stochastic aspects of movement. The SFFC suggests how the nervous system may cope with noise and delays by combining feedforward and feedback motor command components. It can be used
to predict the nominal timing and variability of reaching movements with degraded sensory feedback, as was illustrated on movements carried out without visual feedback. We discuss below the main
aspects of this new model in perspective with experimental results and previous models from the literature.
How existing models predict movement timing and variability
The development of SFFC was prompted by the difficulty to predict movement timing independently of endpoint variability with existing optimal control models. Optimal control being a versatile
framework to model human motor control [47, 48], several classes of models have been proposed with prediction of movement timing and variability summarized in Table 1. Seminal deterministic optimal
control (DOC) models can predict the shape of average arm trajectories corresponding to a given movement duration [17, 18, 49, 50]. The movement duration can be determined in ad hoc ways such as by
setting the task’s effort [51–53] but DOC does not account for the trial-by-trial variability of human movement. Assuming signal-dependent motor noise, SOOC models have been proposed to extend
deterministic models and predict a movement duration corresponding to a fixed level of endpoint variance (e.g. the width of the target) [8, 20], but these models will follow Fitts’ law [54], which
does not hold for self-paced arm movements [55]. Here we showed that SOOC can explain the timing and variability of self-paced movements carried out without sensory feedback by considering the
effects of motor noise together with a minimum effort-variance cost. However, SOOC will not account for the drastic reduction of variability exhibited by movements executed with proprioceptive and/or
visual feedback. Muscle co-contraction and mechanical impedance that could be modelled as in [34] may contribute to reduce this variability but not to the level of movements with online multi sensory
Some ad hoc fixes have been introduced in some models to predict timing and/or variability, unlike the SFFC model.
SOC emphasized the role of high-level feedback to reliably execute a motor task despite relatively large variability in repeated movements. In SOC, the motor command is a function of a limb state
estimate built from internal dynamic predictions and delayed sensory information. By considering sensorimotor noise, and minimizing error and effort [13, 14, 19], these models correct task-relevant
errors according to the minimal intervention principle. However, as the expected cost typically plateaus for visually-guided movements of long duration (see Fig 1A), SOC cannot predict a finite
movement duration without ad hoc criterion. For instance, [22] determined duration in an infinite-horizon SOC formulation by comparing the magnitude of endpoint variance to the target’s width, which
allowed to predict the speed-accuracy trade-off. To model the variability of movements without vision, SOC models will normally assume a large observation noise. This will degrade limb state
estimates and make the controller more dependent on internal predictions corresponding to a feedforward mechanism. The fact that movements carried out with and without vision had a highly correlated
timing in our experimental data is supporting the hypothesis that these two types of movement have a common origin, which can be captured by a feedforward motor command. The same conclusion was drawn
by [45] who found a reduction of feedback gains in a reaching task when visual feedback was removed. The authors suggested that a feedforward motor command is needed to explain that movements with
lower feedback gains had well preserved kinematics and timing. Note however that visually-guided movements have a tendency to be slower likely due to the integration of visual corrections at the end
of the movement, to adjust more accurately the final cursor’s location. This is consistent with the observation that in our experiment the peak velocities with and without vision were even more
similar than movement durations. Overall, SFFC appears as the first model that can explain timing and variability of arm movement trajectories carried out with or without visual feedback from
neuromechanic considerations only.
Is movement timing due to neuromechanic or neuroeconomic factors?
Previous arm movement models [24, 25, 56] used a cost of time to limit the movement duration. In these DOC models, the cost-of-time parameters to accurately reproduce the movement timing observed
experimentally can be determined using inverse optimal control techniques [25, 27]. By extension, SOC with a cost of time has been used to model saccades [41] and, in principle, SOC with a cost of
time may be able to reproduce the above experimental results. However, it is not straightforward to find an optimal duration in SOC from computing the cost for all possible durations, and to adapt
such models to the nonlinear dynamics of the human arm. In contrast, it would be straightforward to include a cost of time in SFFC (in the term l(x,u)) and to use it to determine the optimal movement
duration from necessary optimality conditions. However our objective here was to understand if neuromechanical factors could explain the timing and variability of self-paced arm movements, which led
us to develop the SFFC model. While above simulations and experimental results showed that SFFC could explain the timing of simple pointing movements toward targets without ad hoc hypothesis, further
investigations would be required to determine whether it could also account for individual differences [27, 57–59] and sensitivity to reward [60–62], e.g. by varying the factor r to trade-off
variance and effort for instance. Experiments may also be developed to test the model’s prediction that movement timing should increase with larger constant motor noise and decrease with larger
signal-dependent motor noise.
The role of motion planning and feedforward control
Overall, this study suggests the importance of motion planning in the generation of goal-directed arm movements. A large body of experimental evidence has shown the critical role of motion planning
to select a suitable motor solution for carrying out a task (see [4] for a review). The picture suggested by previous studies and above modeling is that the CNS executes well-learned, unperturbed
movements using an important feedforward component to the motor command, given the intrinsic noise, delays and task dynamics. The sensorimotor plans required for such control strategy may be learned
by gradually minimizing reflexes and integrating voluntary (e.g. visual) corrections after movement [63–65]. This learning will minimize the reliance on high-level feedback corrections to achieve the
task and thus gradually incorporate in the feedforward motor command any feature that can be identified over trials.
The behaviour after learning could be captured by the SFFC model that integrates feedforward and feedback control. The simulation results illustrated how SFFC combines the advantages of SOOC [8, 33,
34] and SOC [10–12] to explain the timing and the variability of arm movements performed with or without visual feedback of the moving limb, by minimizing the consequences of signal-dependent and
constant motor noise on endpoint variance as well as effort or kinematic costs such as smoothness. One important aspect of SFFC is that the feedforward motor command already considers uncertainty
about the task dynamics (e.g. motor noise or unknown perturbations, like in [8]) and can incorporate this knowledge in the plan to adjust the mechanical impedance to the task’s uncertainty [34, 66,
67]. This feedforward motor command is complemented by a high-level feedback motor command that corrects task-relevant deviations resulting from perturbations not handled by the feedforward motor
command, such as accumulation of positional errors due to constant noise [31, 68], visually elicited corrections [64, 69] or long-latency proprioceptive feedback responses to large mechanical
perturbations [70, 71]. The state-feedback gain is also part of the motor plan, the magnitude of which can be adapted depending on the task (by tuning the weights in the feedback cost function in
SFFC). This general planning scheme highlights how feedforward motor commands (which determine the nominal shape, timing and variability of unperturbed trajectories) and feedback motor commands
(which handle the corrections of task-related errors using current limb state estimates) could yield a skillful motor control strategy.
Materials and methods
Ethics statement
The experimental protocol was approved by the Université Paris-Saclay local Ethics Committee (CER-Paris-Saclay-2019–031). Written informed consent was obtained from each participant prior to starting
with the experiment.
Experimental task and procedures
Participants and experimental setup.
21 young adults (24.5 ± 2.0 years old [mean±std], height 1.74 ± 0.09 m, with 11 females and 4 left-handed) participated in this study. All participants had normal or corrected to normal vision, and
no known neurological impairment or mental health issue. Each participant was seated, and had to move a stylus on a Wacom tablet (Wacom Intuos 4 XL) laid on horizontal table. The location of the
stylus on the tablet was displayed on a monitor placed in front of the participant (i.e. on a vertical screen).
Pointing task in two conditions: With and without online visual feedback.
When a participant was ready, a 5 mm diameter disk appeared on the screen indicating the start position, on which they was instructed to move the cursor. Once the center of the cursor was within the
start disk for 1 second, this was replaced by a 3 cm diameter target disk placed at 6, 12, 18 or 24 cm from the start position. Reaching movements were carried out in four directions as indicated in
Fig 8A and 8B. If the start position was at the bottom of the screen (x-y coordinates with respect to the shoulder [-15, 30] cm), the target was placed in the N-E or N-W direction. If the start was
on the left of the screen (coordinates [-29, 34.5] cm, it was in the E direction, and if it was on the right of the screen (coordinates [5, 34.5] cm) in the W direction. This resulted in 16 different
possible movement types.
A: Two-link model of the arm and planar movement used to set the model parameters. B: Horizontal arm movements carried out with and without online vision of the hand (4 directions, W, N-E, N-W and E,
and 4 distances, 6, 12, 18 and 24 cm) in our experiment. C: Arm parameters used in the simulations.
The participants were instructed to move the cursor at comfortable pace in order to reach the target, without leaning the arm on the tablet. Note that their arm was hidden by a cardboard box so that
they could not see it. They had to perform reaching movements either without or with the cursor displaying their hand position on the screen during the movement. In the non-visual condition, the
cursor disappeared at the beginning of the movement and reappeared 1 s after the end of the movement, to indicate the pointing error and thus avoid the endpoint to gradually drift trial after trial.
Each participant started with a familiarization phase of 32 pointing movements including 16 consecutive trials per condition (with and then without visual feedback). Then they had to perform 160
trials, with 80 per visual feedback modality. The different movement types and the visual modalities were presented in pseudo-random order. This resulted in 5 trials of each amplitude and direction
for each starting position. Every 10 trials a break of approximately 1 minute was scheduled, during which they could place the forearm on the tablet or the desk.
Data acquisition and parameters of interest.
The stylus position was recorded at 125 Hz with MATLAB (The MathWorks, Inc.), and the Psychtoolbox [76] was used to display the stimuli on the screen. The system was calibrated so that a movement of
the stylus on the tablet corresponded to a movement of the same length of the cursor on screen. The raw data were smoothened for further analysis using a 5th-order Butterworth low-pass filter with
12.5 Hz cutoff frequency and without delay. Velocity was computed via numerical differentiation. Among the parameters of interest, we computed the movement duration using a velocity threshold of 1 cm
/s, the peak velocity of the maximal value of velocity profiles (in cm/s), and the endpoint variance (in log(mm^2)). In every trial, the movement’s endpoint was determined by the last recorded
position at the end of the movement time. Endpoint variance was then estimated from the trace of the covariance matrix of final positions and the logarithm of this value was computed as in [31].
Statistical analysis.
Two-way repeated measures ANOVAs with condition (with vision and without vision) and amplitude (from 6 to 24 cm) or direction (from E to W) as within-subjects factors were carried out to assess the
variation of movement timing (i.e. duration and peak velocity) and variance across conditions. Moreover, a correlation analysis was performed to assess the relationships between the timing of
movements carried out with and without vision.
Numerical simulations
Arm reaching movements were simulated using a 2-link arm model with joint configuration vector (16) where q[1] is the shoulder and q[2] the elbow angles. The skeletal dynamics of the arm was
described by the rigid body model of Eq (1) with:
For the planar movements considered in this paper the gravity term is set as zero. {I[i], L[i], L[gi]} and {M[i]} are the moments of inertia, lengths of segments, lengths to the centre of mass and
mass of the segments.
Furthermore, we have (17) where the parameters {σ[i]} are used to set the magnitude of additive noise and {d[i]} the magnitude of multiplicative noise.
Regarding the feedforward cost function, we define ϕ(m(T), x[T]) to estimate the covariance of the final hand position. Denoting by J(q) the Jacobian matrix of the two-link arm, an approximation of
this function can be computed by: (18) where m[q](T) is the mean final position of the random variable q[T] (i.e. the 2-dimensional vector of final joint positions) and tr denotes the trace of the
matrix. The expectation of ϕ(m(T), x[T]) can then be rewritten as a function of the mean and covariance of the state process x[t]: (19) where P[q] is the 2×2 covariance matrix of joint positions.
The infinitesimal cost l(m, u) is defined as follows: (20) where x and y denote the mean Cartesian positions of the hand (which can be computed from m(t) and the forward kinematic function). This
cost implements a compromise between effort (here measured as squared torque change) and smoothness (here squared hand jerk) through the α parameter. Evidence for composite cost function mixing
kinematic and dynamic or energetic criteria has been found in previous works [50, 72]. The jerk term is useful to correct for abnormal asymmetries in velocity profiles which may arise partly from the
minimum torque change model (e.g. [73]), but this term does not affect our results otherwise.
For the linear-quadratic-Gaussian sub-problem, we set C = I[6] (identity matrix) meaning that we assume that both position, velocity and force could be estimated from multisensory information as in [
19]. We verified that the same results and conclusions were obtained by limiting the observation matrix to the position and velocity components only. The observation noise matrix D was taken of the
form D = β I[6] where β specifies the overall magnitude of observation noise. This parameter can be varied depending on whether vision of the cursor is available or not during the movement. Finally,
for the feedback cost function, we set R = ρdiag(1, 1, 0, 0, 0, 0) such that only the deviations about the final arm posture defined by the target location were penalized during the post-movement
The SOOC solutions were obtained with the optimal control software that approximates the continuous-time optimal control problem as a sparse nonlinear programming problem [40]. To compute the SFFC
solutions, we considered a discrete time approximation of the linear-quadratic-Gaussian sub-problem around the SOOC solution with a time step of dt = 0.005 s. Standard discrete-time algorithms for
linear-quadratic-Gaussian control were then used to compute the gains [19]. In our simulations, we extended the time horizon by 1 s (T′ = T+1) to consider movements longer than the planned duration T
. We tested different extended horizon between 0.5 s and 2 s and it did not change the results. It is worth noting that sensory feedback delays can be easily handled at this stage due to the discrete
time approximation. All the simulations were performed with MATLAB (Mathworks, Natick, MA).
Selection of model parameters.
The arm parameters used in the simulations (from [42], in SI units) are given in Fig 8C.
The remaining parameters of the model are related to cost functions (α, r and ρ) and noise magnitudes ({σ[i]}, {d[i]} and β). Some of these parameters affect the design of the feedforward command (α,
r, {σ[i]}, {d[i]}) and the others affect the design of the feedback command (ρ, β). First, we verified that the qualitative predictions and principles of the model were robust to parameters choices.
Second, to have simulations that correspond quantitatively to experimental data, we adjusted the parameters using the procedure described hereafter. Note that we did not try to find the best-fitting
parameters using an automated procedure but adjusted the parameters to yield timing and variance of the same order of magnitude as experimental data.
We first fixed α = 0.02 in all simulations, to implement a compromise between torque change and hand jerk. Note that we also considered α = 0 and the results revealed that the smoothness term
contributes to get slightly more linear hand paths with more bell-shaped velocity profiles, but this does not affect the main findings. Second, to reduce the number of parameters, we assumed that the
magnitude of additive and multiplicative motor noise are the same in the two joints of the arm, i.e. σ[1] = σ[2] = σ [rad/s^3/2] and d[1] = d[2] = d [rad/(Nm s^1/2)]. The three remaining free
parameters for SOOC ({σ, d, r}) were then adjusted by considering a movement of 7.4 cm in the N-W direction by using the existing data of [31] as a reference. The initial arm configuration was
approximately q[1](0) = 50° and q[2](0) = 100° in this experiment. In the N-W movement, both joint angles change significantly, so that the effects of noise magnitude can be estimated in the two
degrees of freedom using the three steps as follows:
• Since additive noise dominates at low speed, the magnitude of constant noise was adjusted on 1400 ms long movement in order to obtain an endpoint variance larger than what has been found in [31].
Indeed, these data were obtained for movements without vision in healthy subjects, where proprioceptive feedback was still available, and analog movements in deafferented patients would exhibit a
larger endpoint variance [43, 44]. This resulted in σ = 0.005 [rad/s^3/2] and in about 6 log(mm^2) of endpoint variance (which is larger than the 4.2 log(mm^2) measured in [31]).
• Since multiplicative noise dominates for fast speed movements, which are less affected by feedback, multiplicative noise was adjusted on 350 ms long movements based on the data of [31]. d = 0.01
yielded an endpoint variance about 4.1 log(mm^2).
• The variance weight r was then adjusted to fit the preferred duration of movements observed in the N-W direction. We found that r = 2,000 yields a movement time of about 1080 ms, which is similar
to the preferred duration in [31].
Once the SOOC solution was obtained, we determined the remaining parameters of the SFFC model, which are related to the linear-quadratic-Gaussian sub-problem. We first set the observation noise β and
feedback cost weight ρ by assuming that visually-guided movements are performed accurately at the preferred speed. This resulted in β = 0.003 and ρ = 1,000 for the data of [31]. Without vision, only
proprioceptive feedback can be used and we assume that this leads to an increase of sensory variance. This increase was chosen to match the endpoint variance observed without vision in [31] (<4 log
(mm^2)), and this led to β = 0.03 (i.e. ×10 larger than the magnitude of observation noise with vision). Note that we did not change ρ in the present simulations, but we also considered that the
product ρβ could remain constant (i.e. ρ = 100 if β = 0.03), which reduced the feedback gain without affecting much the simulations for the unperturbed reaching movements under consideration.
When simulating movements without vision (or without feedback at all), a basic stopping mechanism was added by increasing joint friction 50 ms before the planned movement end to ensure that the
terminal velocity always falls below the threshold (we added 3.5 kg m^2/s to , i = 1, 2), which corresponds to a larger muscle viscosity at low speed [74]. Note that to compare simulated and
experimental durations, we systematically applied a 1 cm/s threshold on hand velocity in agreement with experimental data processing (see above and [31]).
This set of parameters was used to simulate movements of different durations and directions, and compare the predictions to existing data. We used Eq (9) and the above parameters to generate reaching
movements of duration 300–1450 ms in the N-W and N-E directions, and then computed the different optimal costs. Next, we tested the model predictions by computing optimal movement durations for
increasing distances ({7.5, 12.5, 17.5, 22.5, 27.5} cm in the N-E direction), and in eight directions as in classical experiments of arm reaching movements without vision [35, 36].
Simulation of new experiment with SFFC.
To simulate movements with and without vision described in Fig 8A and 8B, two previous parameters had to be adjusted to account for the larger variability and the shorter durations observed in our
data compared to the experiment of [31]. This adjustment was made to have a better quantitative fit of the experimental data but the qualitative results would be the same if keeping previous
parameters unchanged. These changes may be due to differences in experimental protocols (target’s width, arm’s weight support, instructions etc.). Therefore, to reflect larger variance and shorter
durations, we set σ = 0.025 and r = 6,000 and kept the other parameters invariant. Here, to also investigate the influence of sensory delays, we performed simulations by considering a 50-ms delay in
sensory feedback loops. This was done in the discrete-time approximation of the linear-quadratic-Gaussian sub-problem by using the classical procedure consisting of augmenting the system’s state to
include delayed instances of the state process (e.g. see [75] for details). Note that delays did not affect much the present simulations. This was verified by simulating SFFC with and without delays
and very similar quantitative results were obtained for the tested movements. We report the simulations for the delayed case. | {"url":"https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1009047","timestamp":"2024-11-08T00:12:52Z","content_type":"text/html","content_length":"288891","record_id":"<urn:uuid:2568b3b6-4fa8-4406-9587-af191114a127>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00362.warc.gz"} |
Trying out resurrecting print after pause and power-loss
I am trying to resurrect a paused print, I did pause it and cut the power of after pause-auto-home X and Y in my coreXY with Duet 2 Ethernet 2.0.4.
I get the following error-message after I put in M916:
M916: Resume prologue file 'resurrect-prologue.g' not found
Am I supposed to create an empty file called 'resurrect-prologue.g' before I try to pause and cut the power so resurrect.g can save content to the file I create?
Or am I able to continue the print with another command since my resurrect.g contains info about print-file and coordinates and looks like following:
; File "0:/gcodes/CFFFP_model.gcode" resume print after print paused at 2021-12-21 02:24
M140 P0 S65.0
T-1 P0
G92 X52.035 Y167.320 Z95.580
G60 S1
G10 P0 S210 R210
T0 P0
M98 P"resurrect-prologue.g"
M290 X0.000 Y0.000 Z0.100 R0
T-1 P0
T0 P6
; Workplace coordinates
G10 L2 P1 X0.00 Y0.00 Z0.00
G10 L2 P2 X0.00 Y0.00 Z0.00
G10 L2 P3 X0.00 Y0.00 Z0.00
G10 L2 P4 X0.00 Y0.00 Z0.00
G10 L2 P5 X0.00 Y0.00 Z0.00
G10 L2 P6 X0.00 Y0.00 Z0.00
G10 L2 P7 X0.00 Y0.00 Z0.00
G10 L2 P8 X0.00 Y0.00 Z0.00
G10 L2 P9 X0.00 Y0.00 Z0.00
M106 S0.33
M106 P1 S1.00
G92 E0.00000
M23 "0:/gcodes/CFFFP_model.gcode"
M26 S15235554
G0 F6000 Z97.680
G0 F6000 X52.035 Y167.320
G0 F6000 Z95.680
G1 F3600.0 P0
Haha yes I did... I was probably to tired when reading because I can't remember the last paragraph about "Setting up the sys/resurrect-prologue.g file"
Works like a charm now! | {"url":"https://forum.duet3d.com/topic/26491/trying-out-resurrecting-print-after-pause-and-power-loss","timestamp":"2024-11-05T15:47:53Z","content_type":"text/html","content_length":"63168","record_id":"<urn:uuid:79a6f2e1-dd2d-4fd1-b2a1-d98e653276bb>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00417.warc.gz"} |
You are working on a ticketing system. A ticket costs $10.
The office is running a discount campaign: each group of 5 people i | Sololearn: Learn to code for FREE!
You are working on a ticketing system. A ticket costs $10. The office is running a discount campaign: each group of 5 people i
You are working on a ticketing system. A ticket costs $10. The office is running a discount campaign: each group of 5 people is getting a discount, which is determined by the age of the youngest
person in the group. You need to create a program that takes the ages of all 5 people as input and outputs the total price of the tickets. Sample Input: 55 28 15 38 63 Sample Output: 42.5 The
youngest age is 15, so the group gets a 15% discount from the total price, which is $50 - 15% = $42.5 #include<iostream> using namespace std; int main() { int i,a[5]; double j,small; for(i=0;i<5;i++)
{ cin>>a[i]; } if((a[0]<=a[1])&&(a[0]<=a[2])&&(a[0]<=a[3])&&(a[0]<=a[4])) { small =a[0]; } else if((a[1]<=a[0])&&(a[1]<=a[2])&&(a[1]<=a[3])&&(a[0]<=a[4])) { small=a[1]; } else if((a[2]<=a[1])&&(a[2]
<=a[0])&&(a[2]<=a[3])&&(a[2]<=a[4])) { small=a[2]; } else small= a[3]; j=50-(small/2); cout<<j; return 0; } i solved it but hidden test case is failing So please guide
You're missing a condition for small = a[4];
B N Mallikarjuna
If you write Hard Code logic you will never get success because inputs may be change for every case so how you can solve this problem just follow this steps: 1 - get youngest person, to do this store
first value in a temporary variable and compare this value with each next value. You can use loop for this. 2 - after getting youngest person calculate discount on total price 3 - subtract this
discount amount from total amount to get balance amount
#include <iostream> #include <string> #include <climits> using namespace std; int main() { int ages[5]; double min = INT_MAX; double total; double discount; for (int i = 0; i < 5; i++) { cin >> ages
[i]; if (ages[i] < min) min = ages[i]; } total = 50 * (min/100); discount = 50 - total; cout << discount; cout << endl; return 0; } | {"url":"https://www.sololearn.com/de/Discuss/2883450/you-are-working-on-a-ticketing-system-a-ticket-costs-10-the-office-is-running-a-discount-campaign-each-group-of-5-people-i","timestamp":"2024-11-09T04:13:39Z","content_type":"text/html","content_length":"923912","record_id":"<urn:uuid:dce26492-e8de-4a44-a3b6-61a350c04860>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00610.warc.gz"} |
Associative Magic Square
An Magic Square for which every pair of numbers symmetrically opposite the center sum to . The Lo Shu is associative but not Panmagic. Order four squares can be Panmagic or associative, but not both.
Order five squares are the smallest which can be both associative and Panmagic, and 16 distinct associative Panmagic Squares exist, one of which is illustrated above (Gardner 1988).
See also Magic Square, Panmagic Square
Gardner, M. ``Magic Squares and Cubes.'' Ch. 17 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, 1988.
© 1996-9 Eric W. Weisstein | {"url":"http://drhuang.com/science/mathematics/math%20word/math/a/a380.htm","timestamp":"2024-11-03T22:01:13Z","content_type":"text/html","content_length":"3969","record_id":"<urn:uuid:9be4a762-9d50-482a-a744-40c7510f0cd7>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00090.warc.gz"} |
Math 18 SLO and CMO
MATH 18B - Support Topics for Calculus II
Student Learning Outcomes (SLOs)
1. Students feel that Math 18B has improved their overall mathematical understanding and ability in Math 181 (measured by survey provided by corequisite committee).
2. Math 18B students will be able to integrate Riemann integrable functions using a variety of techniques.
3. Math 18B students will be able to construct integrals to determine work, hydrostatic force, and center of mass.
4. Math 18B students will be able to apply tests for convergence/divergence of sequences and series using a variety of techniques.
5. Math 18B students will be able to construct Taylor series of C^infty functions.
Course Measurable Objectives Effective through Summer 2024 (CMOs)
1. Evaluate integrals using integration by parts, trigonometric integrals, trigonometric substitution, and integration using partial fractions.
2. Find the volume and surface area of surface of revolution.
3. Find the arc length of a function in Cartesian coordinates, in polar coordinates, and a function in parametric form.
4. Use integrals to determine work, hydrostatic force, and center of mass.
5. Find an equivalent Cartesian equation of a parametric equation and sketch the resulting graph.
6. Use the tests for convergence or divergence of sequences and series using a variety of techniques.
7. Find the power series representation of a function and the interval of convergence.
8. Find the Maclaurin and Taylor series representation of a function.
Course Measurable Objectives Effective Beginning Fall 2024 (CMOs)
1. Use definite integrals to calculate areas between curves and volumes - including solids of revolution, work, the mean value of functions, arc lengths, areas of surfaces of revolution, moments,
centers of mass, and other physics applications.
2. Evaluate indefinite and definite integrals (proper and improper) using integration by parts, trigonometric identities and substitutions, partial fractions, tables, computer algebra systems, and
numerical techniques.
3. Solve separable differential equations with applications.
4. Plot curves parametrically and in polar coordinates, using calculus to compute associated areas, arc-lengths, and slopes.
5. Test for convergence for sequences and series using the integral, comparison, alternating series, ratio, and root tests.
6. Determine representations of functions as power series including Taylor and Maclaurin series.
7. Use power series in applications. | {"url":"https://www.mtsac.edu/math/slo_and_cmo_by_course/math_18b_slo_and_cmo.html","timestamp":"2024-11-04T01:57:16Z","content_type":"text/html","content_length":"29428","record_id":"<urn:uuid:4c234390-3e68-4c2d-a1af-c735489789c3>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00170.warc.gz"} |
How to use absolute function with percentage in oracle?
The ABS function in Oracle can be used to calculate the absolute value of a number. If you want to calculate the absolute value of a percentage, you can first convert the percentage to a decimal and
then use the ABS function.
Here is an example:
1 SELECT ABS(0.25) AS absolute_value
2 FROM dual;
This query will return the absolute value of the percentage 25% (0.25), which is 0.25.
You can substitute 0.25 with any percentage value you want to calculate the absolute value for.
Note that the ABS function will always return a positive value, so if you want to get the absolute value of a negative number, it will return the positive equivalent. | {"url":"https://devhubby.com/thread/how-to-use-absolute-function-with-percentage-in","timestamp":"2024-11-10T08:34:09Z","content_type":"text/html","content_length":"113718","record_id":"<urn:uuid:ec65a2be-3db5-48be-bba3-784516f8cd17>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00271.warc.gz"} |
Can Self-Ordering Scalar Fields explain the BICEP2 B-mode signal?
Cite as:
R. Durrer, D. G. Figueroa, M. Kunz [arXiv:1404.3855]
We show that self-ordering scalar fields (SOSF), i.e. non-topological cosmic defects arising after a global phase transition, cannot explain the B-mode signal recently announced by BICEP2. We compute
the full CBℓ angular power spectrum of B-modes due to the vector and tensor perturbations of SOSF, modeled in the large-N limit of a spontaneous broken global O(N) symmetry. We conclude that the low-
ℓ multipoles detected by BICEP2 cannot be due mainly to SOSF, since they have the wrong spectrum at low multipoles. As a byproduct we derive the first cosmological constraints on this model, showing
that the BICEP2 B-mode polarization data admits at most a 2-3% contribution from SOSF in the temperature anisotropies, similar to (but somewhat tighter than) the recently studied case of cosmic | {"url":"https://cosmology.unige.ch/content/can-self-ordering-scalar-fields-explain-bicep2-b-mode-signal","timestamp":"2024-11-03T03:11:35Z","content_type":"text/html","content_length":"36750","record_id":"<urn:uuid:79e05ee5-001d-4806-a80e-0fd2b4ecb762>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00087.warc.gz"} |
Mastering the Chi-Square Test: A Comprehensive Guide
The Chi-Square Test is a statistical method used to determine if there’s a significant association between two categorical variables in a sample data set. It checks the independence of these
variables, making it a robust and flexible tool for data analysis.
Introduction to Chi-Square Test
The Chi-Square Test of Independence is an important tool in the statistician’s arsenal. Its primary function is determining whether a significant association exists between two categorical variables
in a sample data set. Essentially, it’s a test of independence, gauging if variations in one variable can impact another.
This comprehensive guide gives you a deeper understanding of the Chi-Square Test, its mechanics, importance, and correct implementation.
• Chi-Square Test assess the association between two categorical variables.
• Chi-Square Test requires the data to be a random sample.
• Chi-Square Test is designed for categorical or nominal variables.
• Each observation in the Chi-Square Test must be mutually exclusive and exhaustive.
• Chi-Square Test can’t establish causality, only an association between variables.
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Case Study: Chi-Square Test in Real-World Scenario
Let’s delve into a real-world scenario to illustrate the application of the Chi-Square Test. Picture this: you’re the lead data analyst for a burgeoning shoe company. The company has an array of
products but wants to enhance its marketing strategy by understanding if there’s an association between gender (Male, Female) and product preference (Sneakers, Loafers).
To start, you collect data from a random sample of customers, using a survey to identify their gender and their preferred shoe type. This data then gets organized into a contingency table, with
gender across the top and shoe type down the side.
Next, you apply the Chi-Square Test to this data. The null hypothesis (H0) is that gender and shoe preference are independent. In contrast, the alternative hypothesis (H1) proposes that these
variables are associated. After calculating the expected frequencies and the Chi-Square statistic, you compare this statistic with the critical value from the Chi-Square distribution.
Suppose the Chi-Square statistic is higher than the critical value in our scenario, leading to the rejection of the null hypothesis. This result indicates a significant association between gender and
shoe preference. With this insight, the shoe company has valuable information for targeted marketing campaigns.
For instance, if the data shows that females prefer sneakers over loafers, the company might emphasize its sneaker line in marketing materials directed toward women. Conversely, if men show a higher
preference for loafers, the company can highlight these products in campaigns targeting men.
This case study exemplifies the power of the Chi-Square Test. It’s a simple and effective tool that can drive strategic decisions in various real-world contexts, from marketing to medical research.
The Mathematics Behind Chi-Square Test
At the heart of the Chi-Square Test lies the calculation of the discrepancy between observed data and the expected data under the assumption of variable independence. This discrepancy termed the
Chi-Square statistic, is calculated as the sum of squared differences between observed (O) and expected (E) frequencies, normalized by the expected frequencies in each category.
In mathematical terms, the Chi-Square statistic (χ²) can be represented as follows:
χ² = Σ [ (Oᵢ – Eᵢ)² / Eᵢ ], where the summation (Σ) is carried over all categories.
This formula quantifies the discrepancy between our observations and what we would expect if the null hypothesis of independence were true. We can decide on the variables’ independence by comparing
the calculated Chi-Square statistic to a critical value from the Chi-Square distribution. Suppose the computed χ² is greater than the critical value. In that case, we reject the null hypothesis,
indicating a significant association between the variables.
Step-by-Step Guide to Perform Chi-Square Test
To effectively execute a Chi-Square Test, follow these methodical steps:
State the Hypotheses: The null hypothesis (H0) posits no association between the variables — i.e., independent — while the alternative hypothesis (H1) posits an association between the variables.
Construct a Contingency Table: Create a matrix to present your observations, with one variable defining the rows and the other defining the columns. Each table cell shows the frequency of
observations corresponding to a particular combination of variable categories.
Calculate the Expected Values: For each cell in the contingency table, calculate the expected frequency assuming that H0 is true. This can be calculated by multiplying the sum of the row and column
for that cell and dividing by the total number of observations.
Compute the Chi-Square Statistic: Apply the formula χ² = Σ [ (Oᵢ – Eᵢ)² / Eᵢ ] to compute the Chi-Square statistic.
Compare Your Test Statistic: Evaluate your test statistic against a Chi-Square distribution to find the p-value, which will indicate the statistical significance of your test. If the p-value is less
than your chosen significance level (usually 0.05), you reject H0.
Interpretation of the results should always be in the context of your research question and hypothesis. This includes considering practical significance — not just statistical significance — and
ensuring your findings align with the broader theoretical understanding of the topic.
Steps in Chi-Square Description
State the Hypotheses The null hypothesis (H0) posits no association between the variables (i.e., they are independent), while the alternative hypothesis (H1) posits an association between the
Construct a Contingency Create a matrix to present your observations, with one variable defining the rows and the other defining the columns. Each table cell shows the frequency of observations
Table corresponding to a particular combination of variable categories.
Calculate the Expected For each cell in the contingency table, calculate the expected frequency under the assumption that H0 is true. This is calculated by multiplying the row and column total for
Values that cell and dividing by the grand total.
Compute the Chi-Square Apply the formula χ² = Σ [ (Oᵢ – Eᵢ)² / Eᵢ ] to compute the Chi-Square statistic.
Compare Your Test Evaluate your test statistic against a Chi-Square distribution to find the p-value, which will indicate the statistical significance of your test. If the p-value is less than
Statistic your chosen significance level (usually 0.05), you reject H0.
Interpret the Results Interpretation should always be in the context of your research question and hypothesis. Consider the practical significance, not just statistical significance, and ensure
your findings align with the broader theoretical understanding of the topic.
Assumptions, Limitations, and Misconceptions
The Chi-Square Test, a vital tool in statistical analysis, comes with certain assumptions and distinct limitations. Firstly, it presumes that the data used are a random sample from a larger
population and that the variables under investigation are nominal or categorical. Each observation must fall into one unique category or cell in the analysis, meaning observations are mutually
exclusive and exhaustive.
The Chi-Square Test has limitations when deployed with small sample sizes. The expected frequency of any cell in the contingency table should ideally be 5 or more. If it falls short, this can cause
distortions in the test findings, potentially triggering a Type I or Type II error.
Misuse and misconceptions about this test often center on its application and interpretability. A standard error is using it for continuous or ordinal data without appropriate categorization, leading
to misleading results. Also, a significant result from a Chi-Square Test indicates an association between variables, but it doesn’t infer causality. This is a frequent misconception — interpreting
the association as proof of causality — while the test doesn’t offer information about whether changes in one variable cause changes in another.
Moreover, more than a significant Chi-Square test is required to comprehensively understand the relationship between variables. To get a more nuanced interpretation, it’s crucial to accompany the
test with a measure of effect size, such as Cramer’s V or Phi coefficient for a 2×2 contingency table. These measures provide information about the strength of the association, adding another
dimension to the interpretation of results. This is essential as statistically significant results do not necessarily imply a practically significant effect. An effect size measure is critical in
large sample sizes where even minor deviations from independence might result in a significant Chi-Square test.
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Conclusion and Further Reading
Mastering the Chi-Square Test is vital in any data analyst’s or statistician’s journey. Its wide range of applications and robustness make it a tool you’ll turn to repeatedly.
For further learning, statistical textbooks and online courses can provide more in-depth knowledge and practice. Don’t hesitate to delve deeper and keep exploring the fascinating world of data
Frequently Asked Questions (FAQ)
Q1: What is the Chi-Square Test of Independence?
It’s a statistical test used to determine if there’s a significant association between two categorical variables.
Q2: What type of data is suitable for the Chi-Square Test?
The test is suitable for categorical or nominal variables.
Q3: Can Chi-Square Test establish causality between variables?
No, the test can only indicate an association, not a causal relationship.
Q4: What are the assumptions for the Chi-Square Test?
The test assumes that the data is a random sample and that observations are mutually exclusive and exhaustive.
Q5: What is the Chi-Square statistic?
It measures the discrepancy between observed and expected data, calculated by χ² = Σ [ (Oᵢ – Eᵢ)² / Eᵢ ].
Q6: How is statistical significance determined in the Chi-Square Test?
The result is generally considered statistically significant if the p-value is less than 0.05.
Q7: What happens if Chi-Square Test is used on inappropriate data types?
Misuse can lead to misleading results, making it crucial to use it with categorical data only.
Q8: How do small sample sizes impact the Chi-Square Test?
Small sample sizes can lead to wrong results, especially when expected cell frequencies are less than 5.
Q9: What are the potential errors with the Chi-Square Test?
Low expected cell frequencies can lead to Type I or Type II errors.
Q10: How can one interpret the results of the Chi-Square Test?
Results should be interpreted in context, considering the statistical significance and the broader understanding of the topic. | {"url":"https://statisticseasily.com/chi-square-test/","timestamp":"2024-11-02T12:03:33Z","content_type":"text/html","content_length":"193489","record_id":"<urn:uuid:9bf353e2-87d3-44e6-8478-f158863d9a12>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00356.warc.gz"} |
Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response
This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A
discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the
fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time
domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical
predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can
stabilize chaotic orbits at a precarious equilibrium point. | {"url":"https://dergipark.org.tr/tr/pub/chaos/issue/86422/1300754","timestamp":"2024-11-08T01:31:05Z","content_type":"text/html","content_length":"147131","record_id":"<urn:uuid:22f628a3-2913-4f91-a4c0-3c3c16286168>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00589.warc.gz"} |
The Stacks project
Lemma 10.154.5. Let $R$ be a ring. Let $A \to B$ be an $R$-algebra homomorphism. If $A$ and $B$ are filtered colimits of étale $R$-algebras, then $B$ is a filtered colimit of étale $A$-algebras.
Proof. Write $A = \mathop{\mathrm{colim}}\nolimits A_ i$ and $B = \mathop{\mathrm{colim}}\nolimits B_ j$ as filtered colimits with $A_ i$ and $B_ j$ étale over $R$. For each $i$ we can find a $j$
such that $A_ i \to B$ factors through $B_ j$, see Lemma 10.127.3. The factorization $A_ i \to B_ j$ is étale by Lemma 10.143.8. Since $A \to A \otimes _{A_ i} B_ j$ is étale (Lemma 10.143.3) it
suffices to prove that $B = \mathop{\mathrm{colim}}\nolimits A \otimes _{A_ i} B_ j$ where the colimit is over pairs $(i, j)$ and factorizations $A_ i \to B_ j \to B$ of $A_ i \to B$ (this is a
directed system; details omitted). This is clear because colimits commute with tensor products and hence $\mathop{\mathrm{colim}}\nolimits A \otimes _{A_ i} B_ j = A \otimes _ A B = B$. $\square$
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4 Channel Active Sound Filter Schema Adjustable Frequency4 Channel Active Sound Filter Schema Adjustable Frequency
4 Channel Active Sound Filter Schema Adjustable Frequency
A 4-way active filter scheme is presented here with the particularity of using only easy-to-find components: op amps, potentiometers, resistors and capacitors.
Here is a 4 channel active filter scheme with adjustable transition frequencies. For multi-amplification, an active filter is essential to distribute the frequency bands for their respective amps and
speakers. Here is presented a 4-way active filter. It is possible to modify it according to what one wishes to realize as acoustic system (sound system).
Active sound filter: the diagram
Here is the diagram of the active filter whose 3 transition frequencies are adjustable:
Active filter diagram for 4-channel sound system (adjustable frequencies)
Characteristics of the active sound filter
Here was chosen a 4-way active filter with characteristics:
- channel 1: from 30Hz (fixed) to 50Hz ... 300Hz adjustable by P1 (infrared for subwoofer) - channel 2: from 50Hz ... 300Hz adjustable by P1 to 100Hz ... 600Hz adjustable by P2- channel 3: from 100Hz
... 600Hz adjustable by P2 at 1500Hz ... 9000Hz adjustable by P3- channel 4: from 1500Hz ... 9000Hz adjustable by P3 to 20000Hz and more
The high pass filter (orange box) is optional but highly recommended to protect the subwoofers from frequencies that are too low for them to reproduce. It is a 2nd order filter that gives an
attenuation of -12dB / octave. This channel is intended for subwoofers, ideally based on speakers 46cm (18 inches) or at least 38cm (15 inches). The subwoofers are often laminar vent or better,
toboggan or W-bin type.
Channel 2 will only provide a signal when P1 and P2 are in compatible positions, for example P1 adjusted for 100Hz and P2 adjusted to 250Hz. Transition frequencies are used to adjust channel 2 in a
wide range of frequency bands.
Channel 4 does not have a low pass filter.
Operating principle of the active sound filter
The audio signal containing all the frequencies first arrives on the high frequency filter set at 30Hz. Its purpose is to eliminate frequencies below 30Hz to protect speakers from subwoofers or
subwoofers ("infra"). This is a 2nd order filter based on the U4 op amp. For the sake of simplicity, C1 and C2 are chosen identical. The frequency response around the cutoff frequency is determined
by the damping of the filter (related to R1 and R2, or more exactly to the square root of the ratio R1 / R2).
The signal coming out of U4 is now cleaned of the lowest frequencies and therefore contains frequencies from 30Hz to 20kHz. The limit of 20kHz is arbitrary and in fact only depends on the audio
signal at the input of the filter.
The first low-pass filter (magenta box F1) is a low-pass filter of order 2 adjustable cut-off frequency from 50Hz to 300Hz approximately thanks to P1. When P1 is at its maximum value, the cutoff
frequency is 50Hz. When P1 is at its minimum value, only R3 and R4 remain and the cutoff frequency is then 300Hz. The potentiometer P1 is a 10kOhms and must imperatively be double (stereo). The
damping of the filter of order 2 is equal to the square root of the ratio C4 / C3. This equality is valid because we have chosen the two equal resistors R3 + P2 and R4 + P2. At the end of this low
pass filter F1, we therefore have channel 1 of the filter: fixed cutoff at 30Hz and high cutoff of 50Hz at 300Hz depending on the position of P1.
Remains the high pass filter whose cutoff frequency must be the same as that of the low pass F1 to avoid overlap between two channels or, conversely, a gap between the two channels. It is therefore
necessary that the filter passes high lets pass all the frequencies that have not passed in the low pass. To do this cleverly, we can make the difference (subtraction) between the signal before low
pass filtering and the same signal after low pass filtering.
When the filter low pass passes the signal, this difference is zero. When the low pass filter blocks the signal, the difference is equal to the signal. To realize this mathematical subtraction, one
uses the differential amplifier assembly (gray box) which carries out the operation:
output = signal before low pass filtering - signal after low pass filtering
So the trick is this schema:
Active filter diagram passes high: suppression of the low frequencies to the signal which contains all
As a result, the output of the differential amplification is a high pass filter. We find the frequencies that have been blocked by the F1 low pass filter. This is the trick to route frequencies
without losing or finding on both ways!
Note: it is easy to make an active low-pass filter of order 2 with a double (stereo) potentiometer in a Sallen Key structure, whereas it is not possible to realize a second order high-pass filter
with a potentiometer double if we want a depreciation of the order of 0.5 to 0.7. In fact, to make an adjustable high frequency pass, there is no solution as simple as for the low pass.
In practice, one chooses R5 = R6 = R7 = R8 to realize a simple subtraction in the differential amplifier. The value of 10kOhms is arbitrary (we could have chosen 22k or 47k).
It is possible to stop the diagram at this level if you only want a 2-way active filter:
- from 30Hz (fixed) to 50Hz ... 300Hz (adjustable) - from 50Hz ... 300Hz (adjustable) to 20kHz
The output of the differential amplifier can constitute the treble channel for a satellite in a satellite system 2.1 + subwoofer.
But as here, we want a 4-way active filter, we use this output of the differential amplifier to redivize it in terms of frequencies. The operation is repeated with the low pass filter F2 (which gives
the output 2) and the differential amplifier which is on its right.
Similarly for the filter F3. To better smooth the frequency response of the output 3, a simple filter based on R9 and C9 was added. This is an additional improvement that was found by empirical
testing on a LTSpice IV simulation of complete editing.
Channel 4 (the treble channel) comes from the latest differential amplifier based on U3b.
The purpose of the active filter is a sound system configuration of this kind:
Typical example of a system that requires a 4-way active filter
The amps for channels 1 and 2 must be the most powerful (there is more power in the bass than in the treble)
For the practical realization of the active filter
It is recommended to insert in series with the outputs of the op amps a resistor of 100 Ohms to avoid possible oscillations of the amps because of the parasitic capacitance between the hot point and
the mass of the cables
The amps can be chosen quite freely. Here, the choice fell on the very classic and economical TL072.
The power supply is about +/- 12V and must be regulated, especially on the negative power supply (-Vcc). If one really wants to do without a voltage regulator (zener + transistor, 7812 or LM317), one
can make two stages of capacitors separated by a resistance of 47 Ohms.
If it is desired to make a single printed circuit supply + active filter, it is necessary to avoid humming due to ripple current passages in the capacitors. The routing of the mass must make a
separation between the ground tracks where the charging / discharging currents flow in the supply capacitors and the audio ground. We can of course make two different cards.
The adjustment potentiometers of the transition frequencies have interest to be linear for better ergonomics (to avoid that a quarter of the rotation of the potentiometer makes already almost all the
Last word
This active 4-way filter is ideal for a high-powered sound system (4 separate amplifiers for a mono system). Variations can be made with only two or three channels.
If one wishes to realize a stereo system, it is necessary to duplicate the assembly. However the bass is not stereo and a mono output mixer will suffice for the left boxes and right boxes.
No comments | {"url":"http://en.abdelkadirbasti.com/2018/05/4-channel-active-sound-filter-schema.html","timestamp":"2024-11-07T20:10:54Z","content_type":"application/xhtml+xml","content_length":"311492","record_id":"<urn:uuid:352e50f8-d31b-45e2-ac04-e81ea77bec5c>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00345.warc.gz"} |
Extra parameter file
Extra parameter file
GADMA take an extra parameter file as input. However one probably do not need them. Nevertheless, if one is interested, extra_params_template with all options and their descriptions can be found in
gadma/cli/ folder.
Related options
• Options of parameter bounds:
□ Min N - minimum value (in genetic units) of population size (0.01).
□ Max N - maximum value (in genetic units) of population size (100).
□ Min T - minimum value (in genetic units) of epoch time (0).
□ Max T - maximum value (in genetic units) of epoch time (5).
□ Min M - minimum value (in genetic units) of migration rate (0).
□ Max M - maximum value (in genetic units) of migration rate (10).
• Options of genetic algorithm:
□ Size of generation - number of demographic models on one iteration (generation) of the genetic algorithm (10).
□ Fractions - fractions of best, mutated and crossed models that are taken to the new generation (None).
□ N elitism - number of best models that are taken to the new generation (2).
□ P mutation - fraction of models that are mutants in new generation (0.56).
□ P crossover - fraction of models that are children in new generation (0.19).
□ P random - fraction of models that were randomly generated for new generation (0.13).
□ Mean mutation strength - initial value of mean number of parameters that are mutated in the chosen model during mutation (0.63).
□ Const for mutation strength - constant for ‘one-fifth’ rule to change mutation strength (1.02).
□ Mean mutation rate - initial value of mean rate of parameter change during mutation (0.45).
□ Const for mutation rate - constant for ‘one-fifth’ rule to change mutation rate (1.07).
□ Stuck generation number - genetic algorithm stops when there is no improvement during this number of iterations.
□ Eps - change of log-likelihood that is considered significant.
□ Random N_A - enables random generation of ancestral size value and scales other parameters to this value during random generation of model parameters (True).
• Options of bayesian optimization:
□ Kernel - name of kernel for Gaussian process (Matern52).
□ Acquisition function - name of acquisition function (EI).
• Options of global optimizations:
□ X_init - points for initial design.
□ Y_init - value of log-likelihood on this points. | {"url":"https://gadma.readthedocs.io/en/latest/user_manual/extra_params_file.html","timestamp":"2024-11-11T06:49:31Z","content_type":"text/html","content_length":"14543","record_id":"<urn:uuid:a4f353ee-4c45-42f0-a485-c73e496bbd50>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00863.warc.gz"} |
III Theoretical Physics of Soft Condensed Matter - Active Soft Matter
9Active Soft Matter
III Theoretical Physics of Soft Condensed Matter
9 Active Soft Matter
We shall finish the course by thinking a bit about motile particles. These are
particles that are self-propelled. For example, micro-organisms such as bacteria
and algae can move by themselves. There are also synthetic microswimmers. For
example, we can make a sphere and coat it with gold and platinum on two sides
We put this in hydrogen peroxide H
. Platinum is a catalyst of the decompo-
→ 2H
O + O
and this reaction will cause the swimmer to propel forward in a certain direction.
This reaction implies that entropy is constantly being produced, and this cannot
be captured adequately by Newtonian or Lagrangian mechanics on a macroscopic
Two key consequences of this are:
(i) There is no Boltzmann distribution.
The principle of detailed balance, which is a manifestation of time reversal
symmetry, no longer holds.
Example. Take bacteria in microfluidic enclosure with funnel gates:
In this case, we expect there to be a rotation of particles if they are self-
propelled, since it is easier to get through one direction than the other. Contrast
this with the fact that there is no current in the steady state for any thermal
equilibrium system. The difference is that Brownian motion has independent
increments, but self-propelled particles tend to keep moving in the same direction.
Note also that we have to have to break spatial symmetry for this to happen.
This is an example of the Ratchet theorem, namely if we have broken time
reversal symmetry pathwise, and broken spatial symmetry, then we can have
non-zero current.
If we want to address this type of system in the language we have been using,
we need to rebuild our model of statistical physics. In general, there are two
model building strategies:
Explicit coarse-graining of “micro” model, where we coarse-grain particles
and rules to PDEs for ρ, φ, P, Q.
Start with models of passive soft matter (e.g. Model B and Model H), and
add minimal terms to explicitly break time reversal phenomenologically.
Of course, we are going to proceed phenomenologically.
Active Model B
Start with Model B, which has a diffusive, symmetric scalar field
with phase
φ = −∇ · J
J = −∇˜µ +
We took
F =
To model our system without time reversal symmetry, we put
˜µ =
+ λ(∇φ)
The new term breaks the time reversal structure. These equations are called
active Model B . Another way to destroy time reversal symmetry is by replacing
the white noise with something else, but that is complicated
Note that
is not the functional derivative of any
. This breaks the free energy
structure, and
6= e
for any F [φ]. So time reversal symmetric is broken barring miracles.
We cannot achieve the breaking by introducing a polynomial term, since if
g(φ) is a polynomial, then
g(φ) =
g(u) du
So gradient terms are required to break time reversal symmetry. We will
later see this is not the case for liquid crystals.
The active model B is agnostic about the cause of phase separation at
a < 0. There are two possibilities:
(a) We can have attractive interactions
We can have repulsive interactions plus motile particles: if two parti-
cles collide head-on, then we have pairwise jamming. They then move
together for a while, and this impersonates attraction. This is called
MIPS — mobility-induced phase separation. It is possible to study
this at a particle level, but we shall not.
The dynamics of coarsening during phase separation turns out to be similar,
with L(t) ∼ t
. The Ostwald–like process remains intact.
The coexistence conditions are altered. We previously found the coexistence
conditions simply by global free energy minimization. In the active case,
we can’t do free energy minimization, but we can still solve the equations
of motion explicitly. In this case, instead of requiring a common tangent,
we have equal slope but different intercepts, where we set
(µφ − f)
= (µφ − f)
+ ∆.
This is found by solving J = 0, so
˜µ =
− κ∇
φ + λ(∇φ)
= const.
(vi) There is a further extension, active model B+, where we put
J = −∇˜µ +
2DΛ + ζ(∇
This extra term is similar to
) in that it has two
’s and three
’s, and they are equivalent in 1 dimension, but in 1 dimension only. This
changes the coarsening process significantly. For example, Ostwald can
stop at finite R (see arXiv:1801.07687).
Active polar liquid crystals
Consider first a polar system. Then the order parameter is
. In the simplest
case, the field is relaxational with v = 0. The hydrodynamic level equation is
p = −Γh, h =
We had a free energy
F =
As for active model B,
can acquire gradient terms that are incompatible with
But also, we can have a lower order term in
that is physically well-motivated —
if we think of our rod as having a direction
, then it is natural that
wants to
translate along its own direction at some speed
. Thus,
acquires self-advected
motion wp. Thus, our equation of motion becomes
p + p · ∇p = −Γh.
This is a bit like the Navier–Stokes equation non-linearity. Now couple this to a
fluid flow v. Then
= −Γh,
+ v · ∇
p + Ω · p − ξD · p + wp · ∇p.
The Navier–Stokes/Cauchy equation is now
+ v · ∇)v = η∇
v − ∇P + ∇ · Σ
+ ∇ · Σ
where as before,
∇ · Σ
= −p
+ ∇
− p
) +
+ p
and we have a new term Σ
given by the active stress, and the lowest order
term is
. This is a new mechanical term that is incompatible with
. We
then have
∇ · Σ
= (∇ · p)p.
We can think of this as an effective body force in the Navier–Stokes equation.
The effect is that we have forces whenever we have situations looking like
In these cases, We have a force acting to the right for
ζ >
0, and to the left if
ζ < 0.
These new terms give spontaneous flow, symmetric breaking and macroscopic
fluxes. At high w, ζ, we get chaos and turbulence.
Active nematic liquid crystals
In the nematic case, there is no self-advection. So we can’t make a velocity from
Q. We again have
= −ΓH, H =
is given by
= (∂
+ v · ∇)Q + S(Q, K, ξ).
Here K = ∇v and
S = (−Ω · Q − Q · Ω) − ξ(D · Q + Q · D) + 2ξ
Q +
Tr(Q · K)
Since there is no directionality as in the previous case, the material derivative
will remain unchanged with active matter. Thus, at lowest order, all the self-
propelled motion can do is to introduce an active stress term. The leading-order
stress is
= ζQ.
This breaks the free energy structure. Indeed, if we have a uniform nematic, then
the passive stress vanishes, because there is no elastic distortion at all. However,
the active stress does not since
ζQ 6
= 0. Physically, the non-zero stress is due to
the fact that the rods tend to generate local flow fields around themselves to
propel motion, and these remain even in a uniform phase.
After introducing this, the effective body force density is
f = ∇·Σ
= ζ∇ · Q ∼ ζλ(∇ · n)n.
This is essentially the same as the case of the polar case. Thus, if we see
something like
then we have a rightward force if ζ > 0 and leftward force if ζ < 0.
This has important physical consequences. If we start with a uniform phase,
then we expect random noise to exist, and then the active stress will destablize
the system. For example, if we start with
and a local deformation happens:
then in the
ζ >
0 case, this will just fall apart. Conversely, bends are destabilized
ζ <
0. Either case, there is a tendency for these things to be destabilized,
and a consequence is that active nematics are never stably uniform for large
systems. Typically, we get spontaneous flow.
To understand this more, we can explicitly describe how the activity parameter
ζ affects the local flow patterns. Typically, we have the following two cases:
ζ > 0
ζ < 0
Suppose we take an active liquid crystal and put it in a shear flow. A rod-like
object tends to align along the extension axis, at a 45
If the liquid crystal is active, then we expect the local flows to interact with
the shear flow. Suppose the shear rate is v
= yg. Then the viscous stress is
= ηg
We have
∝ ζλ
nn −
= ζλ
is at 45
exactly. Note that the sign of
affects whether it reinforces or
weakens the stress.
A crucial property is that Σ
does not depend on the shear rate. So in the
contractile case, the total stress looks like
In the extensile case, however, we have
This is very weird, and leads to spontaneous flow at zero applied stress of
the form
Defect motion in active nematics
For simplicity, work in two dimensions. We have two simple defects as before
q = −
q = +
Note that the
charge is symmetric, and so by symmetry, there cannot be
a net body stress. However, in the
= +
defect, we have a non-zero effective
force density.
So the defects themselves are like quasi-particles that are themselves active.
We see that contractile rods move in the direction of the opening, and the
extensile goes in the other direction. The outcome of this is self-sustaining
“turbulent” motion, with defect pairs
are formed locally. The
stay put
and the +
ones self-propel, and depending on exactly how the defect pairs are
formed, the +
defect will fly away.
Experimental movies of these can be found in T. Sanchez Nature 491, 431
(2012). There are also simulations in T. Shendek, et al, Soft Matter 13, 3853 | {"url":"https://dec41.user.srcf.net/h/III_L/theoretical_physics_of_soft_condensed_matter/9","timestamp":"2024-11-11T10:39:10Z","content_type":"text/html","content_length":"270662","record_id":"<urn:uuid:16023412-eaee-41a3-9672-7218e72be827>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00837.warc.gz"} |
Talk of note on Nov. 2: 'Twenty Questions, Mastermind & Entropy'
Ruy Exel
Ruy Exel, a visiting professor in mathematics this semester at the University of Nebraska-Lincoln from the Universidade Federal de Santa Catarina will present "Twenty Questions, Mastermind & Entropy"
on Friday, Nov. 2, at 4 p.m. in 115 Avery Hall on the University of Nebraska-Lincoln City Campus. This talk is free and open to the public. We encourage teachers and students to attend.
"Imagine a table with a large number of objects of different colors, shapes, weights, sizes, flavors, smells … I’ll think of one of the objects and I’ll challenge you to guess it. You are allowed to
ask what is the object’s color, or maybe its shape, which side of the table it is located or any other characteristic until you finally guess it. Which characteristic should you ask about first? If
all objects are white, except for a red one, is it a good strategy to start by asking which color it is? If you get red as an answer, you win the game, but it is much more likely I’ll say white and
you are back to square one!
The purpose of this lecture is to discuss, in a mathematically precise way, how to measure the value of information, leading up to the notion of entropy, and to show how it can be used to gauge how
much information you should expect to get with each question in the above game, and also in games such as 'Twenty Questions' or 'Mastermind.' Should time allow, we will move on to other applications
of these ideas, for example highlighting the famous Gibbs states of statistical mechanics which tell you how to compute the probability of each face of an uneven dice. Entropy is also highly relevant
in physics, statistics, computer science, electrical engineering, natural language processing, cryptography, neurobiology, human vision, the evolution and function of molecular codes
(bioinformatics), quantum computing, linguistics, plagiarism detection and pattern recognition, but unfortunately we will not have time to discuss any of these."
To read more about the Rowlee Lecture Series, please visit: | {"url":"https://newsroom.unl.edu/announce/csmce/8415/49427","timestamp":"2024-11-09T16:09:51Z","content_type":"text/html","content_length":"66213","record_id":"<urn:uuid:9b8e1584-2626-4d98-9d4c-86868deb316d>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00095.warc.gz"} |
C sqrt() Function | CodeToFun
C sqrt() Function
Updated on Oct 06, 2024
By Mari Selvan
đ ī¸ 293 - Views
â ŗ 4 mins
đ Ŧ 1 Comment
Photo Credit to CodeToFun
đ Introduction
In C programming, mathematical operations are essential, and the sqrt() function is a powerful tool for calculating the square root of a number.
This function is part of the math.h library and provides a straightforward way to find the square root in C.
In this tutorial, we'll explore the usage and functionality of the sqrt() function.
đ Ą Syntax
The syntax for the sqrt() function is as follows:
• x: The number for which you want to find the square root.
đ Example
Let's dive into an example to illustrate how the sqrt() function works.
#include <stdio.h>
#include <math.h>
int main() {
double number = 25.0;
// Calculate the square root
double result = sqrt(number);
// Output the result
printf("Square root of %.2f is %.2f\n", number, result);
return 0;
đ ģ Output
Square root of 25.00 is 5.00
đ § How the Program Works
In this example, the sqrt() function is used to calculate the square root of the number 25.0, and the result is printed.
â Šī¸ Return Value
The sqrt() function returns the square root of the given number as a double. If the input is negative, the function returns NaN (Not a Number).
đ Common Use Cases
The sqrt() function is particularly useful when you need to find the length of a side of a square given its area, or when dealing with geometric calculations, physics, or any scenario involving
square roots.
đ Notes
• The sqrt() function operates on double values, so it's suitable for both integer and floating-point calculations.
• Ensure that the math.h header is included at the beginning of your program when using the sqrt() function.
đ ĸ Optimization
The sqrt() function is generally optimized for performance, and there's usually no need for additional optimization. If performance is critical, consider profiling your code to identify potential
đ Conclusion
The sqrt() function in C provides a simple and efficient way to calculate the square root of a number. Whether you're working on mathematical computations or scientific applications, the sqrt()
function is a valuable tool in your programming toolkit.
Feel free to experiment with different numbers and explore the behavior of the sqrt() function in various scenarios. Happy coding!
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For over eight years, I worked as a full-stack web developer. Now, I have chosen my profession as a full-time blogger at codetofun.com.
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Analytic solution of a system of linear distributed order differential equations in the Reimann-Liouville sense
1. Rocca, M.C., Plastino, A.R., Plastino, A., Ferri, G.L., and de Paoli, A. "General solution of a fractional diffusion-advection equation for solar cosmic-ray transport", Physica A: Statistical
Mechanics and its Applications, 447, pp. 402-410 (2016).
2. Bellouquid, A., Nieto, J., and Urrutia, L. "About the kinetic description of fractional diffusion equations modeling chemotaxis", Mathematical Models and Methods in Applied Sciences, 26(02), pp.
249-268 (2016).
3. Rosa, C.F.A.E. and Capelas de Oliveira, E. "Relaxation equations: fractional models", Journal of Physical Mathematics, 6(2) (2015). DOI: 10.4172/2090-0902.1000146. https://projecteuclid.org/
4. Saxena, R.K. and Pagnini, G. "Exact solutions of triple-order time-fractional differential equations for anomalous relaxation and diffusion I: The accelerating case", Physica A: Statistical
Mechanics and Its Applications, 390(4), pp. 602-613 (2011).
5. Bobylev, A.V. and Cercignani, C. "The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation", Applied Mathematics Letters, 15
(7), pp. 807-813 (2002).
6. Mainardi, F., Mura, A., Goren o, R., and Stojanovic, M. "The two forms of fractional relaxation of distributed order", Journal of Vibration and Control, 13(9-10), pp. 1249-1268 (2007).
7. Ansari, A. and Moradi, M. "Exact solutions to some models of distributed-order time fractional diffusion equations via the Fox H functions", Science Asia, 39, pp. 57-66 (2013).
8. Naber, M. "Distributed order fractional sub-diffusion", Fractals, 12(01), pp. 23-32 (2004).
9. Mainardi, F. and Pagnini, G. "The role of the Fox- Wright functions in fractional sub-diffusion of distributed order", Journal of Computational and Applied Mathematics, 207(2), pp. 245-257 (2007).
10. Stojanovic, M. "Fractional relaxation equations of distributed order", Nonlinear Analysis: Real World Applications, 13(2), pp. 939-946 (2012).
11. Langlands, T.A.M. "Solution of a modified fractional diffusion equation", Physica A: Statistical Mechanics and Its Applications, 367, pp. 136-144 (2006).
12. Podlubny, I., Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications 198,
Academic press, San Diego, USA (1998).
13. Li, Y., Sheng, H., and Chen, Y.Q. "On distributed order integrator/differentiator", Signal Processing, 91(5), pp. 1079-1084 (2011).
14. Erdelyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F., Tables of Integral Transforms, 1 (1954).
15. Haubold, H.J., Mathai, A.M., and Saxena, R.K. "Mittag-Leffler functions and their applications", Journal of Applied Mathematics, 2011, Article ID 298628 (2011). DOI: 10.1155/2011/298628.
16. Goren o, R., Kilbas, A.A., Mainardi, F., and Sergei, V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin, Germany (2014).
17. Sandev, T., Chechkin, A.V., Korabel, N., Kantz, H., Sokolov, I.M., and Metzler, R. "Distributed-order diffusion equations and multifractality: Models and solutions", Physical Review E, 92(4),
042117 (2015).
18. Jiao, Z., Chen, Y.Q., and Podlubny, I., Distributed- Order Dynamic Systems: Stability, Simulation, Applications and Perspectives, Springer Briefs in Electrical and Computer Engineering (2012).
19. Chrouda, M.B., El Oued, M., and Ouerdiane, H. "Convolution calculus and applications to stochastic differential equations", Soochow Journal of Mathematics, 28(4), pp. 375-388 (2002).
20. Gossett, E., Discrete Mathematics with Proof, John Wiley & Sons (2009).
21. Abate, J. and Whitt, W. "A unified framework for numerically inverting Laplace transforms", INFORMS Journal on Computing, 18(4), pp. 408-421 (2006). | {"url":"https://scientiairanica.sharif.edu/article_20335.html","timestamp":"2024-11-13T01:17:45Z","content_type":"text/html","content_length":"46637","record_id":"<urn:uuid:d9beae97-2545-41ba-a124-787839d9e05c>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00096.warc.gz"} |
Inverse Of Double Numbers
To calculate the inverse value (1/z) we multiply the top and bottom by the conjugate which makes the denominator a real number.
z plane w plane
Let the components of the input and output planes be:
z = x + D y and w = u + D v
In this case w = 1/z
w = 1/(x + D y)
As usual, we evaluate the inverse by multiplying top and bottom by the conjugate:
w = (x - D y)/(x + D y)(x - D y)
w = (x - D y)/(x² - y²)
so the u and v components are:
u = x /(x²-y²)
v = -y /(x²-y²) | {"url":"http://euclideanspace.com/maths/algebra/realNormedAlgebra/other/doubleNumbers/functions/inverse/index.htm","timestamp":"2024-11-10T12:07:08Z","content_type":"text/html","content_length":"16604","record_id":"<urn:uuid:94195241-2651-452e-b1bc-a953447e0470>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00467.warc.gz"} |
2nd Grade Math: Multiplication
In 2nd Grade, students work to build a conceptual foundation for multiplication, which will prepare them for applying these skills in 3rd grade. Making equal group, drawing arrays, and using number
lines are taught in this unit. With hands-on and engaging activities, students will set the stage for multiplication and division.
In this math unit on Multiplication, students will learn to:
* Use addition to find the total number of objects arranged in a rectangular arrays with up to 5 rows and up to 5 columns.
* Write an equation to express the total as a sum of equal addends.
ALL 10 UNITS INCLUDED!
Here are the 10 Units that will be included in the 2nd Grade: Math Made Fun Curriculum
Unit 1: Number Sense to 1,000
Unit 2: Place Value to 1,000
Unit 3: Addition and Subtraction Fluency within 100
Unit 4: Addition and Subtraction with 2-Digit and 3-Digit Numbers
Unit 5: Geometry and Fractions
Unit 6: Graphs and Data
Unit 7: Time
Unit 8: Money
Unit 9: Measurement
Unit 10: Multiplication and Division
This 2nd Grade Math Made Fun Unit 10 has 20 hands-on math centers and 34 NO PREP/Activity pages!
Each unit includes a scope with the objectives:
The Daily Lesson Plans offer differentiation for on-level, below-level and above-level students.
The lesson plans are broken down into 5 easy-to-follow parts:
1. Objective– What students should be able to do by the end of the lesson.
2. Review- A quick warm-up that has students practice previous skills that will be used in the current lesson.
3. Hook-A fun intro to get students engaged.
4. Mini Lesson– Teach, model, and discuss the new skill in today’s lesson.
5. Practice- Each practice section lists three types of activities that pair well with the specific lesson.
Center(s)- New center(s) to be introduced with the lesson.
Activity Pages- These pages require some basic materials such as scissors, glue or dice.
Practice Pages- These only require a pencil and crayons! They are great for table work, homework or work on the go!
✸Differentiation– Each lesson include scaffold and extension ides to meet the needs of students at all levels!
Pre and Post Assessments for EACH unit!
Material Wrap Up Page!
LET’S LOOK AT THE MATH CENTERS FOR UNIT 10 IN ACTION…
CENTER NUMBER 1: Roll and Draw an Array
Roll two dice. Draw an array to match, and label the array. Record on your recording sheet.
CENTER NUMBER 2: Match an Array
Match the multiplication problem to the correct array. Write the arrays on your recording sheet.
CENTER NUMBER 3: Roll and Build an Array
Roll two dice. Use snap cubes to build an array to match your roll.
CENTER NUMBER 4: Flip and Show Your Array
Flip a card. Show an array on the board to match the multiplication problem.
CENTER NUMBER 5: Model Equal Groups
Flip a card. For each card, use manipulatives or a dry-erase marker to show equal groups.
CENTER NUMBER 6: Flip and Pick an Array
Flip a card. Record the multiplication problem for each card on the recording sheet.
CENTER NUMBER 7: Match an Array (Equal Groups)
Find the equal groups that match the array on the board.
CENTER NUMBER 8: Match an Array (Repeated Addition)
Find the array that matches the repeated addition problem on the board.
CENTER NUMBER 9: Spin and Draw an Array
Spin both spinners. Write a multiplication sentence to match your spin. Model an array to match your spin.
CENTER NUMBER 10: Arrays- Write the Room
Find the array cards around the room. Write the repeated addition problems on the recording sheet to match the arrays.
CENTER NUMBER 11: Number Line Jumps
Flip a card. Use a dry erase marker to show the correct jumps on the number line. Circle the product.
CENTER NUMBER 12: Model an Array Mats
Use play dough or modeling clay to make the array that matches the multiplication problem.
CENTER NUMBER 13: Rows and Columns
Count and record the numbers of rows and columns on each card.
CENTER NUMBER 14: Array Addition
Write a repeated addition sentence for each array.
CENTER NUMBER 15: Arrays- True or False?
Decide if the array is equal to the multiplication problem. Sort to the correct mat.
CENTER NUMBER 16: Multiplication War
Two players play. Deal each player 10 cards. Each person flips a card at the same time. The person with the largest product wins that round and keeps both cards. The person with the most cards at the
end of 10 rounds wins the game!
CENTER NUMBER 17: Array Tic-Tac-Toe (Repeated Addition)
Two players take turns writing a matching repeated addition problem for an array. Each player uses a different marker color. The first person to get three in a row wins.
CENTER NUMBER 18: Array Tic-Tac-Toe (Multiplication Problem)
Two players take turns writing a multiplication problem for an array. Each player uses a different marker color. The first person to get three in a row wins.
CENTER NUMBER 19: Array Tic-Tac-Toe (Drawing Arrays)
Two players take turns drawing an array to match a multiplication problem. Each player uses a different marker color. The first person to get three in a row wins.
CENTER NUMBER 20: Flip and Fill with Fox
Flip a card. Use a dry erase marker to show the correct jumps on the number line. Circle the product.
For each page, there is a grade level standard attached so you know EXACTLY what you are covering! You can feel confident that ALL the standards for Second Grade are being covered!
HOW DO I ORGANIZE THE UNITS?
I chose to store the math centers in Sterilite bins, sinc they don’t take up too much space. It is a tight fit, but I find that they work nicely for me. However, if you choose, you could store the
centers in a larger container as well. Within the bin, each math center is stored in a gallon sized ziplock baggie.
Click Here to view the 2nd Math Made Fun Unit 1 post.
You can purchase Unit 10 individually HERE or
1. Essen Ikan Nila says
Thanks for sharing,.
2. Cynthia says
I knew how difficult it was for me to master multiplication tables. i DON’T WANT THE SAME FOR MY KIDS, THIS WILL BE OF HELP. THANKS.
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Sum of the Squared Deviations - Quant RL
Sum of the Squared Deviations
What is Variance and Why Does it Matter?
In statistical analysis, variance is a fundamental concept that measures the spread or dispersion of a dataset. It provides valuable insights into how individual data points deviate from the mean
value, enabling analysts to identify patterns, trends, and correlations. The sum of the squared deviations method is a widely used technique for calculating variance, and its importance cannot be
overstated. By grasping the concept of variance, analysts can unlock the full potential of their data, driving business success and informed decision-making. In essence, variance is a crucial metric
that helps analysts understand the variability inherent in a dataset, making it an indispensable tool in statistical analysis.
Calculating Variance: The Sum of Squared Deviations Method
The sum of the squared deviations method is a widely used technique for calculating variance, which is a fundamental concept in statistical analysis. The formula for calculating variance using this
method is: σ² = Σ(xi – μ)² / N, where σ² is the variance, xi is each data point, μ is the mean, and N is the number of data points. To calculate variance, follow these steps: first, calculate the
mean of the dataset; then, subtract the mean from each data point to find the deviations; next, square each deviation; finally, sum the squared deviations and divide by the number of data points.
This method provides an accurate measure of variance, enabling analysts to understand the spread of their data and make informed decisions.
How to Calculate the Sum of Squared Deviations in Real-World Scenarios
In real-world scenarios, the sum of squared deviations method is widely applicable in various fields, including finance, education, and healthcare. For instance, in finance, the sum of squared
deviations can be used to analyze stock prices and understand the volatility of the market. Suppose we want to calculate the variance of the daily returns of a stock over a period of 10 days. We can
use the sum of squared deviations method by first calculating the mean return, then subtracting the mean from each daily return to find the deviations, squaring each deviation, and finally summing
the squared deviations and dividing by the number of days. This calculation provides valuable insights into the stock’s price fluctuations, enabling investors to make informed decisions.
In education, the sum of squared deviations can be used to analyze student grades and understand the dispersion of scores. For example, a teacher can use the sum of squared deviations method to
calculate the variance of a class’s scores on a particular exam, identifying areas where students may need additional support. Similarly, in healthcare, the sum of squared deviations can be used to
analyze medical data, such as blood pressure readings or patient outcomes, to understand the variability of the data and make informed decisions about patient care.
By applying the sum of squared deviations method in these real-world scenarios, analysts can gain a deeper understanding of their data, identify patterns and trends, and make informed decisions that
drive business success.
The Difference Between Population and Sample Variance
In statistical analysis, it is essential to understand the distinction between population and sample variance, as each has its own application and calculation method. Population variance refers to
the variance of an entire population, whereas sample variance is an estimate of the population variance based on a subset of data. The sum of squared deviations method can be used to calculate both
population and sample variance, but the formula and application differ slightly.
Population variance is calculated using the formula σ² = Σ(xi – μ)² / N, where σ² is the population variance, xi is each data point, μ is the population mean, and N is the total number of data points
in the population. This formula is used when the entire population is available, and the goal is to understand the dispersion of the data.
Sample variance, on the other hand, is calculated using the formula s² = Σ(xi – x̄)² / (n – 1), where s² is the sample variance, xi is each data point, x̄ is the sample mean, and n is the number of
data points in the sample. This formula is used when only a subset of the population is available, and the goal is to estimate the population variance.
Understanding the difference between population and sample variance is crucial in statistical analysis, as it determines the appropriate calculation method and application. By using the sum of
squared deviations method correctly, analysts can ensure accurate calculations and informed decision-making.
Common Applications of Sum of Squared Deviations in Data Analysis
The sum of squared deviations is a fundamental concept in statistical analysis, and its applications are diverse and widespread. One of the most common applications is in regression analysis, where
the sum of squared deviations is used to calculate the coefficient of determination (R²), which measures the goodness of fit of a regression model. By analyzing the sum of squared deviations,
analysts can determine the proportion of variance in the dependent variable that is explained by the independent variables.
Another important application of the sum of squared deviations is in hypothesis testing, where it is used to calculate the test statistic and p-value. For example, in a t-test, the sum of squared
deviations is used to calculate the variance of the sample mean, which is then used to determine whether the sample mean is significantly different from the population mean.
The sum of squared deviations is also used in confidence intervals, where it is used to calculate the margin of error. By analyzing the sum of squared deviations, analysts can determine the range of
values within which the true population parameter is likely to lie.
In addition to these applications, the sum of squared deviations is also used in other areas of data analysis, such as ANOVA, time series analysis, and machine learning. In ANOVA, the sum of squared
deviations is used to calculate the F-statistic, which is used to determine whether there are significant differences between group means. In time series analysis, the sum of squared deviations is
used to calculate the variance of a time series, which is used to identify patterns and trends. In machine learning, the sum of squared deviations is used as a loss function in regression models,
where the goal is to minimize the sum of squared deviations between predicted and actual values.
By understanding the various applications of the sum of squared deviations, analysts can unlock the full potential of statistical analysis and make informed decisions in a wide range of fields.
Interpreting Results: What Do the Numbers Really Mean?
Once the sum of squared deviations has been calculated, it’s essential to interpret the results correctly to extract meaningful insights from the data. The sum of squared deviations provides a
measure of the dispersion of the data, but it’s crucial to understand what this value represents in the context of the analysis.
A small sum of squared deviations indicates that the data points are closely clustered around the mean, suggesting low variability. In contrast, a large sum of squared deviations indicates that the
data points are spread out, suggesting high variability. By analyzing the sum of squared deviations, analysts can identify patterns, trends, and correlations in the data.
For example, in a regression analysis, a small sum of squared deviations may indicate a strong relationship between the independent and dependent variables. In hypothesis testing, a large sum of
squared deviations may indicate that the null hypothesis should be rejected, suggesting a significant difference between the sample mean and the population mean.
When interpreting the results of sum of squared deviations calculations, it’s also important to consider the context of the analysis. For instance, in medical research, a small sum of squared
deviations may indicate a high degree of precision in the measurement of a medical outcome. In finance, a large sum of squared deviations may indicate high volatility in stock prices.
By correctly interpreting the results of sum of squared deviations calculations, analysts can gain a deeper understanding of the data and make informed decisions in a wide range of fields. The sum of
squared deviations is a powerful tool in statistical analysis, and its correct interpretation is essential for extracting meaningful insights from data.
Common Pitfalls to Avoid When Calculating Sum of Squared Deviations
When calculating the sum of squared deviations, it’s essential to avoid common mistakes that can lead to inaccurate results and misinformed decisions. One of the most critical pitfalls to avoid is
incorrect data entry, which can occur due to human error or data corruption. A single incorrect data point can significantly affect the sum of squared deviations, leading to misleading conclusions.
Another common pitfall is the presence of outliers in the data. Outliers are data points that are significantly different from the rest of the data, and they can greatly inflate the sum of squared
deviations. To avoid this, it’s crucial to identify and handle outliers appropriately, either by removing them or using robust statistical methods that are resistant to outliers.
Bias in the sample is another pitfall to avoid when calculating the sum of squared deviations. A biased sample can lead to a sum of squared deviations that is not representative of the population,
resulting in inaccurate conclusions. To avoid bias, it’s essential to ensure that the sample is randomly selected and representative of the population.
In addition to these pitfalls, it’s also important to avoid using the wrong formula or method for calculating the sum of squared deviations. The sum of squared deviations method is sensitive to the
choice of formula and method, and using the wrong one can lead to inaccurate results.
By being aware of these common pitfalls, analysts can take steps to avoid them and ensure that their calculations of the sum of squared deviations are accurate and reliable. This is critical in data
analysis, where the sum of squared deviations plays a vital role in understanding data dispersion and making informed decisions.
Conclusion: Mastering the Sum of Squared Deviations for Informed Decision-Making
In conclusion, understanding the sum of squared deviations is a crucial aspect of statistical analysis, enabling analysts to measure variability and make informed decisions. By grasping the concept
of variance and its importance, analysts can unlock the power of data analysis and drive business success.
The sum of squared deviations method provides a robust approach to calculating variance, and its applications in data analysis are vast and varied. From regression analysis to hypothesis testing and
confidence intervals, the sum of squared deviations plays a vital role in extracting insights from data.
By avoiding common pitfalls, such as incorrect data entry, outliers, and biased samples, analysts can ensure that their calculations of the sum of squared deviations are accurate and reliable. This,
in turn, enables them to identify patterns, trends, and correlations in data, making informed decisions that drive business success.
In today’s data-driven world, mastering the sum of squared deviations is essential for organizations seeking to gain a competitive edge. By harnessing the power of statistical analysis, businesses
can unlock new insights, optimize processes, and drive growth. The sum of squared deviations is a critical component of this process, providing a powerful tool for measuring variability and making
informed decisions.
By applying the concepts and techniques outlined in this article, analysts can unlock the full potential of the sum of squared deviations, driving business success and informing decision-making in a
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Optimising planar inductors
A numerical simulation program, QvalueC, was developed for the design of planar inductors on lossy substrates in two-dimensional geometry. Integral equations are used for the estimation of the
overall impedance of a circular inductor at a given frequency. The program computes the current density distribution in the wire that has a finite electric conductivity. This so called magnetic
computation gives the series inductance and series resistance of the coil. By using Green functions, integral equations are derived for equivalent surface charges that represent the conductor in the
electric problem. From the surface charges the parallel capacitance and the parallel resistance are obtained. The code is written with the view to designing planar coils in four dielectric layers,
but also solenoids with multilayered conductors can be computed. The approach taken allows an accurate simulation of the following dissipation mechanisms affecting the Q-value: ohmic losses in the
wire, skin-depth effect, proximity (eddy current) effect, and losses in supporting dielectric but conductive layers via capacitive coupling. Simulated and measured results from planar inductors on
lossy silicon and other substrates show a good agreement.
Original language English
Place of Publication Espoo
Publisher VTT Technical Research Centre of Finland
Number of pages 31
ISBN (Print) 951-38-5641-0
Publication status Published - 2000
MoE publication type Not Eligible
Publication series
Series VTT Tiedotteita - Meddelanden - Research Notes
Number 2017
ISSN 1235-0605
• numerical simulation program
• design of planar inductors
• planar coils
Dive into the research topics of 'Optimising planar inductors'. Together they form a unique fingerprint. | {"url":"https://cris.vtt.fi/en/publications/optimising-planar-inductors","timestamp":"2024-11-02T13:58:47Z","content_type":"text/html","content_length":"50518","record_id":"<urn:uuid:dbe11c5d-1be3-48f3-9943-3e41ec1a1706>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00393.warc.gz"} |
MADSEQ: vignettes/MADSEQ-vignette.Rmd
The MADSEQ package is a group of hierarchical Bayesian model for the detection and quantification of potential mosaic aneuploidy in sample using massive parallel sequencing data.
The MADSEQ package takes two pieces of information for the detection and quantification of mosaic aneuploidy:
MADSEQ works on the whole chromosome resolution. It applies all of the five models (normal, monosomy, mitotic trisomy, meiotic trisomy, loss of heterozygosity) to fit the distribution of the AAF of
all the heterozygous sites, and fit the distribution of the coverage from that chromosome. After fitting the same data using all models, it does model comparison using BIC (Bayesian Information
Criteria) to select the best model. The model selected tells us whether the chromosome is aneuploid or not, and also the type of mosaic aneuploidy. Then, from the posterior distribution of the best
model, we could get the estimation of the fraction of aneuploidy cells.
Note: Currently our package only supports one bam and one vcf file per sample. If you have more than one sample, please prepare multiple bam and vcf files for each of them.
There are two sets of example data come with the package:
Note:This is just a set of example data, only contains a very little region of the genome.
We will start with the bam file, vcf file and bed file in the example data to show you each step for the analysis.
Started with bam file and bed file, you can use prepareCoverageGC function to get the coverage and GC information for each targeted regions.
## load the package suppressMessages(library("MADSEQ")) ## get path to the location of example data aneuploidy_bam = system.file("extdata","aneuploidy.bam",package="MADSEQ") normal_bam = system.file
("extdata","normal.bam",package="MADSEQ") target = system.file("extdata","target.bed",package="MADSEQ") ## Note: for your own data, just specify the path to the location ## of your file using
character. ## prepare coverage and GC content for each targeted region # aneuploidy sample aneuploidy_cov = prepareCoverageGC(target_bed=target, bam=aneuploidy_bam, "hg19") # normal sample normal_cov
= prepareCoverageGC(target_bed=target, bam=normal_bam, "hg19") ## view the first two rows of prepared coverage data (A GRanges Object) aneuploidy_cov[1:2] normal_cov[1:2]
The normalization function takes prepared coverage GRanges object from prepareCoverageGC function, normalize the coverage and calculate the expected coverage for the sample. If there is only one
sample, the function will correct the coverage by GC content, and take the average coverage for the whole genome as expected coverage. If there are more than one samples given, the function will
first quantile normalize coverage across samples, then correct the coverage by GC for each sample. If control sample is not specified, the expected coverage is the median coverage across all samples,
if a normal control is specified, the average coverage for control sample is taken as expected coverage for further analysis.
If you choose to write the output to file (recommended)
## normalize coverage data ## set plot=FALSE here because similar plot will show in the following example normalizeCoverage(aneuploidy_cov,writeToFile=TRUE, destination=".",plot=FALSE)
## normalize coverage data aneuploidy_normed = normalizeCoverage(aneuploidy_cov,writeToFile=FALSE, plot=FALSE) ## a GRangesList object will be produced by the function, look at it by names
(aneuploidy_normed) aneuploidy_normed[["aneuploidy_cov"]]
## normalize coverage data normalizeCoverage(aneuploidy_cov, normal_cov, writeToFile =TRUE, destination = ".", plot=FALSE)
## normalize coverage data normed_without_control = normalizeCoverage(aneuploidy_cov, normal_cov, writeToFile=FALSE, plot=TRUE) ## a GRangesList object will be produced by the function length
(normed_without_control) names(normed_without_control) ## subsetting normed_without_control[["aneuploidy_cov"]] normed_without_control[["normal_cov"]]
## normalize coverage data, normal_cov is the control sample normalizeCoverage(aneuploidy_cov, control=normal_cov, writeToFile=TRUE, destination = ".",plot=FALSE)
normed_with_control = normalizeCoverage(aneuploidy_cov, control=normal_cov, writeToFile =FALSE, plot=FALSE) ## a GRangesList object will be produced by the function length(normed_without_control)
Having vcf.gz file and target bed file ready, use prepareHetero function to process the heterozygous sites.
## specify the path to vcf.gz file aneuploidy_vcf = system.file("extdata","aneuploidy.vcf.gz",package="MADSEQ") ## target bed file specified before ## If you choose to write the output to file
(recommended) prepareHetero(aneuploidy_vcf, target, genome="hg19", writeToFile=TRUE, destination=".",plot = FALSE) ## If you don't want to write output to file aneuploidy_hetero = prepareHetero
(aneuploidy_vcf, target, genome="hg19", writeToFile=FALSE,plot = FALSE)
The function runMadSeq will run the models and select the best model for the input data.
## specify the path to processed files aneuploidy_hetero = "./aneuploidy.vcf.gz_filtered_heterozygous.txt" aneuploidy_normed_cov = "./aneuploidy_cov_normed_depth.txt" ## run the model
aneuploidy_chr18 = runMadSeq(hetero=aneuploidy_hetero, coverage=aneuploidy_normed_cov, target_chr="chr18", nChain=1, nStep=1000, thinSteps=1, adapt=100,burnin=200) ## An MadSeq object will be
returned aneuploidy_chr18
Note: In order to save time, we only run 1 chain with a much less steps compared with default settings. For real cases, the default settings are recommended.
## subset normalized coverage for aneuploidy sample from the GRangesList ## returned by normalizeCoverage function aneuploidy_normed_cov = normed_with_control[["aneuploidy_cov"]] ## run the model
aneuploidy_chr18 = runMadSeq(hetero=aneuploidy_hetero, coverage=aneuploidy_normed_cov, target_chr="chr18") ## An MadSeq object will be returned aneuploidy_chr18
Note: The value of delta BIC suggests the strength of the confidence of the selected model against other models. In our model, you can set a threshold to get high confidence result, usually it's 20
in our testing cases. We summarize it as follows
BIC = c("[0,10]","(10,20]",">20") evidence = c("Probably noisy data","Could be positive", "High confidence") table = data.frame(BIC,evidence) library(knitr) kable(table,col.names =c
("deltaBIC","Evidence against higher BIC") ,align="c")
There are a group of plot functions to plot the output MadSeq object from the runMadSeq.
## plot the posterior distribution for all the parameters in selected model plotMadSeq(aneuploidy_chr18)
## plot the histogram for the estimated fraction of aneuploidy plotFraction(aneuploidy_chr18, prob=0.95)
## plot the distribution of AAF as estimated by the model plotMixture(aneuploidy_chr18)
parameters = c("f","m","mu[1]","mu[2]","mu[3] (LOH model)", "mu[3] (meiotic trisomy model)","mu[4]","kappa","p[1]","p[2]", "p[3]","p[4]","p[5]","m_cov","p_cov","r_cov") explains = c("Fraction of
mosaic aneuploidy", "The midpoint of the alternative allele frequency (AAF) for all heterozygous sites", "Mean AAF of mixture 1: the AAFs of this mixture shifted from midpoint to some higher values",
"Mean AAF of mixture 2: the AAFs of this mixture shifted from midpoint to some lower values", "Mean AAF of mixture 3: In LOH model, mu[3] indicates normal sites without loss of heterozygosity", "Mean
AAF of mixture 3: In meiotic model, the AAFs of this mixture shifted from 0 to some higher value", "Mean AAF of mixture 4: the AAFs of this mixture shifted from 1 to some lower value (only in meiotic
model)", "Indicate variance of the AAF mixtures: larger kappa means smaller variance", "Weight of mixture 1: indicate the proportion of heterozygous sites in the mixture 1", "Weight of mixture 2:
indicate the proportion of heterozygous sites in the mixture 2", "Weight of mixture 3: indicate the proportion of heterozygous sites in the mixture 3 (only in LOH and meiotic model)", "Weight of
mixture 4: indicate the proportion of heterozygous sites in the mixture 4 (only in meiotic model)", "Weight of outlier component: the AAF of 1% sites might not well behaved, so these sites are
treated as noise.", "Mean coverage of all the sites from the chromosome, estimated from a negative binomial distribution", "Prob of the negative binomial distribution for the coverage", "Another
parameter (r) for the negative binomial disbribution of the coverage, small r means large variance") table = data.frame(parameters,explains) kable(table,col.names =c("parameters","description")
Any scripts or data that you put into this service are public.
For more information on customizing the embed code, read Embedding Snippets. | {"url":"https://rdrr.io/bioc/MADSEQ/f/vignettes/MADSEQ-vignette.Rmd","timestamp":"2024-11-15T02:49:34Z","content_type":"text/html","content_length":"43974","record_id":"<urn:uuid:8971bd75-3e98-49c9-bc98-c70f2e5d9311>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00843.warc.gz"} |
Decidable fragments of many-sorted logic
We investigate the possibility of developing a decidable logic which allows expressing a large variety of real world specifications. The idea is to define a decidable subset of many-sorted (typed)
first- order logic. The motivation is that types simplify the complexity of mixed quantifiers when they quantify over different types. We noticed that many real world verification problems can be
formalized by quantifying over different types in such a way that the relations between types remain simple. Our main result is a decidable fragment of many-sorted first-order logic that captures
many real world specifications.
Publication series
Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume 4790 LNAI
ISSN (Print) 0302-9743
ISSN (Electronic) 1611-3349
Conference 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007
Country/Territory Armenia
City Yerevan
Period 15/10/07 → 19/10/07
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Baccarat formula 1324, this formula is sure or soft? - tweetj.com
Just seeing the number 1324, many people may wonder, eh, what is this formula? Did it come up randomly or not? Is there anything guaranteed? Anyone who has played baccarat for a long time will know
that playing without using Baccarat money walk formula With the use of the formula along with it gives very different results. So people come up with many formulas to use in playing. and one of the
most popular formulas in the world This is the 1324 Baccarat formula.
Who would call it a strategy? Let me call this Baccarat money walk formula, well, by the 1324 baccarat formula, he has been in use since 2006 and it is popular to this day, more than ten years ago,
it still works well. without having to modify anything With a betting style that uses the principle of 1 down, 1 win, 1 loss, 0 loss, win rate is 50 / 50, just like throwing games. Which corresponds
to the probability that the dealer will win 0.458597 and the player will win 0.446247, with this formula there is an iron rule that always bet on the bank is prohibited. Since it only has a
probability of 0.095156 that it will always land. In addition, if we always bet on the shore, we will be at a disadvantage. The most online casinos, compared to bets on the banker’s side, we have a
disadvantage of only 1.0579% and bet on the player’s side, we will only have a disadvantage of 1.2351%
But wait Even though we can see that we have an advantage over 95% of the casino, this is nothing to guarantee that in 100 bets we will win up to 90 times, otherwise the casino will go bankrupt.
already Anyone who has studied the House Edge value will know that the chance or win rate here is only effective for a short period of time. After a long time, the casino will finally get a refund.
Gambling, it uses statistics to capture thousands of times to see results.
How to use Baccarat 1324 formula?
How to use Baccarat money walk formula This one is nothing complicated. no matter how long we play We will divide the betting round into 4 rounds or 4 steps with the betting principle as follows.
• Round 1 bet 1 unit
• If Round 1 wins, in Round 2, bet 3 units.
• If Round 2 wins, in Round 3 bet 2 units.
• If Round 3 still wins, Round 4, which is the last round of this formula, bet 4 units.
• No matter which round, if a loss occurs, go back to start round 1 again.
• If lucky to win all 4 rounds in a row, then go back to start the 1st round again, where now we have received a profit of 10 times (if winning on the banker side only, you will receive 0.95
From the above formula, I’ll give you an example of how to use it so that it’s easier to understand as follows. If you interested membership with us UFABET
Round 1 bet 1 unit (assuming 1 investment unit equals 10 baht)
• If you win, you will get a profit of 10 baht from this round.
• Retained profit after winning 0 baht because it is the first round
• If it loses, it will only lose 10 baht of capital.
2nd round bet 3 units
In this round, we will use 1 unit of additional capital and 1 unit of profit from the 1st round for a total of 3 units or 30 baht.
• If you win, you will receive a profit from this round of 30 baht.
• Retained earnings from winning 40 baht (Profit 1 + 2 )
• If you lose, you will lose only 2 units of capital and 1 unit of profit from the first round that is used as capital in this round. This means that there is not a single baht of profit left.
Round 3 bet 2 units
In this round we will use profit only to play. because now we have 40 baht profit in hand
• If you win, you will receive a profit from this round of 20 baht.
• Retained earnings after winning 60 baht
• If we lose, this time we will only lose 20 baht of profit that we use to make capital. It means that we don’t waste our own money at all.
• The remaining profit after losing bets is 20 baht.
Round 4 bet 4 units
After being lucky for 3 eyes, this time we will only throw profits into it as usual.
• If you win, you will get a profit of 40 baht from this round.
• Retained profit after winning 100 baht
• If you lose, this time you will lose 40 baht of profit. You won’t lose yourself a single baht as usual.
• The remaining profit after losing bets is 20 baht. | {"url":"https://tweetj.com/football/baccarat-formula-1324-this-formula-is-sure-or-soft/","timestamp":"2024-11-11T20:06:44Z","content_type":"text/html","content_length":"48335","record_id":"<urn:uuid:10a35c1e-9ae2-453c-8aef-f7622150776f>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00843.warc.gz"} |
Forum of Mathematics, Sigma: Volume 4 - | Cambridge Core
Algebraic and Complex Geometry
Research Article
Discrete Mathematics
Research Article
Algebraic and Complex Geometry
Research Article
Number Theory
Research Article
Discrete Mathematics
Research Article
Number Theory
Research Article
Research Article
Algebraic and Complex Geometry
Research Article
Number Theory
Research Article
Research Article
Number Theory
Research Article
Theoretical Computer Science
Research Article
Research Article
Algebraic and Complex Geometry
Research Article
Computational Mathematics
Research Article
Number Theory
Research Article | {"url":"https://core-cms.prod.aop.cambridge.org/core/journals/forum-of-mathematics-sigma/volume/70E829274473D851A72D4CADA4E1377E","timestamp":"2024-11-12T17:03:13Z","content_type":"text/html","content_length":"1049976","record_id":"<urn:uuid:5189b381-3568-4ce6-81b3-4904e14fe9c5>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00053.warc.gz"} |
Simple Aggregations In Power BI
In this blog post, I’ll touch on some simple aggregations in Power BI that you can use in your DAX calculations.
This is a continuation of the blog that I previously published, where I covered the differences between a measure and a calculated column.
I’ll first continue working on the measures that I’ve gone through in the previous blog and then introduce some aggregating functions that you could use as I go on. You may watch the full video of
this tutorial at the bottom of this blog.
The main aim of this blog is to help you become more familiar with creating measures.
Let’s start.
Creating A Measure Group
If you recall, in the previous blog, I created measures that I used to virtually calculate additional information that I want to get from my data.
The measures that I made were the Total Sales and Total Quantity measures.
I’ll first show you how to organize these measures that I made. To do that, I’m going to create a measure group.
First, go to the Home tab and then select Enter data.
After that, change the name of the table to Key Measures.
You can choose any name you want. I just picked this name because it fits the context of what I want to do with the table.
As you can see under the fields tab, the Key Measures table still has nothing in it.
So now, what I’m going to do is fill this up with the measures that I’ve made.
I’ll first add the Total Quantity measure to the newly made table.
To do that, click on the Total Quantity measure, go to the Measure tools tab, and then change the Home table to Key Measures.
And then, do the same to the Total Sales measure.
Click on the Total Sales measure, go to the Measure tools tab, and then change its Home table to Key Measure.
After doing that, you’ll now see that the measures are under the the Key Measures Table.
Now, I’m going to remove the column named Column1 because I don’t really need it.
I will now pane in and pane out in the Fields tab. To do that, click twice the pane in/out button which is highlighted in the upper right corner of the image below.
As you can see, the Key Measures is now a Measure Group as signified by the calculator icon beside its name. It’s now also located at the top of the Fields tab.
I recommend you to start adding this good practice into your development workflow.
Eventually, you’ll start branching out into more complex measures. So organizing them right from the start will help you have an easier time referencing them for future use.
Aggregations In Power BI
In the measures that I’ve already made, I only used iterating functions.
In the Total Sales measure, I used the SUMX iterating function.
While in the Total Quantity measure, I used the SUM function.
Now, since I’ve already shown you some examples of iterating functions, I will start introducing some aggregations in Power BI that are useful as well.
I’m doing this because no matter what calculation you are doing, I want you to be doing it with a DAX measure.
The beginning of anything advanced in Power BI, especially from an analytical perspective, starts with something simple.
It starts with just getting the hang of DAX measures and becoming familiar with how to write them as quickly as possible.
Here, I’m going to show you some simple aggregations in Power BI.
As you can see, the table is sliced by the Short Month and Salesperson Name filters because of what I did in the previous blog.
Even though these filters are here, I can still use this table to show you some examples of how to use aggregating functions.
Don’t get too caught up in minding the filters as long as there’s some calculation happening in the background.
I will also be using these filters later on to show you how the aggregations in Power BI work with them.
To start, go to the Measure tools tab, then click New measure.
The thing with creating measures is that they appear on whatever table you select under the Fields tab. So first, make sure that you clicked the Key Measures table before making a new measure.
Now that I’ve created a new measure, change “Measure” to “Average Quantity” to properly name it.
I’ll start with a calculation that requires a simple aggregating function, the AVERAGE function.
The AVERAGE function returns the arithmetic mean of all the numbers in a column.
I’m going to take the average of the values in the Quantity column from the Sales table.
The formula setup is shown below.
I will sum up all of the values in the Quantity column, and then average them out after.
After that, grab the Average Quantity measure under the Key Measures table in the Fields tab, and then drag it to the visual.
As you can see, the values in the Total Quantity column and the Average Quantity column are all the same except for the Total value.
This is because for every product, they only purchased it in one transaction, but have bought several.
For example, Henry Cox bought 3 quantities of Product 56 in one transaction.
Now, I’ll make another measure just to show you more examples of aggregating functions.
So again, go to the Measure tools tab, and then click New measure.
Another aggregation that you can use in Power BI is the MIN function which returns the smallest numeric or text value in a column.
Another one is the MAX function which returns the maximum numeric or text value in a column.
These are examples of aggregating functions which you can easily understand and use in situations where they fit.
But what I really want to do is to calculate the Total Transactions. To do this, I’m going to use a function called COUNTROWS.
First, rename the measure by changing “Measure” to “Total Transactions.”
Then add the COUNTROWS Function. This function takes a table and then returns the number of rows in that table.
Since I want to calculate the Total Transactions, I’m going to count up how many rows there are in my Sales table.
To do that, inside the COUNTROWS function, reference the Sales table. This is how I’ve set up the formula.
The function will go through the Sales table and then count the number of rows there.
Since every row in the Sales table represents a single transaction, counting every single row is just like counting every single transaction.
Now, grab the Total Transaction measure under the Key Measures table, and then drag it to the visual.
After doing that, you’ll see that there’s only one transaction every single time.
This is the result of having the filters that we have.
This just means that for May, Henry Cox, for example, bought 3 quantities of Product 56 in one transaction from Ernest Wheeler.
I’ll now change things up. First, I’ll remove the Product Name column by clicking the X button, as shown below.
And then I’ll also deselect all the filters.
To do that, I’ll click the box next to Ernest Wheeler’s name.
And also click the box next to May.
You’ll see that the numbers have changed quite a bit.
Let’s take a look at Martin Berry. The Total Sales that I got from him is $87,727, the Total Quantity of the products that he bought is 51, and on Average, he buys 1.89 of my products at each of his
27 Total Transactions with me.
As you can see, after we changed the filters of our calculations, the results changed as well.
This is where the scalability of DAX measures comes in. If you think about it, the formulas that we used are very simple.
We only used the SUMX, SUM, RELATED, AVERAGE, and COUNTROW functions for our measures. These are functions that I hope you get easily used to.
By using these simple functions, we can easily get various calculations just by altering the context.
This is the real power of DAX measures. Without adding other formulas, you can get a lot of insights just by changing your filters.
This is only made possible by the model that you’ve built. So make sure that you have the right model.
The last thing I want to show you is that you can format the results in your table if you need to.
Since I know that the Total Sales should be in Dollars, I will change it to its proper format.
To do that, click on the Total Sales measure, go to the Measure tools tab, and in the Formatting section, change Whole number to Currency by clicking the $ icon.
There are a lot of ways that you can format your results if you need to.
After doing that, the results should now look like this:
***** Related Links*****
Introduction To Filter Context In Power BI
Unpivot And Pivot Basics In Power BI – Query Editor Review
Showcase QoQ Sales Using Time Intelligence In Power BI
In this blog, I went over some examples of aggregating functions that you can use in your DAX calculations.
I showed you the AVERAGE, MIN, MAX, and COUNTROWS functions, which are definitely easy to understand.
I hope this helps you get a grasp of what you can achieve when using DAX measures in Power BI.
All the best,
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A hands-on guide to implementing data analysis projects using DAX, focused on the MAXX function and its combinations with other essential DAX functions.
Learn how to leverage the COUNTX function in DAX for in-depth data analysis. This guide provides step-by-step instructions and practical examples.
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MAXX in Power BI – A Detailed Guide
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Using the FILTER Function in DAX – A Detailed Guide With Examples
DATESINPERIOD Function in DAX – A Detailed Guide | {"url":"https://blog.enterprisedna.co/simple-aggregations-in-power-bi/","timestamp":"2024-11-12T19:02:50Z","content_type":"text/html","content_length":"512923","record_id":"<urn:uuid:baacf914-a7b9-4242-acb0-6b949defc1d5>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00484.warc.gz"} |
Reasoning Ability Quiz For ESIC- UDC, Steno, MTS Prelims 2022- 28th January
Directions (1-5): Study the information carefully and answer the questions given below.
Seven persons are going on attend dance class on seven different days of the week in such a way week starts from Monday. Each of them likes different dance forms i.e. Kathak, Salsa, Folk,
Bharatanatyam, Kathakali, Kuchipudi and Hip-hop but not necessary in the same order.
P likes kathakali and attends class on Wednesday. One person attends class between P and J. The one who likes salsa dance attend class on Friday. Two persons attend class between the one who likes
salsa and the one who likes Kathak. More than three persons attend class between J and F. G attends class on Sunday. The one who likes Kuchipudi dance attends class before the one who likes Folk
dance and after the one who likes hip-hop dance. J does not like hip-hop dance. M attend the class before E. L likes Hip-hop dance.
Q1. Who among the following likes salsa dance?
(a) P
(b) M
(c) E
(d) L
(e) None of these
Q2. Who among the following person like Kuchipudi dance?
(a) E
(b) F
(c) L
(d) G
(e) None of these
Q3. How many persons attend class between the one who likes folk dance and P?
(a) Three
(b) Two
(c) Four
(d) One
(e) None
Q4. Which of the following combination is true?
(a) M- Hip-hop
(b) L-Salsa
(c) E-Kuchipudi
(d) G-Bharatanatyam
(e) None is true
Q5. How many persons attend the class before the one who likes Bharatanatyam?
(a) No One
(b) Two
(c) Three
(d) One
(e) Four
Q6. If in the number 67459138, 3 is subtracted to first five digit of the number and 1 is added to rest of the digits then how many digits are repeating in the number thus formed?
(a) Four
(b) One
(c) None
(d) three
(e) Two
Q7. Which of the following elements should come in a place of ‘?’
GJ11 MO16 RT21 ?
(a) WX26
(b) VX25
(c) WY26
(d) VY26
(e) None of these
Q8. How many pairs of letters are there in the word “ENDURANCE” each of which have as many letters between them in the word as they have between them in the English alphabetical series?
(a) Two
(b) One
(c) Three
(d) More than three
(e) None
Q9. Ravi is 22nd from the left end of a row and Hunny is 32th from the right end of row. If they interchanged their positions then ravi ranks become 21 from left end. How many persons sit between
(a) One
(b) Two
(c) None
(d) Three
(e) None of these
Q10. Among J, K, L, M and N, each of them is different weight. L’s weight is more than K. M’s weight is more than J and less than N. K is not the lightest person. M is not lighter than L. Who among
them is the third heaviest?
(a) J
(b) L
(c) K
(d) M
(e) N
Directions (11-15): Following questions are based on the five three-digit numbers given below.
Q11. If all the digits in each of the numbers are arranged in increasing order within the number then, which of the following number will become the lowest in the new arrangement of numbers?
(a) 947
(b) 863
(c) 739
(d) 694
(e) 376
Q12. If all the numbers are arranged in ascending order from left to right then, which of the following will be the sum of all the three digits of the number which is 2nd from the right in the new
(a) 18
(b) 19
(c) 15
(d) 16
(e) None of these
Q13. What will be the difference, when third digit of the 3rd lowest number is multiplied with the second digit of the highest number and third digit of the 2nd highest number is multiplied with the
second digit of the lowest number?
(a) 21
(b) 20
(c) 15
(e) None of these
Q14. If the positions of the second and the third digits of each of the numbers are interchanged then, how many even numbers will be formed?
(a) None
(b) One
(c) Two
(d) Three
(e) Four
Q15. If one is added to the second digit of each of the numbers and one is subtracted to the third digit of each number then, how many numbers thus formed will be divisible by three in new
(a) None
(b) One
(c) Two
(d) Three
(e) Four
Click Here to Register for Bank Exams 2022 Preparation Material | {"url":"https://www.bankersadda.com/reasoning-ability-quiz-for-esic-udc-steno-mts-prelims-2022-28th-january/","timestamp":"2024-11-12T22:22:43Z","content_type":"text/html","content_length":"606693","record_id":"<urn:uuid:362a46dc-0549-48b0-a83e-bf05a46ece5f>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00894.warc.gz"} |
What is a divergent infinite series? | Socratic
What is a divergent infinite series?
1 Answer
The sum $S$ of a series ${\sum}_{k = 1}^{\infty} {a}_{k}$ is defined as
$S = {\lim}_{n \to \infty} {S}_{n}$,
where ${S}_{n}$ is the nth partial sum defined as
${S}_{n} = {a}_{1} + {a}_{2} + {a}_{3} + \cdots + {a}_{n} = {\sum}_{k = 1}^{n} {a}_{k}$.
So, a series is called divergent when the limit (the sum)
$S = {\lim}_{n \to \infty} {S}_{n}$
does not exist (including infinite limits).
Impact of this question
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Knight's tour problem
The knight in chess is a piece which can move in an L shape. It is said to be the secret ingredient which has made chess such a popular game for so long! Allegedly, the asymmetry introduced to the
board by this weird movement shape and unique property of jumping over other pieces is what makes chess such a beautiful game (all other pieces can only move straight or diagonally).
It is also the only piece that makes sense in an otherwise bizarre game. I suppose a bishop could do damage on the battlefield by being extremely judgemental, but moving a castle multiple times is
impractical to say the least - good luck getting planning permission with no objections at the local council meeting multiple times. Who came up with this insane army setup?
The Queen is dangerous and can move in all directions, but even she can’t jump over other pieces or take a non-linear path like a knight.
The original knight’s tour puzzle involves the Knight being placed in the top corner of the board, and goes around the board on a ‘tour’. This involves the knight jumping around on the board, and not
revisiting the same square twice.
According to the Knight’s tour Wikipedia page, the puzzle has been around for a while (back to the 9th century!) with some OG mathematicians like Euler having a go at it. There are a few variations
on it (different board sizes, etc) but the original 8 x 8 board has exactly 26,534,728,821,064 directed closed tours (closed meaning the Knight’s final position means for its next move it can return
to the same square it started so can start the tour all over again if visiting each square once wasn’t thrilling enough for it). If you count the open tours (finishing in any old spot) the number of
solutions goes up to 19,591,828,170,979,904. As you can see, it is a large number and also explains why my laptop nearly melted trying to solve it prior to using optimising heuristics.
There are a few ways to solve the original puzzle. The one I looked at used a heuristic named Warnsdorff’s rule, which optimises the brute force style recursion algorithm down to linear time by
defaulting to taking the move where the knight has the fewest possible options for the subsequent move. Programatically you can represent the board as a graph and sort the nodes based on the number
of possible next moves. This causes the path to default to going along the edges of the board, working inwards, which supposedly saves your computer the pain of going through the dead variations
where it gets stuck and can’t find a way to visit an edge square (note in the gif above showing a complete tour the pattern ends up like a thorny crown). Another way to get it down to linear time is
using a divide and conquer algorithm to cut up the board and patch up the sections after completing tours on the smaller pieces.
As explained on Wikipedia: A graphical representation of Warnsdorff's Rule. Each square contains an integer giving the number of moves that the knight could make from that square. In this case, the
rule tells us to move to the square with the smallest integer in it, namely 2.
Here is a solution from the website Geeksforgeeks in C++ that does it blazingly fast in linear time: | {"url":"https://www.gabrielslog.com/","timestamp":"2024-11-06T23:16:26Z","content_type":"text/html","content_length":"130266","record_id":"<urn:uuid:d9d44ffc-3580-4566-90e6-5e2163941b38>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00452.warc.gz"} |
MTA 07015
Journal Home Page
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Minimax Theory and its Applications 07 (2022), No. 2, 339--364
Copyright Heldermann Verlag 2022
Nonlinear Curl-Curl Problems in R^3
Jaroslaw Mederski
Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
Jacopo Schino
Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
We survey recent results concerning ground states and bound states $u\colon\mathbb{R}^3\to\mathbb{R}^3$ to the curl-curl problem $$ \nabla\times(\nabla\times u)+V(x)u= f(x,u) \qquad\hbox{ in } \
mathbb{R}^3, $$ which originates from the nonlinear Maxwell equations. The energy functional associated with this problem is strongly indefinite due to the infinite dimensional kernel of $\nabla\
times(\nabla\times \cdot)$. The growth of the nonlinearity $f$ is superlinear and subcritical at infinity or purely critical and we demonstrate a variational approach to the problem involving the
generalized Nehari manifold. We also present some refinements of known results.
Keywords: Time-harmonic Maxwell equations, ground state, variational methods, strongly indefinite functional, curl-curl problem, Orlicz spaces, N-functions.
MSC: 35Q60; 35J20, 78A25.
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How undefined signed overflow enables optimizations in GCC
Signed integers are not allowed to overflow in C and C++, and this helps compilers generate better code. I was interested in how GCC is taking advantage of this, and here are my findings.^1
Signed integer expression simplification
The nice property of overflow being undefined is that signed integer operations works as in normal mathematics — you can cancel out values so that (x*10)/5 simplifies to x*2, or (x+1)<(y+3)
simplifies to x<(y+2). Increasing a value always makes it larger, so x<(x+1) is always true.
GCC iterates over the IR (the compiler's Internal Representation of the program), and does the following transformations (
, and
are signed integers,
, and
are positive constants, and
is a comparison operator. I have only listed the transformations for positive constants, but GCC handles negative constants too in the obvious way)
• Eliminate multiplication in comparison with 0
(x * c) cmp 0 -> x cmp 0
• Eliminate division after multiplication
(x * c1) / c2 -> x * (c1 / c2) if c1 is divisible by c2
• Eliminate negation
(-x) / (-y) -> x / y
• Simplify comparisons that are always true or false
x + c < x -> false
x + c <= x -> false
x + c > x -> true
x + c >= x -> true
• Eliminate negation in comparisons
(-x) cmp (-y) -> y cmp x
• Reduce magnitude of constants
x + c > y -> x + (c - 1) >= y
x + c <= y -> x + (c - 1) < y
• Eliminate constants in comparisons
(x + c1) cmp c2 -> x cmp (c2 - c1)
(x + c1) cmp (y + c2) -> x cmp (y + (c2 - c1)) if c1 <= c2
The second transformation is only valid if c1 <= c2, as it would otherwise introduce an overflow when y has the value INT_MIN.
Pointer arithmetic and type promotion
If an operation does not overflow, then we will get the same result if we do the operation in a wider type. This is often useful when doing things like array indexing on 64-bit architectures — the
index calculations are typically done using 32-bit int, but the pointers are 64-bit, and the compiler may generate more efficient code when signed overflow is undefined by promoting the 32-bit
integers to 64-bit operations instead of generating type extensions.
One other aspect of this is that undefined overflow ensures that a[i] and a[i+1] are adjacent. This improves analysis of memory accesses for vectorization etc.
Value range calculations
The compiler keeps track of the variables' range of possible values at each point in the program, i.e. for code such as
int x = foo();
if (x > 0) {
int y = x + 5;
int z = y / 4;
it determines that x has the range [1, INT_MAX] after the if-statement, and can thus determine that y has the range [6, INT_MAX] as overflow is not allowed. And the next line can be optimized to
int z = y >> 2;
as the compiler knows that
is non-negative.
The undefined overflow helps optimizations that need to compare two values (as the wrapping case would give possible values of the form
[INT_MIN, (INT_MIN+4)]
[6, INT_MAX]
that prevents all useful comparisons with
), such as
• Changing comparisons x<y to true or false if the ranges for x and y does not overlap
• Changing min(x,y) or max(x,y) to x or y if the ranges do not overlap
• Changing abs(x) to x or -x if the range does not cross 0
• Changing x/c to x>>log2(c) if x>0 and the constant c is a power of 2
• Changing x%c to x&(c-1) if x>0 and the constant c is a power of 2
Loop analysis and optimization
The canonical example of why undefined signed overflow helps loop optimizations is that loops like
for (int i = 0; i <= m; i++)
are guaranteed to terminate for undefined overflow. This helps architectures that have specific loop instructions, as they do in general not handle infinite loops.
But undefined signed overflow helps many more loop optimizations. All analysis such as determining number of iteration, transforming induction variables, and keeping track of memory accesses are
using everything in the previous sections in order to do its work. In particular, the set of loops that can be vectorized are severely reduced when signed overflow is allowed.
1. Using GCC trunk r233186, "gcc version 6.0.0 20160205 (experimental)"
This blog post was updated 2016-02-23:
• Corrected first sentence to say "overflow"instead of "wrap".
• Removed one incorrect transformation from "Eliminate Negation" where I had misread the GCC source code.
• Corrected the ranges in the "Value range calculations" example.
17 comments:
1. Nice writeup.
These optimizations also mean UNsigned integers should only be used when really needed. E.g. when you need the overflow wrap around.
2. In "Value range calculations" shouldn't it be
(0, INT_MAX]
instead of
[0, INT_MAX]
because the if-statement checks to make sure x > 0, not x >= 0?
Great write-up!
3. Thanks! I have updated the ranges in the blog post.
4. I'm afraid that as regards the C++ language you've fallen victim to some purely associative propaganda, I'm sorry: very few of the opportunities you list, are examples where the UB contributes to
optimization of actual C++ code.
[Snipped concrete discussion of first 7 cases, because that exceeded the 4096 character limit on postings. Conclusion: only 6 and 7 are real. Silly limit! Gag the critics!]
Okay there are more cases, and loops are especially interesting. They offer some valid good optimizations, and some that are more in the class of perverse compiler behavior (which you can just
take as my personal opinion, or investigate, sorry I don't have more time here). But in conclusion, the optimization possibilities offered by signed arithmetic UB, are somewhat hyped up: there
are some such possibilities, even some good ones, but many alleged ones are not really optimizations at all.
Still there are good reasons for preferentially using signed integers for numbers, and those good reasons include both clarity (less complexity, more concise code), and less opportunities for
e.g. promotion bugs to creep in.
5. Hi Alf,
signed overflow is undefined behavior in C++ too, and GCC does all of the described transformations for both C and C++.
We may argue about the benefit of these transformations, but I think that is a topic for a separate blog post... :-)
6. Oh. You misunderstood. I mentioned the language because a comment argument for optimization of sillycodes like `x*Constant > x` (in one of your examples) is that such code can be generated by
macros. Those are at best a C-specific arguments; there is no reason a sane C++ programmer would do this, or indeed, need to have it optimized.
Cheers & hth.,
- Alf
7. @Krister, nice article!
@Alf, I think you are underestimating the amount of C++ code written by non-humans. Many code generators produce idioms like this. Convoluted template shenanigans can also lead to such
expressions appearing in a translation unit.
@Koen, yes and no. Unsigned types are much easier to reason about in many situations. It is true that there are cases like the one Krister identified where an optimisation is only enabled when
operating on signed types. However, there are so many cases of undefined behaviour relating to signed but not unsigned types that it can be a minefield for the insufficiently cautious programmer.
E.g. `1 << 31`, `INT_MIN / -1`, ...
8. @Koen: I second what Matthew is saying. The standard says that signed overflow leads to undefined behavior. This is because the IBM 360 and successors trapped on signed integer overflow.
Since undefined behavior can be anything, programmers must avoid creating such code.
Thus, modern instances of GCC and other compilers assume that programmers are infallible and have ensured that their code does not cause overflow, hence giving the compilers license to perform
these optimizations.
If however, the code was written with the assumption that signed overflow is treated exactly like unsigned arithmetic, as was the case for previous instances of these compilers on most machines,
these optimization can cause the code to fail.
Although I can understand compiler writers' interest in implementing these optimizations, one hast to wonder if a programmer that creates code with such obvious optimization opportunities has
really thought through his code, e.g., in regards to integer overflow.
And honestly, I think programmers would be better served by having code generated that traps on overflow, at least for debug builds.
9. @Konz In some cases of undefined behavior gcc and clang may use __builtin_trap which let's say on x86 may generate a ud2 instruction which will trap. They both currently do this when
dereferencing a null pointer see this godbolt example: https://goo.gl/VoV7zH
The compiler may not always be able to prove undefined behavior, on a stackoverflow question I answered a while ago: http://stackoverflow.com/q/32506643/1708801
A simple cout of the variable was sufficient to confuse the compiler and prevent a warning of undefined behavior. Although the optimizer still managed to turn a finite loop into an infinite one
in this case.
10. This is wrong for the case y = -1:
(-x) / (-y) -> x / y
since with y = -1 the optimized code would crash when x = INT_MAX (the CPU traps).
11. Is it common to see loop like
for (int i = 0; i <= m; i++)
"Most"[1] loops that I've seen are written as
for (int i = 0; i < m; i++)
in which case you don't need UB-on-signed-overflow (you can prove no-overflow directly, even if spec is to wrap).
[1]: In quotes since I have no way at the moment to quantify this
12. When the when (m is unsigned) or (m is larger bit size than int), and m is greater than INT_MAX, then the loop will never terminate. (IOW the loop is not countable).
13. There are a few cases where signed overflow is the desired behavior, although they aren't too common:
- Generating -1 when input is negative without a branch:
(int32_t)val >> 31; // equivalent to val < 0 ? -1 : 0;
Fast random number generator in -128 to 127 range:
int32_t randMem;
randMem *= 1103515245;
randMem += 12345;
randOut = randMem >> 24;
What's the proper way to get GCC to generate the proper code in this kind of case? Cast to uint32_t to force limited range, then apply wrapping arithmetic shift right? Or is there an intrinsic as
in the case of stuff like 32bit * 32bit -> 64bit multiply on 32bit architectures?
1. There are no relevant intrinsics, but the compiler is in general smart enough to handle many interesting cases. For example, your generation of -1 if \(\verb!val!\) is negative can be done as
\(\verb!(val < 0) ? -1 : 0!\) — GCC generates a shift for this!
Or you can make your operations safe by casting to larger types/unsigned etc. For example, if you have
\(\verb!int32_t a, b, c;!\)
then you can implement a wrapping addition as
\(\verb!c = (int32_t)((int64_t)a + (int64_t)b);!\)
GCC generates a 32-bit wrapping addition for this.
Or you can use the \(\verb!-fwrapv!\) command-line option, that treats wrapping integers as being defined (but which of course disables the optimizations described in the blog post)
2. > c = (int32_t)((int64_t)a + (int64_t)b);
This still causes an overflow and therefore is an UB. The correct way is to cast to unsigned first and then memcpy the result into a signed int. Obviously, code like this is rather painful to
14. How many genuinely-useful optimizations are enabled by treating signed overflow as UB, rather than saying that it will yield a value that behaves as any mathematical integer--not necessarily
within the range of the type--whose value is congruent to the correct value mod 2³² (or 2⁶⁴, etc. based on type). Such a guarantee would so far as I can tell very seldom interfere in any way with
any of the optimizations you listed, but would allow programmers to write shorter and more efficient code in cases where the above behavior would satisfy application requirements, than would be
possible without such a guarantee.
1. I'd say this is true for essentially all of the optimizations mentioned in the blog post — e.g. it uses the fact that wrapping is UB to be allowed to simplify e.g. \(\verb!x+1 < x!\) to \(\
verb!1 < 0!\) by subtracting \(\verb!x!\) from both sides, but the rule could be expressed as if the operation was done in a wider type.
The only optimization that cannot be expressed in this way is the loop-related optimizations (that calculates iteration count based on that the values do not wrap. And that \(\verb!a[i]!\)
and \(\verb!a[i+1]!\) are adjacent, which is important for vectorization). | {"url":"https://kristerw.blogspot.com/2016/02/how-undefined-signed-overflow-enables.html","timestamp":"2024-11-11T11:15:01Z","content_type":"application/xhtml+xml","content_length":"103483","record_id":"<urn:uuid:653ab900-9d2e-4c0c-b71a-c390ec0eaaf9>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00271.warc.gz"} |
Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits
We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of
these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a
constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution
produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a
soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential
shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large
value of the differential shift parameter converts the triplet into a pure singlet.
Dive into the research topics of 'Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits'. Together they form a unique fingerprint. | {"url":"https://researchportalplus.anu.edu.au/en/publications/breather-solutions-of-a-fourth-order-nonlinear-schr%C3%B6dinger-equati","timestamp":"2024-11-13T21:05:29Z","content_type":"text/html","content_length":"55426","record_id":"<urn:uuid:289187eb-b168-4510-82e0-9f8bb992813e>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00245.warc.gz"} |
The following bodies are made to roll up (without slipping) the same i
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The Stacks project
Lemma 5.28.7. Let $X$ be a topological space. Suppose $X = T_1 \cup \ldots \cup T_ n$ is written as a union of constructible subsets. There exists a finite stratification $X = \coprod X_ i$ with each
$X_ i$ constructible such that each $T_ k$ is a union of strata.
Comments (3)
Comment #6474 by Owen on
It appears that each $X_i$ is moreover locally constant constructible in the statement of the lemma. In the proof, $S$ seems to be doing notational double duty as a set of closed subsets of $X$
and as indices for such. Perhaps introduce a separate finite index set $\Lambda$ so that $S$ is the set of $Z_\lambda$ with $\lambda\in\Lambda$, so that in the end the stratification $X=\coprod_
{\lambda\in\Lambda}X_\lambda$ will be indexed by $\Lambda$, with $X_\lambda=Z_\lambda\setminus\bigcup_{\lambda'<\lambda}Z_{\lambda'}$.
Comment #6475 by Owen on
*locally closed constructible
Comment #6550 by Johan on
OK, I have fixed up the notation. See changes. The parts of a partition or the strata of a stratification are locally closed by Definitions 5.28.1 and 5.28.3.
There are also:
• 2 comment(s) on Section 5.28: Partitions and stratifications
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Contributions to Books:
M. Feischl, M. Karkulik, J. Melenk, D. Praetorius:
"Quasi-optimal convergence rate for an adaptive boundary element method";
in: "ASC Report 28/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.
English abstract:
For the simple layer potential V
that is associated with the 3D Laplacian, we consider the weakly
singular integral equation V\phi=f.
This equation is discretized by the lowest order Galerkin boundary
element method.
We prove convergence of an h-adaptive algorithm that is driven by a
weighted residual error estimator. Moreover, we identify the
approximation class for which the adaptive algorithm converges
quasi-optimally with respect to the number of elements. In particular,
we prove that adaptive mesh refinement is superior to uniform mesh
Electronic version of the publication:
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Timo Berthold
The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to
generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The … Read more
Conflict-Free Learning for Mixed Integer Programming
Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP
relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, … Read more
MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library
We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of 5,721 instances, the new MIPLIB 2017 collection consists of
1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, these sets were compiled using … Read more
Structure-driven fix-and-propagate heuristics for mixed integer programming
Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In
this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously … Read more
A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial
branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and … Read more
Local Rapid Learning for Integer Programs
Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP
solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn … Read more
Four good reasons to use an Interior Point solver within a MIP solver
“Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex.” This is the common conception which disregards that an interior
point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of … Read more
Parallel Solvers for Mixed Integer Linear Optimization
In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving
MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development … Read more
Experiments with Conflict Analysis in Mixed Integer Programming
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to
generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The … Read more
Three ideas for a Feasibility Pump for nonconvex MINLP
We describe an implementation of the Feasibility Pump heuristic for nonconvex MINLPs. Our implementation takes advantage of three novel techniques, which we discuss here: a hierarchy of procedures
for obtaining an integer solution, a generalized definition of the distance function that takes into account the nonlinear character of the problem, and the insertion of linearization … Read more | {"url":"https://optimization-online.org/author/timoberthold/page/2/","timestamp":"2024-11-13T16:15:29Z","content_type":"text/html","content_length":"105884","record_id":"<urn:uuid:382c7d5f-99a5-4b0d-aebe-535334eb43bc>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00111.warc.gz"} |
The Elusive Search for Balance - Complementary Mathematics
The Elusive Search for Balance
The Elusive Search for Balance
By Matt Larson, NCTM President
February 20, 2017
In a recent President’s blog post on the need to make homework comprehensible, I referred to the Fordham Institute Report, Common Core Math in the K–8 Classroom: Results from a National Survey. The
report offers another interesting finding: “The math wars aren’t over.”
The authors of the report observe, “The Common Core math standards seek to bring a peaceful end to the ‘math wars’ of recent years by requiring equal attention to conceptual understanding, procedural
fluency, and application (applying math to real-world problems). Yet striking that balance has not been easy. We see in these results several examples of teachers over- or underemphasizing one
component to the detriment of another” (p. 6).
I found this statement particularly striking. This over- or underemphasis may be less a function of independent teacher actions in the classroom than a result of teachers doing their best to
interpret and implement what they find in their curricular materials, which, as the Fordham report indicates, are aligned (or not) with the Common Core State Standards to varying degrees. The over-
or underemphasis of a particular component may also reflect teachers’ trying hard to comply with mandates at the district or school level.
It is critical to appreciate that the over- or underemphasis phenomenon is not a new one. Mathematics teachers in the United States today are just the latest generation of U.S. educators to be caught
in a 200 plus–year pendulum swing between an overemphasis of rote practice of isolated skills and procedures and an overemphasis of conceptual understanding, with their respective overreliance on
either teacher-directed or student-centered instruction.
It all began in 1788 (the same year that the U.S. Constitution was ratified), when Nicolas Pike published the first major U.S. mathematics textbook, entitled Arithmetic. The process that Pike
recommended for teachers was to state a rule, provide an example, and then have students complete a series of practice exercises very similar to the example. If that teaching process sounds familiar,
it is probably because that was the way you experienced math instruction as a student yourself. This process became the U.S. script for teaching mathematics and is deeply embedded in our
culture—expected by the vast majority of students and parents alike.
In the 1820s the pendulum swung for the first time when Warren Colburn published a series of texts, including Colburn’s First Lessons: Intellectual Arithmetic, Upon the Inductive Method (1826).
Colburn recommended that teachers use a series of carefully sequenced questions and concrete materials so that students could discover mathematical rules for themselves. By the 1830s the pendulum was
swinging back with the publication of the Southern and Western Calculator (1831) and The Common School Arithmetic (1832), which once again emphasized direct instruction of rules and procedures,
taught the “good old fashioned way.”
The late 1950s and 1960s were the era of “New Math.” Proponents of new math worked to make the pendulum swing from rote learning to discovery teaching approaches that emphasized developing students’
understanding of the structure of mathematics, how mathematical ideas fit together, and the reasoning (or habits of mind) of mathematicians. The 1970s and 1980s saw the pendulum swing in the opposite
direction yet again as these two decades became known as the “back to the basics” era, with a focus again on procedural skills and direct instruction.
In 1989 NCTM gave birth to the standards-based education reform effort with the release of Curriculum and Evaluation Standards for School Mathematics, and subsequently NCTM followed up this
transformative publication with a series of other standards publications, culminating in Principles and Standards for School Mathematics (2000). By the mid-1990s over 40 states had created state math
standards or curriculum frameworks consistent with the NCTM standards. But by the late 1990s the pendulum began to swing back to the basics when the “math wars” erupted in California and then spread
across the country as parents and others demanded a renewed emphasis on procedural skills and direct instruction.
And that brings us to the latest perceived pendulum swing: the Common Core State Standards and the associated myriad of misinformation and misinterpretations surrounding them, as well as the historic
and seemingly inevitable pushback that now benefits from and is fueled by social media. So what should a mathematics teacher caught up in these historic and continual pendulum swings do? My advice:
Seek balance.
In many ways it seems as though we live in a world that is out of balance—pushed to extremes—that has “lost the middle” in various ways. To move mathematics teaching and learning forward, we have to
resist the urge to be pushed to extremes. We have to do our part to break the historic cycle of pendulum swings. As Hung-Hsi Wu, professor emeritus of mathematics at the University of
California–Berkeley, wrote nearly two decades ago, “Let us teach our children mathematics the honest way by teaching both skills and understanding.” This is essentially what the Common Core authors
argue when they state, “[M]athematical understanding and procedural skill are equally important” (National Governors Association and Council of Chief State School Officers 2010, p. 4).
Over a decade ago the National Research Council (NCR) published Adding It Up (2001), which promoted a multifaceted and interwoven definition of mathematical literacy:
Procedural fluency and conceptual understanding are often seen as competing for attention in school mathematics. But pitting skill against understanding creates a false dichotomy … Understanding
makes learning skills easier, less susceptible to common errors, and less prone to forgetting. By the same token, a certain level of skill is required to learn many mathematical concepts with
understanding, and using procedures can help strengthen and develop that understanding. (p. 122).
We need to return to, promote, and implement in our classrooms the NRC definition of mathematical literacy. The goal of mathematics education is not complicated. We want students to know how to solve
problems (procedures), know why procedures work (conceptual understanding), and know when to use mathematics (problem solving and application) while building a positive mathematics identity and sense
of agency. How? Why? And when? These questions are the very essence of rigor in the Common Core. We can ask ourselves simple reflective questions at the end of each lesson and over the course of a
1. Are my students learning how to solve a problem (or problems)?
2. Are my students developing an understanding of why certain solution strategies work?
3. Are my students learning when and where they might apply particular solution strategies?
4. Did the experiences in my class help my students see themselves as capable doers and users of mathematics?
If the answer to all four questions is yes, that is more than likely a good sign. If we stay focused on all four learning goals, and resist (or dodge) the pendulum swings in any one direction while
steadily building students’ positive mathematics identity, perhaps the constant criticism that moves the pendulum will stop. When we stay the course and let students engage, learn, and develop their
understanding, skills, and abilities to use mathematics, our students will be the beneficiaries of our efforts to find and maintain that balance.
For more information, see Balancing the Equation: A Guide to School Mathematics for Educators and Parents. | {"url":"https://complementarymathematics.com/the-elusive-search-for-balance/","timestamp":"2024-11-03T22:28:22Z","content_type":"text/html","content_length":"111519","record_id":"<urn:uuid:93e1deda-dcb1-45ff-8e96-6c48f7524e58>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00266.warc.gz"} |
Computational Technology Resources - CCP - Paper
Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 301
Vibration of an Axisymmetric Laminated Cylinder
P.P. Prochazka
, A.E. Yiakoumi
and S. Peskova
^1Society of Science, Research and Advisory, Czech Association of Civil Engineers, Prague, Czech Republic
^2Department of Structural Mechanics, Czech Technical University Prague, Czech Republic
P.P. Prochazka, A.E. Yiakoumi, S. Peskova, "Vibration of an Axisymmetric Laminated Cylinder", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on
Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 301, 2008. doi:10.4203/ccp.88.301
Keywords: laminated hollow cylinder, vibration, eigenfrequencies, general plane strain, finite element approximation.
In various structures cylinders of circular shape are exposed to impact loading. Such structures involve the linings of tunnels of different kinds, aircrafts structures, submersibles, etc. The
problem is solved as pseudo three-dimensional, i.e. generalized plane strain is considered. This assumption is in very good compliance with natural behaviour of the above mentioned structures and
moreover, it enables us to describe mathematically several phenomena such as dissipation layers inside the cylinders, optimal distribution of reinforcement, and so on. In the radial direction a
linear finite element like approach is introduced. This approach is introduced so that the layers are considered thin enough and because the explicit solution leads us to the Bessel functions and the
work with them is not easy and transparent. Eigenfrequencies are calculated using the standard approach for generalized plane strain and the finite element approximation.
This paper is concerned with a pilot study of vibration of cylindrical laminated cylinders or arches. Hamilton's principle is the starting point for the formulation of axisymmetric problem.
Introducing a very important simplification: generalized plane strain, and deriving a weak formulation (involving the above mentioned simplification) in cylindrical coordinates, boundary conditions
are obtained and the finite element method is employed in radial direction. In former papers of the first author it was shown that the pseudo 3D formulation utilizing the idea of the generalized
plane strain condition is usable and delivers results which are in reasonable agreement with the 3D formulation. Assuming generalized plane strain, the only problem occurs in creating relations
connected with the axial direction, as considering thick layers the stresses are not in compliance with requirements on their regularity. This is overcome by engaging definition of average stress,
which is calculated in cylindrical coordinates. Then a sum of these averages is required to be in equilibrium with the pressure (stress) employed at the face of the cylinder.
Simple examples are studied in the end of this paper. The eigenfrequencies are aggregated with mass density and the arisen coefficient lambda linearly depends on the length of the cylinder. The other
eigenfrequencies does not depend on the length, only on the thickness and radius of the structure. If the ratio L/b<1, the coefficient lambda increases exponentially.
The approach in this paper develops ideas presented in [1,2]. Similar problems to that solved in this paper can be found in other papers, such as [3].
P. Prochazka, "Optimal eigenstress fields in layered structures", Journal of Computational and Applied Mathematics, 63(1-3), 475-480, 1995. doi:10.1016/0377-0427(95)00093-3
G.J. Dvorak, P. Prochazka, "Thick-walled composite cylinders with optimal fiber prestress", Composites Part B: Engineering Volume 27(6), 643-649, 1996. doi:10.1016/S1359-8368(96)00001-7
G.A. Kardomateas, "Koiter-based solution for the initial post buckling behavior of moderately thick orthotropic and shear deformable cylindrical shells under external pressure", J. Appl. Mech.
64, 885-896, 1996. doi:10.1115/1.2788996
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Show Posts - inquisitive
« on: January 01, 2023, 11:02:33 PM »
The WGS83 model gives all the details you need. Also the angles of dishes for broadcast satellites.
WGS83 takes data from small flat maps: https://wiki.tfes.org/World_Geodetic_System_1984
I haven't seen a study of triangulation of satellites to prove that we live on a globe. This is an assumption that such studies exist.
Your position is flawed. Unless they did something like walking around with a digital measuring wheel and physically measured the earth with a tactile method, there were assumptions in
measuring long distances.
Actually, they generally used chains back in the day.
surveyor’s chain, also called Gunter’s chain, measuring device and arbitrary measurement unit still widely used for surveying in English-speaking countries. Invented by the English
mathematician Edmund Gunter in the early 17th century, Gunter’s chain is exactly 22 yards (about 20 m) long and divided into 100 links. In the device, each link is a solid bar.
Measurement of the public land systems of the United States and Canada is based on Gunter’s chain. An area of 10 square chains is equal to one acre.
This is equivalent to saying that surveyors had rulers. Maybe they did have rulers. But it doesn't prove that they measured long distances with them.
If they used a digital measuring wheel then that would also mean making an assumption - that the wheel is calibrated correctly and accurate.
Your objection to “assumptions” is very selective. The Bishop Experiment makes assumptions, Rowbotham made assumptions. You have no issues with that. Only when an experiment or technique
yields results you don’t like do you switch to the skeptical context and start objecting to “assumptions”.
You have previously agreed that GPS can accurately give your longitude and latitude. How can it do that without distances being known? Leaving aside how that would work in the middle of an
ocean, as it demonstrably does, which rules out any land based solution
There are ways to test whether a digital measuring wheel is calibrated and accurate. This would be more of an experiment where the conditions can be controlled.
Other methods are not as controlled, and assume a lot about astronomy or the weather.
Latitude and Longitude are references ultimately based on astronomical phenomena. The Latitude is based on the angle of the North Star in the sky (for the NH) and Longitude is related to clocks
and time zones. You might know your Lat/Lon coordinate point, but this would do nothing to show the distance between those points. This is how GPS, and formally the land-based LORAN, operate. The
station knows its own coordinates and it is giving you your own coordinates based on triangulation.
Much of professional GPS and GIS work, by the way, assumes that the earth is flat.
From https://www.e-education.psu.edu/geog862/book/export/html/1644
“ Welcome to Lesson Six of this GPS course. And this time, we'll be talking about two coordinate systems. And I have a little bit of discussion concerning heights. We've touched on that a
little bit. Now these coordinate systems that we're going to discuss are plane coordinate systems based upon the fiction that the earth is flat, which, of course, immediately introduces
distortion. However, much of GIS work—and GPS work as well—is done based upon this presumption. ”
The fact that the calculations to align a satellite dish actually work and are based on a round earth should satisfy you. The locations of geostationary satellites are well documentated. Dishes near
the equator point up around 90⁰. Those north and south at a lower angle. | {"url":"https://forum.tfes.org/index.php?PHPSESSID=q6lirc5hdi73dvm5jr9v9sguv2&action=profile;area=showposts;u=5489","timestamp":"2024-11-14T06:45:51Z","content_type":"application/xhtml+xml","content_length":"71361","record_id":"<urn:uuid:23916e9b-2a6d-4f98-863e-6b3411f9ed1f>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00689.warc.gz"} |
The Stacks project
Remark 87.9.8. The classical affine formal algebraic spaces correspond to the affine formal schemes considered in EGA ([EGA]). To explain this we assume our base scheme is $\mathop{\mathrm{Spec}}(\
mathbf{Z})$. Let $\mathfrak X = \text{Spf}(A)$ be an affine formal scheme. Let $h_\mathfrak X$ be its functor of points as in Lemma 87.2.1. Then $h_\mathfrak X = \mathop{\mathrm{colim}}\nolimits h_{\
mathop{\mathrm{Spec}}(A/I)}$ where the colimit is over the collection of ideals of definition of the admissible topological ring $A$. This follows from (87.2.0.1) when evaluating on affine schemes
and it suffices to check on affine schemes as both sides are fppf sheaves, see Lemma 87.2.2. Thus $h_\mathfrak X$ is an affine formal algebraic space. In fact, it is a classical affine formal
algebraic space by Definition 87.9.7. Thus Lemma 87.2.1 tells us the category of affine formal schemes is equivalent to the category of classical affine formal algebraic spaces.
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limma interaction term
Last seen 7.8 years ago
United States
Hi everybody,
I have a model with 2 main factors and its interaction:
designmodel = model.matrix(~0 + Factor1 + Factor2 + Factor1:Factor2)
Factor 1 has two levels and factor 2 has 4 levels. My question is if when I test the interaction term I can add all 8 groups as follow:
contrastInteraction = makeContrasts(((Factor1.Level1Factor2 - Factor1.Level2Factor2 - Factor1.Level3Factor2 - Factor1.Level4Factor2 ) - (Factor2.Level1Factor2 - Factor2.Level2Factor2
- Factor2.Level3Factor2 - Factor2.Level4Factor2)), levels=design)
Or shoud I test the interaction in 4 separate contrasts (one for each level of factor 2)? Thanks for you advice!
You don't provide a lot of details - what's your experimental design? What does Factor1 or Factor2 contain? - so it's hard to tell what the coefficient names mean, let alone whether you're doing
something sensible with your contrasts. | {"url":"https://support.bioconductor.org/p/84267/","timestamp":"2024-11-05T19:04:10Z","content_type":"text/html","content_length":"19156","record_id":"<urn:uuid:fd21893d-5617-4bc8-8ec7-4197f89769c6>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00606.warc.gz"} |
Introduction & Course Overview
Welcome to the After the Analysis: Communicating results from Excel in PowerPoint course. I am glad you have invested in learning how to quickly and effectively take data from Excel and present it in
Here is an outline of the modules and lessons in this course.
Module 1: Options for using Excel in PowerPoint
In this document I outline the three options for using Excel data in a PowerPoint presentation and when you would want to select each approach.
Module 2: Hyperlinking to Excel
This module covers the first approach for using Excel data in PowerPoint. Once you have decided that hyperlinking to the Excel workbook in your presentation is the best approach, you will go through
three steps, each is shown in its own video in this module.
Step 1: Create the hyperlink
You can attach a hyperlink to any object on a PowerPoint slide. The video for this step shows the best ways to create hyperlinks that don’t stand out to the audience. Hidden hyperlinks allow you to
activate them if needed, but don’t advertise to the audience that there is the option to go to the spreadsheet, thereby reducing the temptation of some audience members to ask for the details in
order to bring up unrelated issues.
Lesson 2-1: Video: Creating hyperlinks
Step 2: Using the hyperlink during the presentation
The video for this step demonstrates the two methods for activating a hyperlink on a PowerPoint slide. Use whichever method is more comfortable for you.
Lesson 2-2: Video: Activating a hyperlink during a presentation
Step 3: Return to the presentation from Excel
If you do use the hyperlink, full Excel runs on top of your PowerPoint presentation. The video for this step shows two methods for exiting Excel and shows how these methods do not lose any changes
you may have made to the Excel workbook.
Lesson 2-3: Video: Returning to the presentation after using a hyperlink to Excel
Module 3: Preparing Excel data to be inserted into PowerPoint
Depending on what method you use to insert your Excel content into PowerPoint, you may or may not have the option to make formatting changes once the Excel content is in PowerPoint. The video on
formatting cells in this module shows you which of the common cell formatting options you should consider. It includes the Excel conditional formatting feature and when it will or will not copy to
PowerPoint. The video on formatting graphs goes through the steps to remove distracting elements from the default graphs and how to add elements that will make the graph easier to understand.
Following these steps makes inserting much easier and reduces re-work later.
Lesson 3-1: Video: formatting Excel cells
Lesson 3-2: Video: Cleaning up Excel graphs
Module 4: Inserting Excel data with no link to the source file
One of the biggest decisions you will need to make when inserting Excel data into PowerPoint is whether you want the data in the presentation to change when the data in the source Excel file changes.
If you don’t need that link, this approach will be the one you use. The module includes comparisons of the different techniques for cells and for graphs so you can decide which one will work best for
your situation. The videos show you four techniques for inserting tables of data and three techniques for inserting graphs. Each video shows only one technique, so it is easy to learn just what you
need without having to scroll through a long video.
Lesson 4-1: Comparison of techniques for inserting tables
Lesson 4-2: Video: Default paste of cells
Lesson 4-3: Video: Formatted text paste of cells
Lesson 4-4: Video: Metafile picture paste of cells
Lesson 4-5: Video: Pasting cells as a worksheet object
Lesson 4-6: Comparison of techniques for inserting graphs
Lesson 4-7: Video: Metafile picture paste of a graph
Lesson 4-8: Video: Paste a graph with embed of data
Lesson 4-9: Video: Creating a PowerPoint graph with copied Excel data
Module 5: Linking inserted data to the source Excel file
You will learn how to have the inserted data update when the data in the source Excel file changes in this module that covers the third approach for using Excel data in PowerPoint. The videos show
one technique for tables of data and four techniques for graphs. The module includes a comparison of the different techniques for graphs so you can decide which one will work best for your situation.
Lesson 5-1: Video: Linking cells as a worksheet object
Lesson 5-2: Comparison of techniques for inserting graphs
Lesson 5-3: Video: Inserting a graph as an object
Lesson 5-4: Video: Default paste of a graph
Lesson 5-5: Video: Paste link a graph as a chart object
Lesson 5-6: Video: Creating a PowerPoint graph with linked Excel data
Module 6: Keeping your Excel data protected
Depending on which method you use for including Excel data in PowerPoint, confidential data in the Excel file could be released in the PowerPoint file. The videos in this module show how to break
links to data that is linked to source Excel files and how to detect if Excel data has been embedded in the PowerPoint file.
Lesson 6-1: Video: Breaking links to source files
Lesson 6-2: Video: Finding if Excel data is embedded in a PowerPoint file
Note before watching the video lessons
The video lessons are like sitting beside me at my computer because you see my screen, hear me narrate what I am doing, and see the exact steps for that method. I demonstrate the steps in PowerPoint
2013/2016, but the steps work pretty much exactly the same in PowerPoint 2007 and later. You can pause the video at any time and try the techniques on your own slides in PowerPoint. Click on the Full
Screen icon in the lower right corner of the video to make it larger.
Complete and Continue | {"url":"https://thinkoutsidetheslide.teachable.com/courses/after-the-analysis/lectures/493428","timestamp":"2024-11-02T14:39:55Z","content_type":"text/html","content_length":"117825","record_id":"<urn:uuid:041ec6ad-89a4-4703-b668-7e1f92a468e6>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00791.warc.gz"} |
The Mystery of How Big Animal Brains Should Grow May Finally Be Solved
Nature15 July 2024
The idea that animals' brain mass and body mass are correlated makes intuitive sense: larger animals, after all, tend to have larger brains than their smaller cousins.
However, it's proven difficult to find a definitive model for exactly how these two figures relate to one another.
A new study published in Nature Ecology and Evolution this month suggests that this problem arises from a fundamental error in a long-held assumption about the mathematical relationship between the
two masses.
The study proposes an alternative model, one that both fits the data better and promises explanations for several other long-standing questions about cerebral evolution.
As the study explains, the general assumption for decades has been that the relationship between the body's and the brain's masses follows a relatively simple power law. However, this proposed
relationship is hotly debated as it doesn't seem to apply to all species groups.
As of yet, researchers haven't been able to find a configuration of this equation that works across the board. In particular, the variation between different taxonomic tiers has been vexing enough
that it's been given its own name: the taxon-level problem.
While both the value and the source of a critical piece of the relationship referred to as the allometric component have been the subject of plenty of debate, the new paper addresses a more
fundamental question: whether we're correct in assuming that the relationship between brain mass and body mass follows some sort of logarithmic linear relationship.
To do so, the authors took an extensive dataset comprising 1,504 mammalian brain/body mass values and looked at what sort of model best fit the data.
They found that instead of being log-linear, the relationship was log-curvilinear: when plotted on a logarithmic scale, the graph itself must curve to accommodate it.
The authors tested several different equations to construct this curve, and found that the one that fit best was a second-order polynomial – the sort of quadratic equation one tends to encounter in
high school.
The curve's key feature is that "as mammals increase in mass, the rate at which brain mass increases with body mass decreases". It thus predicts that very large animals have smaller brains than
predicted by the linear model – which is exactly what the dataset shows.
Having a single curve to which the brain/body relationship can be fitted allows for comparisons between groups that had markedly different allometric coefficients under the previous model.
The study demonstrates one advantage of the new model: "[it] makes it possible to study evolutionary trends in trait (or relative trait) evolution through time." To this effect, it examines the rate
at which brain mass increases – or, in other words, the speed at which larger brains evolve. It finds significant differences between species.
Unsurprisingly, primates evolved large brains exceptionally quickly, but so too did rodents and carnivores. Only three groups of animals showed a relationship of increasing brain to body mass through
The study concentrates on mammals, but the authors also examined a dataset of body/brain mass pairs for birds, and found that the curvilinear relationship also fit that data well. But perhaps the
most intriguing mystery that remains to be solved is why brain and body mass are correlated in this manner.
That question remains very much an open one, and its answer may well have a great deal to say about how and why animals have evolved in the manner that they have.
As the study says in its conclusion, "seeking both the theoretical and empirical underpinning for curvilinear relationships across species will probably lead to major contributions across biology."
This research was published in Nature Ecology and Evolution. | {"url":"https://www.sciencealert.com/the-mystery-of-how-big-animal-brains-should-grow-may-finally-be-solved","timestamp":"2024-11-06T08:57:30Z","content_type":"text/html","content_length":"138537","record_id":"<urn:uuid:9cbaee9e-36bc-45ac-8a00-3f0b5d331a53>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00761.warc.gz"} |
Electronics Engineering Calculat
Electronics Engineering Calculators
formulas & calculators for electronics engineering can be used to perform or verify the results of electronics engineering calculations that involve resistance, impedance, current, voltage,
capacitor, frequency etc. The main objective of theis formula reference sheet & calculators is to assist students, professionals and researchers quickly perform or verify the electronics engineering
based calculations. | {"url":"https://dev.ncalculators.com/electronics/","timestamp":"2024-11-12T19:59:47Z","content_type":"text/html","content_length":"24152","record_id":"<urn:uuid:364dda70-811b-42b3-bd43-6e38d89d568a>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00504.warc.gz"} |
Performance Measure
So, as our target variable contains continuous values, we can say that it's a regression task.
Our next step is to select a performance measure for a regression task so we can check how well our machine learning model is performing.
We generally use RMSE (Root Mean Square Error) metric as a performance measure for regression tasks.
Its formula is as-
Predicted is the target value or label that our model predicts for a data point,
actual is the actual label for that data point and
N is the number of instances in the datasets.
So, by taking the difference between both, it calculates the error in prediction(as how much difference is there in predicted and actual value). As large is the difference between both, large will be
the error in our model.
So for example, in the above figure, suppose we want to predict output by our model for input as 2. So, as we can see the actual value(which lies as a blue data point), for x = 2 is 2. But our model
will predict it on the regression line and so the predicted value will come as 2.75. Hence there will be an error of (2.75-2), which is 0.75. This error is shown by the red dashed line. And this is
the objective of our training- to reduce this error as much as we can.
Loading comments... | {"url":"https://cloudxlab.com/assessment/displayslide/7434/performance-measure?playlist_id=1275","timestamp":"2024-11-04T02:31:04Z","content_type":"text/html","content_length":"121250","record_id":"<urn:uuid:ec09dd17-e3fe-49bf-9f59-d8ad3e7f297f>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00702.warc.gz"} |
The Stacks project
Lemma 42.3.2. Let $R$ be a Noetherian local ring. Let $x \in R$. If $M$ is a finite Cohen-Macaulay module over $R$ with $\dim (\text{Supp}(M)) = 1$ and $\dim (\text{Supp}(M/xM)) = 0$, then
\[ \text{length}_ R(M/xM) = \sum \nolimits _ i \text{length}_ R(R/(x, \mathfrak q_ i)) \text{length}_{R_{\mathfrak q_ i}}(M_{\mathfrak q_ i}). \]
where $\mathfrak q_1, \ldots , \mathfrak q_ t$ are the minimal primes of the support of $M$. If $I \subset R$ is an ideal such that $x$ is a nonzerodivisor on $R/I$ and $\dim (R/I) = 1$, then
\[ \text{length}_ R(R/(x, I)) = \sum \nolimits _ i \text{length}_ R(R/(x, \mathfrak q_ i)) \text{length}_{R_{\mathfrak q_ i}}((R/I)_{\mathfrak q_ i}) \]
where $\mathfrak q_1, \ldots , \mathfrak q_ n$ are the minimal primes over $I$.
Comments (2)
Comment #4980 by Kazuki Masugi on
Does this lemma hold in general $M$? (Is "Cohen-Macaulay module"-ness nessesary?)
Comment #5227 by Johan on
@#4980: No, I think the lemma is wrong as soon as $M$ has depth $0$ (but everything else kept the same).
There are also:
• 2 comment(s) on Section 42.3: Calculation of some multiplicities
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Maintained virological reaction throughout people with HCV helped by
Airport gates will be the primary locations for aircraft to receive surface services. With all the increased quantity of routes, limited gate resources near to the terminal make the gate project work
more complex. Conventional option methods centered on mathematical programming models and iterative formulas are usually made use of to fix these static circumstances, lacking learning and real-time
decision-making capabilities. In this paper, a two-stage crossbreed algorithm based on replica discovering and hereditary algorithm (IL-GA) is recommended to resolve the gate project problem. To
begin with, the thing is defined from a mathematical model to a Markov decision procedure (MDP), with the goal of making the most of the number of flights assigned to make contact with gates in
addition to complete gate choices. In the 1st stage of the algorithm, a deep policy system is established to get the gate selection possibility of each trip. This plan community is trained by
imitating and discovering the project trajectory data of individual probiotic supplementation professionals, and this procedure is offline. In the 2nd stage for the algorithm, the insurance policy
network is employed to create a beneficial initial populace for the hereditary algorithm to calculate the optimal answer for an online example. The experimental results show that the genetic
algorithm combined with imitation understanding can significantly reduce the iterations and improve population convergence speed. The flight price assigned to the contact gates is 14.9% higher than
the handbook allocation result and 4% more than the standard hereditary algorithm. Learning the expert assignment information also makes the allocation scheme much more consistent with the
inclination associated with the airport, which is frozen mitral bioprosthesis great for the practical application of the algorithm.In a wavefunction-only philosophy, thermodynamics must certanly be
recast with regards to an ensemble of wavefunctions. In this perspective we study how exactly to build Gibbs ensembles for magnetic quantum spin models. We reveal by using no-cost boundary problems
and distinguishable “spins” there are no finite-temperature stage transitions as a result of large dimensionality of this phase room. Then we concentrate on the most basic situation, specifically the
mean-field (Curie-Weiss) model, to discover whether phase changes are also possible in this model course. This strategy at the least diminishes the dimensionality associated with issue. We unearthed
that, also assuming trade symmetry in the wavefunctions, no finite-temperature stage transitions appear as soon as the Hamiltonian is given by the most common energy phrase of quantum mechanics (in
this situation the analytical argument isn’t completely satisfactory therefore we relied partially on some type of computer evaluation). Nonetheless, a variant design with extra “wavefunction power”
does have a phase transition to a magnetized condition. (With respect to dynamics, which we don’t give consideration to right here, wavefunction energy causes a non-linearity which nonetheless
preserves norm and energy. This non-linearity becomes significant only at the macroscopic amount.) The 3 outcomes collectively claim that magnetization in big wavefunction spin chains seems if and
just if we start thinking about indistinguishable particles and block macroscopic dispersion (in other words., macroscopic superpositions) by energy conservation. Our principle technique requires
changing the problem to one in probability principle, then applying outcomes from big deviations, especially the Gärtner-Ellis Theorem. Finally, we discuss Gibbs vs. Boltzmann/Einstein entropy into
the choice of the quantum thermodynamic ensemble, as well as open problems.Reversible data hiding (RDH), a promising data-hiding technique, is widely analyzed in domain names such as medical image
transmission, satellite picture transmission, crime research, cloud processing, etc. Nothing of the existing RDH systems addresses a solution from a real-time aspect. An excellent compromise
involving the information embedding rate and computational time makes the scheme suitable for real-time programs. As a remedy, we propose a novel RDH plan that recovers the first picture by keeping
its quality and removing the concealed data. Here, the address picture gets encrypted making use of a stream cipher and it is partitioned into non-overlapping blocks. Key information is inserted into
the encrypted blocks associated with cover image via a controlled local pixel-swapping strategy to achieve a comparatively great payload. This new plan MPSA allows the data hider to hide two bits in
every encrypted block. The present reversible data-hiding schemes modify the encrypted picture pixels causing a compromise in image safety. Nevertheless, the proposed work balances the support of
encrypted image safety by maintaining similar entropy of the encrypted picture regardless of hiding the data. Experimental outcomes Etanercept chemical structure illustrate the competency regarding
the suggested work accounting for assorted parameters, including embedding rate and computational time.This report shows that some commodity currencies (from Chile, Iceland, Norway, South Africa,
Australia, Canada, and New Zealand) predict the synchronisation of metals and energy commodities. | {"url":"https://drugdiscoveryscreenings.com/index.php/maintained-virological-reaction-throughout-people-with-hcv-helped-by/","timestamp":"2024-11-06T23:31:35Z","content_type":"text/html","content_length":"17026","record_id":"<urn:uuid:4ec56bd0-5663-46fc-89f4-07fce50da339>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00311.warc.gz"} |
Function Visualizer Model
Detail Page
Function Visualizer Model
written by Wolfgang Christian and Francisco Esquembre
The Function Visualizer Model displays the graph of a function f(x) with arbitrary parameters. The function can contain polynomial, trigonometric, and exponential expressions as well a
parameters. Parameters are connected to sliders that can be adjusted to observe the effect of varying parameter values.
This item was created with Easy Java Simulations (EJS), a modeling tool that allows users without formal programming experience to generate computer models and simulations. To run the
simulation, simply click the Java Archive file below. To modify or customize the model, See Related Materials for detailed instructions on installing and running the EJS Modeling and
Authoring Tool.
Please note that this resource requires at least version 1.5 of Java (JRE).
Subjects Levels Resource Types
Education Practices
- Active Learning
= Modeling - High School
- Instructional Material
- Technology - Lower Undergraduate
= Simulation
= Multimedia - Middle School
Mathematical Tools
- Algebra
Appropriate Courses Categories Ratings
- Algebra-based Physics - Activity
- AP Physics - New teachers
Intended Users:
Access Rights:
Free access
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Wolfgang Christian
create a graph, function, interactive, plot, plotter, simulation
Record Creator:
Metadata instance created June 27, 2009 by Wolfgang Christian
Record Updated:
June 6, 2014 by Andreu Glasmann
Last Update
when Cataloged:
June 27, 2009
Other Collections:
AAAS Benchmark Alignments (2008 Version)
9. The Mathematical World
9B. Symbolic Relationships
• 9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.
• 9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed.
Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.
11. Common Themes
11B. Models
• 9-12: 11B/H2. Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive. Therefore,
computers can reveal the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and simulated testing of Supplements
devices and structures and in the simulation of complicated processes.
AAAS Benchmark Alignments (1993 Version)
9. THE MATHEMATICAL WORLD Materials
B. Symbolic Relationships Similar
• 9B (9-12) #6. The reasonableness of the result of a computation can be estimated from what the inputs and operations are.
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Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 1 Fractions Intext Questions
You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.
Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 1 Fractions Intext Questions
(Try These Textbook Page No. 2)
Question 1.
If all the three cakes are divided among the total participants of the function what would be each one’s share? Discuss.
Total participants of the function = 9
Total number of cakes = 3
∴ Each cake should be divided into 3 equal parts.
∴ Total number of equal parts of cake = 9
∴ Each one’s share may be \(\frac{1}{9}\) of total cakes or \(\frac{1}{3}\) of a cake.
Question 2.
Observe the following and represent the shaded parts as fraction.
(i) Total number of equal parts = 8
Shaded Parts = 3
Fraction representing the shaded parts = \(\frac{3}{8}\)
(ii) Total number of equal parts = 15
Shaded parts = 5
∴ Fraction representing the shaded parts = \(\frac{5}{15}\)
(iii) Total number of equal parts = 9
Shaded parts = 3
∴ Fraction representing the shaded parts = \(\frac{3}{9}\)
(iv) Total number of equal parts = 9
Shaded parts = 5
Fraction representing the shaded parts = \(\frac{5}{9}\)
Question 3.
Look at the following beakers, express the quantity of water as fraction and arrange them in ascending order:
Quantity of water in the first beaker = 1 full
Quantity of water in the second beaker = \(\frac{1}{4}\)
Quantity of water in the third beaker = \(\frac{3}{4}\)
Quantity of water in the fourth beaker = \(\frac{1}{2}\)
Ascending order \(\frac{1}{4}\) < \(\frac{1}{2}\) < \(\frac{3}{4}\) < 1
Question 4.
Write the fraction of shaded part in the following.
(i) Total number of equal parts = 3
Shaded parts = 2
Fraction representing the shaded portion = \(\frac{2}{3}\)
(ii) Total number of equal parts = 4
Shaded parts = 3
Fraction representing the shaded parts = \(\frac{3}{4}\)
(iii) Total number of equal parts = 5
Shaded parts = 4
Fraction representing the shaded parts = \(\frac{4}{5}\)
Question 5.
Write the fraction that represents the dots In the triangle.
Total number of dots = 24
Number of dots in the triangle = 6
∴ Fraction represents the dots in the triangle = \(\frac{6}{24}\)
Question 6.
Find the fractions of the shaded and unshaded portions in the following.
(a) Total number of equal parts = 8
Shaded parts = 2
∴ Fraction representing shaded parts = \(\frac{2}{8}\)
(b) Total number of equal parts = 8
Unshaded parts = 6
∴ Fraction of unshaded portion = \(\frac{6}{8}\)
(Activity Textbook Page No. 3)
Take a rectangular paper. Fold it into two equal parts. Shade one part, write the fraction. Again fold it into two halves. Write the fraction for the shaded part. Continue this process 5 times and
write the fraction of the shaded part. Establish the equivalent fractions of \(\frac{1}{2}\) in the folded paper to your friends.
First time = \(\frac{1}{2}\)
Second time = \(\frac{2}{4}\)
Third time = \(\frac{4}{8}\)
Fourth time = \(\frac{8}{16}\)
Fifth time = \(\frac{16}{32}\)
(Try These Textbook Page No. 4)
Question 1.
Find the unknown in the following equivalent fractions.
(Try These Textbook Page No. 7)
Question 1.
Shade the rectangle for the given pair of fractions and say which is greater among them.
Question 2.
Which is greater \(\frac{3}{8}\) or \(\frac{3}{5}\) ?
LCM of the denominators 8 and 5 is 40.
Finding the equivalent fractions.
Question 3.
Arrange the fractions in ascending order : \(\frac{3}{5}, \frac{9}{10}, \frac{11}{15}\)
Question 4.
Arrange the fractions in descending order : \(\frac{9}{20}, \frac{3}{4}, \frac{7}{12}\)
(Try These Textbook Page No. 9)
(i) \(\frac{2}{3}+\frac{5}{7}\)
By cross multiplication technique
(ii) \(\frac{3}{5}-\frac{3}{8}\)
By cross multiplication technique
(Activity Textbook Page No. 10)
Question 1.
Using the given fractions \(\frac{1}{5}, \frac{1}{6}, \frac{1}{10}, \frac{1}{15}, \frac{2}{15}, \frac{4}{15}, \frac{1}{30}, \frac{7}{30} \text { and } \frac{9}{30}\) fill in the missing ones in the
given 3 × 3 square in such a way that the addition of fractions through rows, columns and diagonals give the same total \(\frac{1}{2}\)
(Try These Textbook Page No. 10)
Question 1.
Complete the following table. The first one is done for you.
(Try These Textbook Page No. 11)
Question 1.
(i) Are 5\(\frac{2}{3}\) and 5\(\frac{4}{6}\) equal?
(ii) \(\frac{3}{2} \neq 3 \frac{1}{2}\) why?
Question 2.
Convert 3\(\frac{1}{3}\) into improper fraction.
Question 3.
Convert \(\frac{45}{7}\) into mixed fraction.
(Try These Textbook Page No. 13)
Question 1.
Find the sum of 5\(\frac{4}{9}\) and 3\(\frac{1}{6}\).
Question 2.
Subtract 7\(\frac{1}{6}\) and 12\(\frac{3}{8}\)
Question 3.
Subtract the sum of 6\(\frac{1}{6}\) and 3\(\frac{1}{5}\) from the sum of 9\(\frac{2}{3}\) and 2\(\frac{1}{2}\).
(Try These Textbook Page No. 15)
Question 1.
2\(\frac{1}{4}\) × 3 is not equal to 6\(\frac{1}{4}\). Why?
Question 2.
Simplify : 35 × \(\frac{3}{7}\).
Question 3.
Find the value of \(\frac{1}{5}\) of 15.
\(\frac{1}{5}\) of 15 = \(\frac{1}{5}\) × 15 = \(\frac{15}{5}\) = 3
Question 4.
Find the value of \(\frac{1}{3}\) of \(\frac{3}{4}\)
Question 5.
Multiply 7\(\frac{3}{4}\) by 5\(\frac{1}{2}\).
(Activity Textbook Page No. 15)
Take a paper. Fold it into 4 parts vertically of equal width. Shade one part of it with red. Then, fold it into 3 parts horizontally of equal width. Shade two parts of it with blue. Now, you count
the number of shaded grids which have both the colours. (Hint: The total number of grids is the product of \(\frac{2}{3}\) and \(\frac{1}{4}\))
Activity to be done by the students themselves
(Try These Textbook Page No. 17)
Question 1.
(i) How many 6s are there in 18?
Number of 6s in 18 are \(\frac{18}{6}\) = 3
(ii) How many \(\frac{1}{4}\)s are there in 5?
Number of \(\frac{1}{4}\) s in 5 are 5 ÷ \(\frac{1}{4}\) = 5 × \(\frac{4}{1}\) = 20
(iii) \(\frac{1}{3}\) ÷ 5 = ?
\(\frac{1}{3}\) ÷ 5 = \(\frac{1}{3} \times \frac{1}{5}\) = \(\frac{1}{15}\)
(Try These Textbook Page No. 18)
Question (i)
Find the value of 5 ÷ 2\(\frac{1}{2}\).
Question (ii)
Simplify: \(1 \frac{1}{2} \div \frac{1}{2}\)
Question (iii)
Divide 8 \(\frac{1}{2}\) by 4\(\frac{1}{4}\).
Leave a Comment | {"url":"https://samacheerkalvi.guru/samacheer-kalvi-6th-maths-term-3-chapter-1-intext-questions/","timestamp":"2024-11-14T18:27:19Z","content_type":"text/html","content_length":"175671","record_id":"<urn:uuid:42e832b5-aede-4aaf-9ac4-8e48de72a65f>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00047.warc.gz"} |
The matrix $M$ of a linear complementarity problem can be viewed as a payoff matrix of a two-person zero-sum game. Lemkeā s algorithm can be successfully applied to reach a complementary solution or
infeasibility when the game satisfies the following conditions: (i) The value of $M$ is equal to zero. (ii) For all principal minors of $M^T$ (transpose of $M$) the value is non-negative. (iii) For
any optimal mixed strategy $y$ of the maximizer either $y_i>0$ or $(My)_i>0$ for each coordinate $i$. | {"url":"https://math.iisc.ac.in/seminars/2024/2024-02-20-tes-raghavan.html","timestamp":"2024-11-02T11:52:46Z","content_type":"text/html","content_length":"19017","record_id":"<urn:uuid:b42085f5-ba90-4eb8-b250-a10d4a410a39>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00567.warc.gz"} |
Common Multiple Calculator
Common Multiple Calculator
Common Multiple Calculator
Understanding the Common Multiple Calculator
The Common Multiple Calculator on our website is a tool created to help users find common multiples between two numbers. By entering two integers, you can get the lowest common multiple (LCM) and, if
needed, all common multiples within a specified range.
Real-World Applications
This calculator can be beneficial in numerous scenarios:
• Scheduling: If you’re trying to find out when two recurring events (e.g., meetings, classes) will coincide, the LCM can help you determine the next overlap.
• Packaging: If you need to combine items in groups without leftovers, common multiples can help you figure out the optimal grouping.
• Construction: For tasks requiring precise intervals, such as laying tiles or setting up chairs, knowing common multiples can ensure even placement.
How the Calculation Works
The calculator uses a straightforward mathematical approach. Firstly, it determines the greatest common divisor (GCD) of the two numbers, which is then used to find the LCM by dividing the product of
the numbers by the GCD.
Once the LCM is established, the tool can list down all multiples of this value that fall within a user-defined range. This ensures you have all the necessary multiples for your specific need.
Benefits and Features
This calculator stands out with its responsive design and intuitive layout, making it accessible on various devices. Tooltips are added to guide users through each input field for better clarity. The
option to specify a range helps to find all relevant common multiples, not just the LCM. Additionally, a reset button is included to clear the inputs and start fresh, ensuring user convenience.
The calculator also includes a unit system toggle, allowing users to switch between metric and imperial units as necessary. Lastly, a footer note acknowledges the source, providing a professional
With this tool, users can handle multiple calculations quickly and efficiently, making it a valuable addition to our extensive collection of calculators.
What is a common multiple?
A common multiple of two numbers is a number that is a multiple of both numbers. For instance, for the numbers 4 and 5, common multiples include 20, 40, 60, and so on.
How do you calculate the Lowest Common Multiple (LCM)?
To find the LCM of two numbers, first determine their greatest common divisor (GCD). Then divide the product of the two numbers by their GCD. This result is the LCM.
What is the Greatest Common Divisor (GCD)?
The GCD of two numbers is the largest number that can exactly divide both numbers. For example, the GCD of 8 and 12 is 4.
Can I find all common multiples within a range using this calculator?
Yes, you can specify a range and the calculator will list all the common multiples of the two numbers within that range.
Does the calculator support both metric and imperial units?
Yes, the calculator includes a unit system toggle that lets you switch between metric and imperial units according to your needs.
Why would I need to find common multiples?
Understanding common multiples is useful in various real-world scenarios such as scheduling recurring events, packaging items into groups without leftovers, and ensuring even intervals in
construction projects like tile placement.
Can I use this calculator on mobile devices?
Absolutely. The calculator features a responsive design that works well on different devices, including smartphones and tablets.
Is there a way to reset the input fields?
Yes, a reset button is included to clear all inputs so you can start fresh with new numbers.
Are there tooltips to help me use the calculator?
Yes, each input field has tooltips to provide guidance and clarity, making the calculator easy to use.
This FAQ provides technical details and answers to common questions users might have about the "Common Multiple Calculator," ensuring they can efficiently utilize the tool for their needs. | {"url":"https://www.onlycalculators.com/other/common-multiple-calculator/","timestamp":"2024-11-05T20:31:02Z","content_type":"text/html","content_length":"237189","record_id":"<urn:uuid:fb58d4a7-b483-42d7-9e76-52dc8f543896>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00045.warc.gz"} |
Betz Limit: Max Efficiency for Horizontal Axis Wind Turbines
In physics, the Betz limit is the maximum power that can be extracted from a wind turbine. This limit is based on the Betz equation, which states that no more than 59.3% of the kinetic energy in a
flow of wind can be converted into electrical energy.
The Betz limit is important because it helps us understand the maximum amount of power we can extract from a domestic wind generator. While there are ways to improve on this limit, it serves as a
good starting point for designing turbines that produce renewable energy.
(Original article and sketches by Dr. Les Bardbury / PelaFlow Consulting)
Can the Betz Limit be exceeded and does it apply to vertical axis wind turbines?
The simplest model of a wind turbine is the so-called actuator disc model where the turbine is replaced by a circular disc through which the airstream flows with a velocity Ut and across which there
is a pressure drop from P1 to P2 as shown in the sketch.
At the outset, it is important to stress that the actuator disc theory is useful (as will be shown) in discussing the overall efficiencies of turbines but it does not help at all with how to design
the turbine blades to achieve the desired performance.
The power developed by the wind turbine is:
where At is the turbine disc area. Volume flow continuity gives:
From momentum conservation, the force exerted on the turbine is equal to the momentum change between the flow far upstream of the disc to the flow far downstream of the disc. Thus:
The final basic equations are Bernoulli's equation applied upstream and downstream of the actuator disc:
where P∞ is the ambient pressure in the flow both far upstream and far downstream of the actuator disc.
From equations (4a),(4b), (3) and (2)
i.e. the velocity through the actuator disc is the mean of the upstream and downstream velocities in the stream tube.
Finally, from equations (1), (5), and (3), the efficiency is given by:
The figure below shows the variation of efficiency (often referred to as the power coefficient, cp) with the ratio of downstream to upstream velocity. By differentiating equation (7), it is easy to
show that the maximum turbine efficiency occurs when Ud/Uu=1/3 (i.e. when Ad/Au=3).
The efficiency is then η=16/27 ≈ 59%. This is the maximum achievable efficiency of a wind turbine and is known as the Betz limit - after Albert Betz who published this result in 1920. There are
assumptions in the above analysis such as the neglect of radial flow at the actuator disc but these have only a small effect on the final limiting result.
The point to note here is that as you reduce the downstream velocity in the expectation of increasing the power extracted from the wind, the area of the upstream stream tube that passes through the
turbine reduces in size.
In the limit, as the downstream velocity is reduced to zero, the area of the upstream stream tube that passes through the turbine is just half the turbine area and the efficiency is thus 50%.
Can the Betz limit be exceeded for horizontal axis wind turbines?
It is important to note that the equations leading up to the Betz limit represent an overall momentum balance argument and therefore the argument still applies to any horizontal axis 'device' that
replaces the actuator disc in the above derivation.
The only question is what is the effective diameter of the stream tube that is influenced by the device?
There have been numerous devices that claim to improve the efficiency of a wind turbine and the shrouded turbine shown on the right is rather typical of these designs.
In these 'shrouded' turbines, the general idea seems to be to use the shroud to create a low-pressure region downstream of the turbine and thus draw more air through the turbine.
Generally, with these designs, there is little in the way of experimental data to support the efficiency claims but an exception to this seems to be some experimental and theoretical work carried out
mainly at Kyushu University in Japan. The reference is given below. The figure on the right shows this design with a layout sketch.
In their report, the authors measure the turbine efficiency and, from a graph, they show a peak value of about 29% for the turbine on its own and a figure of about 110% with the shroud in place. In
both cases, the efficiency or power factor is based on the swept rotor area.
However, as can be seen from the sketch, the ratio of the shroud diameter to the rotor diameter is about 2.53 (i.e. 1013/400) and, if we base the efficiency of the shrouded turbine on the shroud
cross-sectional area, the peak efficiency falls to 17%.
In other words, a straightforward turbine with the diameter of the shroud would perform better in terms of efficiency than the shrouded turbine.
The point here is that the Betz derivation still applies, but the stream tube's diameter influenced by the shrouded turbine is closer to the shroud diameter than the turbine diameter.
This seems a fairly obvious conclusion and emphasizes the point that there is no way of getting around the overall momentum balance between far upstream and far downstream in the derivation of the
Betz limit.
Moreover, in the case of the shrouded turbine, the drag on the shroud contributes nothing to the turbine power.
• Abea K., Nishidab M., Sakuraia A. et al (2005) Experimental and numerical investigations of flow fields behind a small wind turbine with a flanged diffuser.
• Journal of Wind Engineering and Industrial Aerodynamics Volume 93, Issue 12, December 2005, Pages 951–970.
FloDesign-Ogin shrouded wind turbine
An example of a shrouded wind turbine that is being put forward as a practical design is one that was originally designed by a company called FloDesign based in Massachusetts.
A quite large demonstrator unit was put up in 2011 at Deer Island in Massachusetts as shown in the figure. It was a design rated at 100 kilowatts.
The astonishing thing about this design is that it seems to have attracted multi-million dollar investments and yet nowhere in the web pages or downloadable literature is there any apparent awareness
of the intrinsic limitations imposed by the arguments behind the Betz limit.
It is almost certainly the case that the design will be less efficient than a conventional design whose rotor diameter is the same as the shroud diameter.
It is difficult to see any advantages in designs like this and it is significant that no test results on the turbine have been published which meet the IEC 61400-12 standards.
Does the Betz limit apply to vertical axis wind turbines?
The short answer to this question is 'No' although it is not obvious how to produce an equivalent theorem for a VAWT. The arguments that are used to derive the Betz limit for a HAWT do not apply
directly to a vertical-axis wind turbine.
It is possible that an equivalent theorem can be produced by splitting the approaching stream tube into two parts; one passing through the advancing blades and the other passing through the
retreating blades.
The torque exerted on the VAWT will have to be matched by an equal and opposite angular momentum in the stream far downstream. It is much less obvious how to set up all the conservation relationships
for a VAWT than for a HAWT but it would make a good student or even a good post-graduate project.
From an experimental point of view, the efficiencies of VAWTs based on their frontal area seem always to be lower than a HAWT of equivalent frontal area and no VAWT has yet been tested to IEC61400-12
standards that have efficiencies in the upper range of large HAWTs - which can be in the region of 45%.
In spite of their lower efficiency, there are situations where a VAWT might be preferable to a HAWT (i.e. a gusty urban environment or some location with severe space constraints).
Although this is a fairly weighty article, and the maths may be too involved for some users. If you arrived at this site looking for sustainable alternatives to everyday products, please don't feel
put off, we don't normally do such a deep dive into physics!
Nevertheless, I felt it was important to preserve the work from the original Wind Power Program website, as it does provide one of the most comprehensive and detailed explanations of the Betz limit
and its application in calculating the efficiency of horizontal axis turbines. Despite the fact that the original article is now a few years old, these formulae do not go out of date and remain
useful and applicable today. | {"url":"https://theroundup.org/betz-limit/","timestamp":"2024-11-08T18:06:47Z","content_type":"text/html","content_length":"152695","record_id":"<urn:uuid:c27ca674-c72a-4cff-84e5-eb94f674ac36>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00143.warc.gz"} |
Algebra 2 Polynomial Long Division Worksheet | Long Division Worksheets
Algebra 2 Polynomial Long Division Worksheet
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Algebra 2 Polynomial Long Division Worksheet
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Name Prof. Dr. Manfred Einsiedler
Field Mathematics
Professur für Mathematik
ETH Zürich, HG G 64.2
Address Rämistrasse 101
8092 Zürich
Telephone +41 44 632 31 84
E-mail manfred.einsiedler@math.ethz.ch
URL http://www.math.ethz.ch/~einsiedl
Department Mathematics
Relationship Full Professor
Number Title ECTS Hours Lecturers
401-3378-19L Entropy in Dynamics 8 credits 4G M. Einsiedler
Abstract Definition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Ergodic theorem for entropy. Topological entropy and variational principle. Measures
of maximal entropy. Equidistribution of periodic points. Measure rigidity for commuting maps on the circle group.
The course will lead to a firm understanding of measure theoretic dynamical entropy and its applications within dynamics. We will start with the basic properties of (conditional)
Learning entropy, relate it to the question of effective coding techniques, discuss and prove the Shannon-McMillan-Breiman theorem that is also known as the ergodic theorem for entropy.
objective Moreover, we will discuss a topological counter part and relate this topological entropy to the measure theoretic entropy by the variational principle. We will use these methods to
classify certain natural homogeneous measures, prove equidistribution of periodic points on compact quotients of hyperbolic surfaces, and establish a measure rigidity theorem for
commuting maps on the circle group.
Lecture notes Entropy book under construction, available online under
Prerequisites No prior knowledge of dynamical systems will be assumed but measure theory will be assumed and very important. Doctoral students are welcome to attend the course for 2KP.
/ Notice
401-5370-00L Ergodic Theory and Dynamical Systems 0 credits 1K M. Akka Ginosar, M. Einsiedler, University lecturers
Abstract Research colloquium
401-5530-00L Geometry Seminar 0 credits 1K M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University
Abstract Research colloquium
Algebra I and II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional
406-2005-AAL admission requirement. 12 credits 26R M. Burger, M. Einsiedler
Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this
course unit.
Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.
The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
Basic notions and examples of groups;
Subgroups, Quotient groups and Homomorphisms,
Group actions and applications
Basic notions and examples of rings;
Ring Homomorphisms,
ideals, and quotient rings, rings of fractions
Content Euclidean domains, Principal ideal domains, Unique factorization
Basic notions and examples of fields;
Field extensions, Algebraic extensions, Classical straight edge and compass constructions
Fundamentals of Galois theory
Representation theory of finite groups and algebras
Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Literature Graduate Studies in Mathematics,Volume 165
American Mathematical Society | {"url":"https://www.vorlesungen.ethz.ch/Vorlesungsverzeichnis/dozent.view?lang=en&dozide=10029965&ansicht=2&semkez=2021S&","timestamp":"2024-11-08T05:22:42Z","content_type":"text/html","content_length":"13481","record_id":"<urn:uuid:c2f6e146-eeef-4ba0-b3e3-01643a0f4d59>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00288.warc.gz"} |
srm325 week 4 assignment Other Assignment Help -
srm325 week 4 assignment Other Assignment Help
srm325 week 4 assignment Other Assignment Help. srm325 week 4 assignment Other Assignment Help.
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The National Collegiate Athletic Association (NCAA) is the dominant and most influential entity in inter-collegiate athletics. In a four- to five-page paper (excluding the title page and reference
page), formatted according to appropriate APA style, complete a review and analysis of the National Collegiate Athletic Association. In a narrative format, based on Chapters 13, 14, and 15 out of the
course text and three scholarly sources, write an paper including:
Explanation of the NCAA organizational structure and governance.
Evaluation of the impact of the NCAA on the business of collegiate sports.
Analysis of the relationship between Federal Laws and the NCAA rules and standards of compliance.
srm325 week 4 assignment Other Assignment Help[supanova_question]
Algebra questions need help Mathematics Assignment Help
The sum of two numbers is 32
. One number is
times as large as the other. What are the numbers?
Larger number 24
smaller number 8
Algebra homework help needed Mathematics Assignment Help
Betsy, a recent retiree, requires 6,000 per year in extra income. She has 70,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate deposit (CD) paying 7% per year. How
much money should be invested in each to realize exactly 6,000 in interest per year?
The amount of money invested at 15%=
The amount of money invested at 7%=
Algebra homework help needed Mathematics Assignment Help
Betsy, a recent retiree, requires 6,000 per year in extra income. She has 70,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate deposit (CD) paying 7% per year. How
much money should be invested in each to realize exactly 6,000 in interest per year?
The amount of money invested at 15%=
The amount of money invested at 7%=
Spiral Other Assignment Help
Starting with the number 1 and moving to the right
in a clockwise direction a 5 by 5 spiral is formed as follows:
It can be verified
that the sum of the numbers on the diagonals is 101.
What is the sum of
the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
how to do it?? please give the answer fully
ASK QUESTION ABOUT “A Rose for Emily” Humanities Assignment Help
What foreshadowings of the discovery of the body
of Homer Barron are we given earlier in the story?
<span style='font-size:16.0pt;font-family:Calibri;
EN-US;mso-bidi-language:AR-SA’>Did the foreshadowings give away the story for
you? Did they heighten your interest
ASK QUESTION ABOUT “A Rose for Emily” Humanities Assignment Help[supanova_question]
quiz question help #2 Business Finance Assignment Help
A firm that is considering doing business abroad must have a rationale and logic for how it can compensate for and overcome the liabilities and disadvantages that arise from its;strategies
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quiz question help #4 Business Finance Assignment Help
———————- Mathematics Assignment Help
To obtain the sequence 1,
, …, what domain should be applied to the exponential function shown here?
https://anyessayhelp.com/ To obtain the sequence 1,
, …, what domain should be applied to the exponential function shown here?
https://anyessayhelp.com/ To obtain the sequence 1,
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What is Linear Regression
Linear Regression
What is Linear Regression?
Linear regression is a way to model the relationship between a response variable and one or more explanatory variables. In linear regression, the data is modeled by a linear function.
Examples of Linear Regression
Linear regressions can be used in business to evaluate trends and make estimates or forecasts. For example, if a company's sales have increased steadily every month for the past few years, by
conducting a linear analysis of the sales data with monthly sales, the company could forecast sales in the coming months. Consider the example below.
Product development
Advertising and revenue: Businesses use linear regression to better understand the relationships between advertising spending and revenue.
For example, they might fit a simple linear regression model using advertising spending as the predictor variable and revenue as the response variable. The regression model would take the following
form: revenue = β0 + β1(ad spending).
The coefficient β0 would represent the total expected revenue when ad spending is zero. The coefficient β1 would represent the average change in total revenue when ad spending is increased by one
unit, a dollar.
If β1 is negative, it would mean that more ad spending is associated with less revenue. If β1 is close to zero, it would mean that ad spending has little effect on revenue. And if β1 is positive, it
would mean more ad spending is associated with more revenue.
Why is Linear Regression Important?
Linear regression models are an important and proven way to reliably predict future outcomes. Because linear regression is a long-established statistical procedure, the properties of linear
regression models are well understood and can be trained very quickly.
Linear Regression FAQs
How do you calculate linear regression?
Consider the linear regression equation Y= a + bX, where Y is the dependent variable (that's the variable that goes on the Y-axis), X is the independent variable (i.e. it is plotted on the X-axis), b
is the slope of the line and a is the y-intercept.
What are some benefits of using linear regression?
• Ease of use. The model is simple to implement. It does not require a lot of engineering overhead, neither before launch nor during maintenance.
• Interpretability. Linear regression is straightforward to interpret.
• Scalability. The algorithm is not computationally heavy, which means that linear regression is perfect for use cases where scaling is expected.
• Performs well online. Due to the ease of computation, linear regression can be used in online settings, meaning that the model can be retrained with each new example and generate predictions in
near real-time.
What is the difference between simple linear regression and multiple linear regression?
The difference lies in the number of independent variables that they take as inputs. Simple linear regression takes a single feature, while multiple linear regression takes multiple x values.
H2O.ai and Linear Regression: H2O AI Cloud is a platform that helps data scientists apply linear regression models to their datasets much faster. The AI Cloud allows data scientists to get past the
technology layer that changes daily and get straight to making, operating, and innovating with AI. As a result, businesses can innovate faster using proven AI technology. H2O.ai enables teams of data
scientists, developers, machine-learning engineers, DevOps, IT professionals, and business users to work together with the same toolset toward a common goal.
Linear Regression vs Other Technologies & Methodologies
Linear Regression vs Logistic Regression
Linear Regression is used to manage regression problems and logistic regression is used to manage the classification problems.
Linear Regression vs Multiple Regression
Linear regression is used for simple calculations and multiple linear regression tends to be used for more specific calculations. When relationships are more straightforward, linear regression can
capture the relationship between the two variables. For complex relationships, multiple linear regression can be more useful.
Linear Regression vs Correlation
Regression is often used to build models/equations to predict a key response, Y, from a set of predictor (X) variables. Correlation is often used to quickly summarize the direction and strength of
the relationships between a set of 2 or more numeric variables.
Linear Regression vs ANOVA
Regression is often used on variables that are fixed or independent in nature. ANOVA is often used to find commonalities between variables of different groups unrelated to each other.
Linear Regression Resources | {"url":"https://h2o.ai/wiki/linear-regression/","timestamp":"2024-11-12T16:04:26Z","content_type":"text/html","content_length":"200012","record_id":"<urn:uuid:ebe014bf-23bb-4e0e-aa97-c054531c0f3c>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00619.warc.gz"} |
Project Update – Whole Home Generator
It’s been a busy time lately. Lots of personal matters that have had my attention, but I have started to continue to progress on building backup power for our home. Between Icestorm outages in
February, ERCOT changing people’s home air conditioner settings in the summer due to lack of available power, and with hurricane season ramping up, it seems a strong given that another power outage
is due before the end of the year.
The process for me began with a lot of research that I would reference later during the other steps as I learned more. The single most important requirement I had was choosing a generator. Since
whole home standby generators and installations are back ordered until after hurricane season is over, I had few choices to use other than a portable generator. To determine which one, I used
Generatorbible. It lists 502 portable generators by various criteria.
How to know which one was right for me? Well, I started with building out a spreadsheet based on my requirements. For me, the top criteria included THD (the lower the value, the cleaner the power),
Running Watts (to be able to power a 2.5 ton air conditioner unit), 50A output (to get the power from the generator to the breaker box), and an alternate fuel type from gasoline (which is difficult
to store and get prior to a hurricane). I went with propane, but would use the propane line to modify it for natural gas.
There are several good choices available that met my needs which is why they are highlighted in blue and green. In this case, the blue is the one I settled on. Using the Pulsar PG12000B meant that I
could use gasoline or propane. During my research, I discovered that you can even get propane tanks delivered to you for a reasonable cost with several different services. However, as I have lived
through many hurricanes during my life with some having power outages of 3 weeks, I looked at what that would cost from a propane perspective.
Generatorbible lists the propane consumption of the generators they list. For the Pulsar PG12000B, it lists the following:
Source: GeneratorBible.com
Ok, so now we know the amount of time we will have an estimated power duration (3 weeks) and the rate of propane consumption (0.94 gallons per hour). That means our propane needs will be for 24 hours
* 7 days * 3 weeks * 0.94 gallons of propane. That is 473.76 gallons or close to 500 gallons of propane. Here is our first challenge. That is a ton of propane, where are we going to put all these
propane tanks at? What about cost? There are services that can drop off 100 gallon propane tanks for about $250 a tank, but that would be $1,250 in propane. The solution is natural gas if available.
Natural gas is plentiful and cheap, but how do we get it to the generator? In my case, I have a natural gas line in my backyard which was put in during construction. I have never used it so I am
going to try to tie into that. But the question is, will it be enough to power a generator? Let’s do the math.
Measuring the pipe in the backyard and it appears that the gas outlet is 3/4″. However, the natural gas meter is at the front of the house and the label on it says that it delivers 250 cubic feet per
hour. Using a tape measure to go from the meter at the front of the house to the gas outlet at the back of the house appears to be roughly 67 feet. Now we can simply use the sizing guide for metallic
pipe which shows the following chart.
Source: Gas Pipeline Calculation Sizing
For 3/4″ metallic pipe at 67 feet rounded up to 70 feet shows a value of 126 cubic feet of gas per hour. This is roughly half of the 250 cubic feet of gas per hour the meter can provide. That sounds
good, but what does that mean for the generator? Will it be able to run at full load, half load, or no load?
That’s a bit trickier. We need to convert the natural gas power source which is a gas into BTU which is a thermal unit of power. The conversion rate is 1 CFH = 1,050 BTU. So for the meter at 250 CFH
(cubic feet per hour) that means it delivers about 262,500 BTU. Based on the same conversion that means our back of house natural gas tap probably provides close to 132,300 BTU.
Big reminder, it is important to not run a generator inside or close to a home. It kills hundreds of people every year. It may not seem like it, but carbon monoxide is odorless and can in fact go
through walls due to the size of the molecule. Gasoline generators are recommended to be 20 feet away from a home because of the amount of CO (carbon monoxide) particles that are given off. From what
I have read propane generators are around 10 feet and natural gas generators are no closer than 5 feet to a structure due to the fuel sources being mildly cleaner.
Given that, if we add in a 10 foot 3/4″ hose from the tap to the generator to give it some distance from the house that drops the BTU by about 10,000 to 122,850 BTU. That means this is probably what
we can expect to get as a maximum amount of fuel for our generator at any given point in time.
Okay, so we have the CFH and BTU, but how does that relate to the propane gallons per hour which is a liquid? Natural gas and propane are pretty close when it comes to fuel efficiency. Propane is
technically more fuel dense than natural gas, but the difference between the two is close to 10%. Some websites say that this number is a misnomer. For our experiments, we will ignore that for now
and continue with the math, but you can modify the number by 10% if desired.
Remember our propane consumption rate from earlier? A gallon of propane has 91,500 BTU of energy in it. So 0.94 GPH (gallons per hour) for propane is about 86,010 BTU. That means our backyard pipe
should be efficient enough to run at a half load. Since a full load on propane is about 8,550 rated watts then a half load using 86,010 BTU should be 4,275 running watts. Peak will be much higher
than that.
Next question, is that enough power to run a whole home air conditioner? What about a fridge?
Ok, let’s break it down. Here is the power utilization of a 2.5 ton Goodman GXS140301 air conditioner.
Source: Goodman Air Conditioners
This chart is really good. It even tells us the power consumption as the outside temperature changes. In the South, you can expect temperatures to get to 95 Fahrenheit pretty regularly during the
summertime. Based on that temperature, that tells us we should expect a power utilization of 2,420 watts. With our half load generator running at 4,275 watts, we should still have 1,855 watts left.
What about the refrigerator?
Source: Kenmore Refrigerator
The refrigerator uses 6.5A at 115V. Based on Ohm’s law that equates to 747.5 or about 750 watts.
Cool. So a whole home AC and fridge use 2,420 + 747.5 or about 3,167.5 watts. That seems great. What else?
Modems? Phones? Laptops? LED lights? All of those devices are pretty good on power. There are some webpages that can help list approximate values of power usage. DaftLogic is a site that has a
database of appliances as well as their wattage uses.
So what’s not great? Coffee pots, microwaves, vacuums, and clothes dryers. Thankfully, the coffee pot, microwave, and vacuum only use power for short increments of time which just means you can plan
for them and you might need to shuffle when some devices are on. Note, the refrigerator does not run all the time. Once it hits the temperature inside it turns off the compressor and no longer uses
power. Provided the AC is running, it will help keep the temperature cool longer.
Here is our worst case scenario and something difficult to plan for… the clothes dryer. Here is a relatively new Samsung.
Source: Samsung Dryer
Yes, that does say 5,300 watts. That means it will use as much power as all other devices combined and still need more power. It also means the generator will be running beyond half load which means
things get tricky again with calculating power. In our original estimates we were using 86,010 BTU of an estimated 122,850 BTU. In theory, that means that there is additional fuel for the generator
to scale up to a higher output of about 30% more. Wattage wise, 30% of 4,725 is 1,417.5 so our theoretical maximum power output is 6,142.5 watts.
So yes, we could be able to run it, but that means at the sacrifice of the air conditioner, refrigerator, and some other devices. What about putting the clothes outside? Well, while some people live
in a dry climate where you can put them outside to dry in the sun, but for coastal cities in the South, you often have 95% humidity which means clothes do not dry out very well. There is a solution,
one which the ancient Greeks showed us, which was the middle ground… compromise. Instead of running at high heat, run at a lower temperature which uses less power for a longer period of time.
Estimates vary, but I have read roughly 40% less energy for low power. In our example above, that would mean 2,120 watts which would work for keeping all critical items running.
Here are some other good tips for a clothes dryer.
Source: Direct Energy
Ok, now that I have settled on the generator, I built another spreadsheet to gather my choices for other required components and to start the estimated cost process. From there, I started building
out what the order of operations would be. I will put that in my next update. | {"url":"https://www.ideasquantified.com/project-update-home-whole-generator/","timestamp":"2024-11-04T13:27:20Z","content_type":"text/html","content_length":"135494","record_id":"<urn:uuid:7ff9dec0-e3e6-45a0-b499-831eb9a3e059>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00523.warc.gz"} |
How to calculate $L'(1,\chi)/L(1,\chi)$?
How to calculate $L'(1,\chi)/L(1,\chi)$?
Question as in title, where $L(s,\chi)$ is the Dirichlet $L$-function associated with the nontrivial character modulo $3$. Please provide complete SAGE code. Thank you in advance.
Maybe you could start by showing us how much you have already?
Have you had a look at the [L-function tutorial](http://wiki.sagemath.org/days33/lfunction/tutorial) from Sage days 33? In particular, it has some fairly recent comments on the development status. I
have no idea whether Sage yet implements, for example, the insights in Ihara, Murty & Shimura's paper from circa 2007, [On the Logarithmic Derivative of Dirichlet L-Functions at s=1](http://
Actually I managed to calculate the particular example "by hand", using that $L(1,\chi)=\sum\chi(n)/n$ and $L'(1,\chi)=-\sum\chi(n)\log(n)/n$. Of course it would be nicer to use some built-in
function for that purpose. Note that I am a beginner at SAGE. Also, I looked at http://wiki.sagemath.org/days33/lfunction/tutorial, but the command "LSeries" did not work at http://www.sagenb.org/
(upon calling "L=LSeries(DirichletGroup(3).0)" I get the error message "name 'LSeries' is not defined").
1 Answer
Sort by ยป oldest newest most voted
We can try to compute using bare hands. The following is thus not useful if the question wants more than this particular case. I cannot see how sage supports better this now.
First of all, we can compute $\displaystyle L(\chi,1)=\sum_{n\ge 0}\left( \frac 1{3n+1} - \frac 1 {3n+2}\right)=\sum_{n\ge 0}\frac 1{(3n+1)(3n+2)}$ exactly, for instance:
sage: sum( 1/(3*n+1)/(3*n+2), n, 0, oo )
and the result is connected to "polylogarithmic computations".
Comment: We may start with $1+x^3 +x^6+\dots =1/(1-x^3)$ and integrate twice, first with $x$ from $0$ to $y$, then with $y$ from $0$ to $1$. Fubini shows we can forget about polylogarithms, since $$
L(\chi, 1) = \int_0^1 dy\int_0^ydx\; \frac 1{1-x^3} = \int_0^1dx\int_x^1dy\; \frac 1{1-x^3} =\int_0^1\frac {dx}{1+x+x^2}=\frac 1{\sqrt 3}\pi\ .$$
The derivative is more complex. Pari/GP gave
? sum( n=0,10000000, -log(3*n+1)/(3*n+1)+log(3*n+2)/(3*n+2) )
%6 = 0.2226631782653383756620209560
but suminf( n=0,-log(3*n+1)/(3*n+1)+log(3*n+2)/(3*n+2) ) was testing my patience.
At any rate, the rest can be estimated by rewriting the sum as a sum over $$ \frac 1{(3n+1)(3n+2)} \left[\ \ln \left(1+\frac 1{3n+1}\right)^{3n+2} -\ln(3n+2) \ \right] $$ or over $$ \frac 1{(3n+1)
(3n+2)} \left[\ \ln \left(1+\frac 1{3n+1}\right)^{3n+1} -\ln(3n+1) \ \right]\ . $$
edit flag offensive delete link more | {"url":"https://ask.sagemath.org/question/8961/how-to-calculate-l1chil1chi/?sort=votes","timestamp":"2024-11-09T16:05:34Z","content_type":"application/xhtml+xml","content_length":"58343","record_id":"<urn:uuid:44484524-4a7e-4dc8-856b-a67667da193d>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00668.warc.gz"} |
SUMIFS with OR function (multiple criteria in same column)
I am trying to get a sum if the criterion in a certain column meets one of several conditions. If the country code equals one of the country codes in the "country" column, I would like to sum the
Total MVE for each country code. Right now I have"
=SUMIFS([Total MVE]1:[Total MVE]66, Country1:Country66, ="AU", Country1:Country66, ="BR", Country1:Country66, ="CA", Country1:Country66, ="CN", Country1:Country66, ="DE", Country1:Country66, ="RF",
Country1:Country66, ="IL", Country1:Country66, ="IN", Country1:Country66, ="JP", Country1:Country66, ="KR", Country1:Country66, ="MX", Country1:Country66, ="RU", Country1:Country66, ="SG",
Country1:Country66, ="TW", Country1:Country66, ="WO", Country1:Country66, ="FOREIGN: OTHER")
I'm getting $0.00 when I should be getting $4,500.
I think I'm missing the OR part of this function, but I can't figure out where it goes. So many arguments!
Can anyone help?
Best Answer
• Hey @Kayla Q
Try this
=SUMIFS([Total MVE]1:[Total MVE]66, Country1:Country66, OR(@cell="AU", @cell ="BR", @cell ="CA", @cell ="CN", @cell="DE", @cell ="FR", @cell="IL", @cell ="IN", @cell="JP", @cell="KR", @cell =
"MX", @cell ="RU", @cell="SG", @cell ="TW", @cell ="WO", @cell ="FOREIGN: OTHER"))
I noticed that the OR includes all of the countries in the screenshot. If this is an unfiltered view, eg this is the entire list, the OR function is unnecessary.
=SUMIFS([Total MVE]1:[Total MVE]66, Country1:Country66, <>""). In fact, you could use a SUM function and just SUM the range since you have designated the row numbers
SUM([Total MVE]1:[Total MVE]66)
Do any of these work for you?
• Hey @Kayla Q
Try this
=SUMIFS([Total MVE]1:[Total MVE]66, Country1:Country66, OR(@cell="AU", @cell ="BR", @cell ="CA", @cell ="CN", @cell="DE", @cell ="FR", @cell="IL", @cell ="IN", @cell="JP", @cell="KR", @cell =
"MX", @cell ="RU", @cell="SG", @cell ="TW", @cell ="WO", @cell ="FOREIGN: OTHER"))
I noticed that the OR includes all of the countries in the screenshot. If this is an unfiltered view, eg this is the entire list, the OR function is unnecessary.
=SUMIFS([Total MVE]1:[Total MVE]66, Country1:Country66, <>""). In fact, you could use a SUM function and just SUM the range since you have designated the row numbers
SUM([Total MVE]1:[Total MVE]66)
Do any of these work for you?
Help Article Resources | {"url":"https://community.smartsheet.com/discussion/91787/sumifs-with-or-function-multiple-criteria-in-same-column","timestamp":"2024-11-06T05:05:39Z","content_type":"text/html","content_length":"402056","record_id":"<urn:uuid:cefdffc1-5288-4607-bda2-f59c608aa938>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00117.warc.gz"} |
Computer Architecture & Programming
I am a big fan of Nicholas Renotte’s channel on YouTube. I also love computer vision and its combination with deep learning. A few months ago, Nicholas posted this video, which is about YOLOv5. I
usually am too lazy to watch videos which are longer than 15 minutes and I watch them in a few episodes. But this video made me sit behind the laptop screen for over an hour and I’m sure I won’t
regret it.
So let’s start the article and see where this story begins. As I mentioned earlier, I love computer vision specially when it’s combined with deep learning. I believe it can help us solve very complex
problems of our projects with ease. My journey in world of these YOLO models have started almost a year ago, when I wanted to develop a simple object detection for detecting street signs.
Firstly, I found a lot of tutorials on darknet based training but l did not manage to get it to the work, specially since I have a mac, it could be a very realistic nightmare. So I guess YOLOv5 was a
miracle. In this article, I am going to explain why I love YOLOv5 and why I prefer it to other YOLO versions.
What is YOLOv5?
According to their github repository, YOLOv5 is a family of deep learning models which is essentially trained on Microsoft’s COCO dataset. This makes it a very very general-purpose object detection
tool which is fine for basic research and fun projects.
But I also needed to have my own models because I wanted to develop some domain-specific object detection software. So I realized they also provide a python script which helps you fine-tune and train
your own version of YOLOv5.
So I basically fell in love with this new thing I have discovered. In the next sections, I will explain why I love YOLOv5!
Why I love YOLOv5?
Firstly, I invite you to see this chart, which shows the comparison of YOLOv5 with other commonly used object detection models:
And since there’s been a controversy about YOLOv5 claims about training time, inference time, model storage size, etc. I highly recommend you read this article on Roboflow’s blog.
So we can conclude the very first thing which made me happy is the speed and that’s right. The second thing by the way is the fact I am lazy. Yes, I am lazy and I know it.
I always tried to compile darknet and use it for having a YOLOv4 model and make my projects on top of YOLOv4 but when I saw how hard it can get and since I have a mac and I didn’t really want to
fire-up an old computer for these projects, I was looking for something which does everything with a bunch of python scripts.
Since I discovered the YOLOv5, I started working with it and the very first project I have done was this pedestrian detection for a self-driving car.
Then, I started doing a lot of research and asking about what I can do with YOLOv5. I find out I can do pretty much anything I want with ease as they provided a lot of stuff themselves. Isn’t that
good enough? Fine. Let me show you another youtube video of mine which I solved my crop problem with their internal functions.
If you’re not convinced yet, I have to tell you there is a great method which is called pandas in this family of models.
As the name tells us, it really outputs a pandas dataframe which you can easily use data from that dataframe. Let me set a better example for you. Considering we want to find out which plants are
afflicted and which ones are not in a drone footage.
By using this method, we can simply make an algorithm which counts the amount of afflicted ones in a single frame, so we can easily find out how many afflicted plants we have in a certain area. The
whole point here is that we have statistically right data for most of our researches.
The other example would be the same as my pedestrian detection system. We can command the car to get data first from the cameras to make sure we’re dealing with pedestrians and second get data from
distance measurement system (which can be an Ultrasonic or LiDAR) to make sure when it should send braking command.
Let’s make a conclusion on the whole article. I love YOLOv5 because it made life easier for me, as a computer vision enthusiast. It provided the tools I wanted and honestly, I am really thankful to
Ultralytics for this great opportunity they have provided for us.
In general I always prefer easy-to-use tools and YOLOv5 was this for me. I need to focus on the goal I have instead of making a whole object detection algorithm or model from scratch.
I finally can conclude that having a fast, easy-to-use and all-python tool for object detection was what I was always seeking and YOLOv5 was my answer.
I am glad to have you as a reader on my blog and I have to say thank you for the time you’ve spent on my blog reading this article. Stay safe!
How to make video games like movies!
It was a long time that I did not write any thing in this blog. Now, I decided to write a topic about “video games” (as I wrote in my Persian blog). I was member of a game development team for about
three months and I learned a lot. At least, I know the way they were doing the job was “How to not make a video game”. So, When I left the team, I decided to research about game development process.
In this topic, I explain everything I found (experience and research result!)
When I was in the team…
It was in October (2017), a person sent me a message in Telegram, and the message was like this :
Mr. Haghiri, we need a musical composer for our game, we did a search and we found you. Please come here Wednesday 4:00 PM to talk about the project and your role.
Wednesday, I went to their office. That guy greeted me so nicely and started talking to me, about their project. I found the game is a horror game (horror games are popular in Iran, but there’s no
“good” horror game “made in Iran”.) and it made me happy! Because it was the first time I heard about an indie team decided to make such a great game. They let me two weeks to research about “Sound
and Music” in Unity Engine and I did it. I composed two pieces and also I tried to learn some tools for mixing and mastering sounds in the game (But it wasn’t actually my role, I just did that as a
After two and half months, they said “Mr. Haghiri, you don’t do what we wanted you to do”, anyway, they haven’t paid me even a “rial” in those days and expected me do great music composition, and
they also wanted me to do what wasn’t my actual role. And this was not a good experience actually. But in those two months, I learned Unity game engine and I also met other “game developers”. And, I
decided to publish my experience on my blog.
Why movies?
Recently, I read a book called Making Short Films : Complete Guide from Script to Screen, by Clifford Thurlow. In the book, I found great names like “Salvador Dali” or “Charlie Chaplin”, and also
great movies and books also mentioned in the book, like “One Flew Over Cuckoo’s Nest”. Everything was perfect, In I think about process of making a video game! It’s so similar to process of making a
But I realize game and movie have lots of differences. The biggest difference is that games are interactive and players interact with the environment or other characters, but movies are not. Anyway,
the main procedure – I mean “writing” – is %90 the same! So, I decided to mention some movies I watched, then tell you how I make a video game like them!
Great movies gave me ideas!
An Andalusian Dog
Movie is written by Louis Bunuel and Salvador Dali. I think these names are enough. But, after I watched the movie (it’s now available on YouTube and other video-sharing platforms, you can easily
find and watch it), I discovered “product of a melancholic and depressed mind”. And both “Melancholia” and “Depression” are good subjects for a story or game.
Phantom of The Opera (Musical)
The book is about a musician, in a better word, a “genius” and smart person who hided himself. Andrew Lloyd Webber, just made that sad and creepy story to a romantic story by his music! First time I
watched the movie, I could not understand it well. Because it’s not following the book’s story, and I’m not a native English speaker! I watched that movie 4 times. I watched the live performance 2 or
3 times and finally, I got the concept.
It has “Misanthropy” and “Romance” at once. I think these two things are also good for people who want to make video games (Please go and check “INSIDE” by Playdead! It’s the Misanthropy! Pure
School of Rock
It’s a bit different, School of Rock is comedy, and it’s also attractive for children. Because the topic is about a guy who teaches a bunch of 4th grade children to ROCK! Yes, he teaches them how to
play electric guitars, bass, drums and keys. I think the concept of “Music” can be a good idea, too! Specially if you plan for a game like “Guitar Hero”.
Only Lovers Left Alive
If you like Vampires, please watch this movie. This movie has no “teenager” content, but it still tells stories about two vampires who married for centuries. Movie is directed by Jim Jarmusch and he
also made music for his movie, in his rock trio SQRL. This movie has two things for game developers. It’s and independent movie and it can be a good idea bank for indie developers and also, it has
“Romance” and “Fear” and “History”. All of these three factors can make a game great!
Ok, I talked a lot about movies! Let’s find “how can I make a game like a movie?”
Finally, let’s make a game like a movie!
The most basic thing you must have for a movie is “plot”. Plot is the main idea, it’s developed and tells people your concept, but it’s not a completed “script”. Writing plot in both games and movies
is the same. To write a good plot, you need to study and read books, scripts and other plots. I prefer printed (and Persian) books in this case.
You will need research on the topic you want to write a plot about. For example, if you want to write about a middle eastern civilization (for example : Sassanid Empire or Ottoman Empire), you have
to read history of Iran, Turkey, Afghanistan, Iraq, etc. If you want to write a plot about Satan, you have to search about Satan’s role in Judaism, Christianity and Islam, and find which belief is
closer to what you want. So, you need to have a background.
After you wrote the plot, you have to write the script. But, writing script is different here, you have to clarify where and when the scene is interactive and when and where is not. The best example,
is “Bioshock Infinite”. You know why? Because when you’re not interacting with the environment, you still can move camera and see what happens around you. I’m not a good script writer (But I try to
be!) and I will write a post about how to write script from plot, when I manage to do that.
After you wrote the script, you have to make your basic ideas in the engine. Please! Please! Please! Call an experienced game developer before doing that, because the experienced one can help you
find experienced character/concept and environment artist and game-play designer. After that, I can say you’re ready to start making your game! With a good team, you can make a good game!
Finally, I wrote this article but it wouldn’t be the last article about games in my English blog. I try to continue this, because I even couldn’t find good articles about being “game script writer”
or “game director” even in English! I hope you like my post 🙂
How to be a hardware engineer
A computer, is made up of hardware and software. Lots of people like to write and develop software, so the internet is full of topics like “How to be a software engineer” or “how to write a computer
program” and also, there is a lot of great and free tutorials on programming languages and frameworks. But, hardware engineering guides on the internet, are not as many as software’s.
In this post, I really want to write about “How to” be “a hardware engineer”. As it’s my favorite field in computer science and I study it in the university. So, if you want to be a computer hardware
engineer, just read this and start searching about your favorites.
A computer engineer in general, is an engineer who designs, develops and tests computers. Both hardware and software. But, there are different types of “Computer engineer”. For example, I am a
hardware engineer, my friend is software engineer, my other friend is network engineer, etc.
So, a hardware engineer is a computer engineer, who knows electronic and electrical engineering (I know, some of electronics/electrical engineering courses are taught to students of software
engineering). But, if we go further, we’ll find that the “Hardware Engineer” is who “combines computer science and electronics”. So, this is what he/she does, learns computer science and electronics,
then combines them and makes computer hardware.
Expertise and Fields
There are these fields in hardware engineering, and people can learn one of them to find a job or start their own business.
1. Computer architecture :
a computer architect, is a computer scientist who knows how to design logical level of a computer. In my opinion it’s the most-needed role in a team who design a new computer. When you study
computer architecture, you learn mathematics behind the computer hardware, and also you learn how to design different logical circuits, and connect them together and make a computer at the
logical level.
So, if you love mathematics, and love computer programming and in general, computer science, this is your field. to learn more, you also can read my book (link)
2. Digital Electronics :
This one, is actually my favorite. Digital electronics is about implementation of logical designs. So, with digital electronics, you can make what you have designed using logic and mathematics.
But for this field of hardware engineering, you need to know electronics and electrical engineering. So, if you like digital electronics, start studies on electrical engineering today!
3. Digital Design :
This part, is also my favorite, and I really like it more than digital electronics. It’s about simulation and synthesis, so you can really ‘feel’ the hardware you have designed.
But how is it possible? The “Digital Designer” is a person who’s familiar with simulation and synthesis tools. Such as hSpice, LTSpice, ModelSim and languages such as Verilog or VHDL. It’s about
design and programming, so if you’re a software engineer who wants to learn hardware engineering, this field is yours! But, usually hardware engineers learn this field after learning digital
If you like to be a digital designer, start improving your programming and algorithm design today, it’s important to know how to code, and how to write an algorithm.
4. Microcontrollers and Programmable devices :
This field is not actually “Hardware Engineering”. But, it’s still dealing with hardware. Actually, it’s not “design and implementation” of the hardware, it’s “making hardware usable”. When you
program an ATMega32 chip for example, you make a piece of silicon usable for driving motors and sensors.
5. Artificial Intelligence :
And finally, the common field! Artificial intelligence is the widest field in computer science. It’s applicable and functional in all fields of computer science.
But how we can use it in hardware engineering? We can use AI to improve our hardware, for example our architectures can be analyzed by AI. We can make a hardware which has AI to solve problems
(a.g. ZISC processors). And finally, we can use AI in Signal processing, which is usually referred as a field of hardware/electronics/audio engineering.
Start point
I tried to explain start points in previous part, but now, I explain general start point. To learn hardware engineering, you need to know discrete mathematics and logic. Also, you need to know how to
show boolean functions like electrical circuits (a.k.a logical circuits). After learning these, you need to get familiar with computer architecture, and at the end, you can choose your favorite
field. I have experiences in all fields (except AI and Signal processing) but my most favorites are digital design and digital electronics.
It all depends on you, to choose which field, but you need those basics and fundamentals to understand it. Also, if you improve your knowledge about computer science in general, you will be a
successful computer engineer!
Good Luck 🙂
Importance of IoT
For the last 25 years, a ghost is flying over our world, it’s the ghost of “Internet”. From 80’s, internet became one of the most used tools for international communications, such as knowledge
sharing. So, a lot of people started using internet to share knowledge, to do research or even to have fun. We can use internet in many different ways and this is why internet is important. You know,
humans can’t live without air and water, but actually, electricity and internet are as important as them!
In 1982, a truck connected to the internet, it was the first attempt to connect non-digital things to the internet. Years after that, someone asked people of the world to call “connecting non-digital
things to the internet”, Internet of Things or IoT for short. Actually a computer or a mobile phone is designed to be connected to internet, so we can’t call that IoT. But a wheelchair, a cigarette
lighter, a coffee maker or even an oven are not designed to be connected to internet, so if we connect them to the internet, it’s IoT!
Concepts and Applications
The concept of IoT is to make everything around us online. You can control your coffee maker from work, and when you arrive home, you can have a cup of warm coffee. But, This is not the only
concepts. It comes to make our lives safe, it comes to make our things accessible from everywhere. And about applications? As I told, the online-coffee maker is one of the best examples of IoT
The main application of IoT is controlling everything remotely. Before IoT, remote controls used infrared to control lamps, outlets, TV’s, etc. But today, thanks to IoT, we can do that from longer
distances, using the internet. For example, your home is in Iran, and you are in a vacation in Armenia, but you can control everything from Armenia! Everything you need is a reliable internet
The importance
Now, let’s talk about the importance. Why IoT is important? is it anything except connecting devices like ovens and coffee makers to the internet? of course it is! It is actually the future of the
hardware engineering and even the online world. Hardware engineers like me should learn IoT, because in near future, every single home accessory will become online, every streets of cities will be
online, all farms will be online!
So, we need to learn IoT, but how? learning IoT is easy. You only need to know how to program microcontrollers, how to setup a development board (at all, hardware engineering), how to connect your
board to the network and how to implement remote controls and connections. For example, you can use a NodeMCU board and a bunch of LED’s to make a bedside lamp, it’s even easier than writing a simple
computer program for daily accounting.
Communication with other fields of computer science
IoT can’t be a complete knowledge/technology alone. All IoT experts have to know about one of fields of computer science. For example, a person who designed a system for traffic control, needs to
store data from traffic lights or cameras, and then he/she needs to do data mining on that. Because this thing can be helpful in predictions about traffic. Or, if you design that simple bedside lamp,
you have to write at least a good single-page interface for it. These are not basic things, and you can’t do all of them alone. To be honest, an IoT team is made up of some professionals/experts.
What they do is cooperating about these issues.
Good Luck 🙂
Reverse engineering of 8086, from a calculator to the most used processor
If you have a laptop or desktop computer, you probably use a 8086-based CPU, or one implementation of x86 family to be exact. For example, I have a Lenovo laptop with a Core i5 CPU, which is based on
x86 architecture. In this article, I want to talk about x86 architecture, and to explain how it works, I just start with the simplest one : 8086.
8086, is probably the first general-purpose processor made by Intel. This is why it’s famous, and in a lot of cases, people prefer to use it or study it. Everything is well-documented and also there
are billions of tutorials and examples on how to use it! For example, if you search for “Interfacing Circuits”, you will find a lot of 8086-based computers made by people, connected to interface
devices such as monitors, keyboards or mice.
Before we start reverse engineering, and make our simple x86-compatible computer, let’s take a look on the machine code structure of 8086. In this case, we just review Register addressing mode,
because this mode is easier to understand or re-implement.
In this case, we can only take a look on a two-byte (or 16 bit) instruction code. Our instruction code looks like this :
Byte 1 Byte 0
|Opcode|D|W| |MOD|REG|R/M|
What are these? and why we should learn this? As we want to reverse engineer 8086 architecture and learn how it works, we need to know how this processor can understand programs! So, let’s check what
are those fields in these bytes :
• Opcode : a 6-bit number, which determines about operation (for example ADD, SUB, MOV, etc. )
• D : Determines source or destination operand. To make reverse engineering process simple, we consider that as constant 1. So, REG field in byte 0 is always destination.
• W : Determines data size, and like D, to make reverse engineering process simple, we consider it as a constant 1. So, we only can do operations on 16 bit numbers.
• MOD : Determines mode, as we decided before, we only model the register addressing mode, so we need to consider mode as constant 11.
• REG and R/M : REG shows us source, R/M shows us destination. Please pay attention, we made this special case because we are going to model register addressing mode. For other modes, we can’t
consider R/M as destination.
Now, we learned how 8086 can understand programs, for now, we have some instruction code like this :
Opcode D W MOD REG R/M
xxxxxx 1 1 11 xxx xxx
Let’s assign codes to our registers. As we decided to simplify our reverse engineering process, and also we decided to use only 16 bit registers, I prefer to model four main registers, AX, BX, CX and
DX. This table shows us codes :
Code Register
000 AX
001 CX
010 DX
011 BX
As you can see, now we are able to convert instructions to machine code. To make reverse engineering process even simpler, we can ignore “MOV”, but I prefer to include MOV in my list. So, let’s find
opcodes for MOV, ADD and SUB.
Opcode Operation
100010 MOV
000001 ADD
010101 SUB
Now, we can convert every 8086 assembly instruction using the format we have. For example this piece of code :
MOV AX, CX
MOV BX, DX
ADD AX, BX
Now, if we want to convert this piece of code to machine code, we have to use the tables we made. Now, I can tell you these codes will be :
=> 0x8bc1
=> 0x8bda
=> 0x07c3
Now, we can model our very simple x86-based computer. But a note to mention, this has a lot of bugs! For example, we can’t initialize registers, so we need to study and implement immediate addressing
mode, also, we can’t read anything from memory (x86 is not a load/store architecture, and it lets people work with data stored in memory directly!). But I think, this can be helpful if you want to
study this popular processor or do any projects with it.
How to make a computer program
This is a cliché in IT and computer related blogs. You can find at least one topic on How to make a computer program in every blog written by a computer expert (scientist, engineer or experimental
expert). So, I also decided to write about it. In this topic, I’m going to explain how your idea can be a program.
I’m not a startup or business person, and I hate when someone wants to teach other people how to have an idea so I consider you already have an idea, and you want to implement your idea as a computer
program. Let’s start!
Choose your target hardware
Unfortunately, a lot of programmers ignore this important step, but if you consider a special hardware to develop and implement your ideas, you will have two points :
1. You learn a new hardware architecture (and maybe organization)
2. You help someone who wants a specific application on that hardware.
Sometimes, you realize that writing a calculator is pretty stupid. Of course it is when you write a calculator for Windows or macOS. But, when you write a calculator for Arduino, which can interact
with a keypad and displays, it’s not.
Write Algorithm
Actually, algorithm is explaining the way we solve the problems. So, we need to write the steps of our solution and test it. Sometimes, when we write a simple algorithm, it’s not efficient at all,
and needs a lot of improvements. Imagine this (This algorithm makes all even numbers lesser than 100:
while( a < 100){
if(a%2 == 0){
This is a piece of larger code. But wait, how can we improve that? That if there can make this piece of code slower. But, if we consider a = 0, we can write something like this :
for(int a = 0; a < 100; a + 2){
You know, I wrote a shorter code here. Also, this short code has a better structure of making all even numbers lesser than 100. But I think both of these codes have the same time complexity, so
there is no difference. If we had two nested loops, and the inner loop’s condition had effects on the outer loop’s condition, we had to spend time on calculating time complexity and optimizing it.
Finally, you will realize there are some “classic” algorithms, which are already optimized, and you can just use them, and model your idea with them.
Choose the language
This step is also one of the most important ones. Imagine if you want to program an AVR chip, of course JavaScript is not the best choice. There are tools which allow you to write programs for those
chips in JS, but the language is not made for communication with AVR! But, when you want to program a website, specially when you’re dealing with front-end stuff, C is not your best choice! But wait,
if the program we want to make is a general purpose desktop program or a school/university project, we are actually free to choose the language!
Imagine we want to write a simple program, which does Addition with bitwise operations. We can write our program in C/C++ like this :
#include <stdio.h>
int bitwiseAdd(int x, int y){
while(y != 0) {
int carry = x & y;
x = x ^ y;
y = carry << 1;
return x;
int main(){
printf("%d\n", bitwiseAdd(10 , 5));
return 0;
And you can write it in Ruby like this :
def bitwiseAdd(x, y)
while y != 0
carry = x & y
x = x ^ y
y = carry << 1
return x
puts bitwiseAdd(10, 15)
But, when you want to directly communicate with hardware, you’ll need a low-level language. C/C++ are actually mid-level languages. They can help you communicate with hardware (like this piece of AVR
code) :
PORTC.1 = 0;
PORTC.1 = 1;
or like that bitwiseAdd(x, y) function , they can help us write normal programs. But Assembly language is a really low-level language. We can use it when we need to talk to our hardware directly.
You see, all programming languages can help us, but depending on the conditions, we can use different languages.
And …?
And now, you probably know how a computer program is made. But, if you really want to become a developer, you have to study about paradigms, methodologies, etc. I tried to keep it simple in this
article, but later, I’ll write about those topics more.
Microcontrollers, Design and Implementation released!
It was about two years I started serious study on computer architecture. In these years, I learned a lot and I could simulate and implement a microprocessor, similar to real ones. In Summer 2016, I
decided to share my experience with others. Then, I started writing this book. This book has seventeen chapters, and after reading this book, you will have a concept of computer architecture.
• License – Licensing and Copyrights
• Introduction – A quick review of the book, defining target audience of the book.
• Chapter 1 : What’s a microcontroller? – This chapter, defines a microcontroller. After reading this chapter you’ll understand the internal parts of a microcontroller. It’s completely theory, but
you need the concepts.
• Chapter 2 : How to talk to computer? – In this chapter, we have a quick view on programming and then, machine language. We determine the word size of our processor in this chapter.
• Chapter 3 : Arithmetic Operations – This chapter focuses on arithmetic operations in base 2.
• Chapter 4 : Logical Operations – This is all about boolean algebra, the very basic introduction to logical circuits.
• Chapter 5 : Logical Circuits – Our journey starts here, we learn how to make logics using NAND in this chapter, and then, we learn the logic gates.
• Chapter 6 : Combinational Circuits – This chapter is where you learn how to combine simple logics together and make more complex logics. Actually, you learn how to implement Exclusive OR and
Exclusive NOR using other gates.
• Chapter 7 : The First Computer – In this chapter, we make a simple Addition Machine.
• Chapter 8 : Memory – In this chapter, we just take a look on sequential circuits.
• Chapter 9 : Register File – After we learned sequential circuits, we make registers and then, we make our register file.
• Chapter 10 – Computer Architecture – In this chapter, we’ll learn theory and basics of computer architecture and organization .
• Chapter 11 – Design, Advanced Addition Machine – In this chapter, we add memory blocks to our addition machine.
• Chapter 12 – The Computer (Theory) – In this chapter, we decide about what our computer should do. Actually, we design a simple ISA.
• Chapter 13 – Arithmetic and Logical Unit – Now, it’s time to design our ALU.
• Chapter 14 – Program Structure – In this chapter we decide about programming and machine language, and we design a simple instruction code.
• Chapter 15 – Microcontroller – And finally, we add the RAM to our ALU, and we’ll have our simple microcontroller.
• Chapter 16 – Programming and Operating System – In this chapter, we actually talk about the software layer of computers.
• Chapter 17 – The Dark Side of The Moon – The final chapter, is all about making real hardware, we take a look at transistors, integrated circuits and HDL’s here.
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The Effect Of Numeracy On Attitude And Conceptual Understanding Of Mole Concept By Grade 11 Students.
Volume 3 - Issue 9, September 2019 Edition
[Download Full Paper]
Misheck Mukuta, Asiana Banda
Chemistry education, Effect, Mole concept, Numeracy
The achievement of students in chemistry and in mole concept in particular in Zambia’s secondary schools has remained low. One of the reasons contributing to the low achievement is the failure by
the students to deal with the mathematical aspect of the mole concept. This study therefore, sought to investigate the effect of mathematical aspect of the mole concept on the achievement of the
learners. In addition, the study sought to determine learners’ attitude towards the mathematical aspect of the chemistry subject. The study further sought to determine whether the effect of
numeracy on achievement differ by gender. The study used a Pre-Post-test quasi experimental research design. The target population was 100 grade eleven pupils at a Secondary School in Zambia. Simple
random sampling was used to select and assign two classes to be used as the experimental and control groups. The data collection instruments were Chemistry Performance Assessment Test (CPA) and a
Likert scale Chemistry Related Attitude Questionnaire (CAQ).Data was presented descriptively using frequency tables and analysed using means and percentages while hypotheses were tested using the
independent sample t-test. The results show that incorporating the teaching of basic mathematics concepts in the teaching and learning of the mole concept has a positive effect on student’s
achievement. When incorporated, the understanding of the concept is enhanced and this results in high achievement. The results also show that positive attitude towards the mathematical aspect of
chemistry subject fosters high achievement. However, the results showed that numeracy skills has no effect on achievement in mole concept depending on one’s gender. These results have an
implication to teaching and learning of mole concept.
[1] Banda, A, Mumba, F & Chabalengula, V.M. (2014) Zambian Pre-Service Chemistry Teachers Views on Chemistry Education Goals and Challenges for Achieving Them in Schools. Science Educator, Vol.23, No
[2] Bridges, C.D. (2015) Experiencing Teaching Stoichiometry to Students in grade 10 and 11. Walden University.
[3] Britner, S., & Pajares, F. (2006). Sources of science self-efficacy beliefs of middle school students. Journal of Research in Science Teaching, 43(5), 485-499.
[4] Charles, O.G, Arokoya, A.A & Amadi, J.C. (2017) Effects of Mathematics Knowledge on Chemistry Students Academic performance in Gas law. Port Harcourt, University of Port Harcourt.
[5] Creswell, J.W. (2008). Research Design: Qualitative, Quantitative and Mixed Methods Approaches (3rd ed.). London: SAGE.
[6] Dahsah, C., & Coll, R. (2007). Thai grade 10 and 11 students’ conceptual understanding and ability to solve stoichiometry problems. Research in Science &Technology Education, 25(2), pp 227-241.
[7] Examinations Council of Zambia (2013, 2014, 2015 &2017). Performance Review Report, Lusaka, Zambia.
[8] Gabel, D. & Sherwood, R.D. (1984). Analyzing difficulties with mole-concept task by using familiar analog tasks. Journal of Research in Science Teaching, 21, 843-851.
[9] Gultepe, N , Yalcin, C.A. & Kilic.Z.(2013) Exploring Effects of High School Students‘ Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem
Solving. Australian Journal of Teacher Education
[10] Hafsah, T. et al, (2014) The influence of Students Concept of Mole, Problem, Representation Ability and Mathematical Ability on Stoichiometry problem solving. University of Pendidikan Sultan
Idris, Perak, Malaysia.
[11] Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. Science 326(5958), 1410-1412. doi:10.1126/science.1177067
[12] Johnstone, A. H. (2006). Chemical Education Research in Glasgow in perspective. Chemistry Education Research Practice. 2006, 7 (2), pp 49−63.
[13] Johnson, E. B. (2002). Contextual teaching and learning: What it is and why it’s here to stay. Thousand Oaks, CA: Corwin Pres.
[14] Johnson, David W., & Roger T. Johnson (2002). “Using Cooperative Learning in Mathematics,†Cooperative Learning in Mathematics: A Handbook for Teachers, Neil
[15] Kurbanoglu, N.I., & Akin, A. (2012). The relationships between university students’ organic chemistry anxiety, chemistry attitudes, and self-efficacy: a structural equation model.
[16] Larson, O.J. (1997) Constructing Understandings of the Mole Concept: interactions of chemistry text, teacher, and learners. Paper presented at the Annual Meeting of the National Association for
Research in Science Teaching (70th, Oak Brook, IL, March 21-24,)
[17] Maltese, A. V., & Tai, R. H. (2010). Eyeballs in the fridge: Sources of early interest in science. International Journal of Science Education, 32(5), pp 669-685.
[18] Meyer,J.H.F & Land R.(2003) Threshold Concepts and Troublesome Knowledge- Linkages to ways of Thinking and practicing in Improving Students Learning- Ten years on. C. Rust(Ed) OCSLD, Oxford.
[19] Michelli, M. P. (2013). The Relationship between Attitudes and Achievement in Mathematics among Fifth Grade Students, Honors Theses. Paper 126. The University of Southern Mississippi.
[20] Moss, K & Pabari A. (2016) The Mole Misunderstood. Centre for Effective Learning in Science, NottinghamTret University.
[21] Odili, G.A (2006). Mathematics in Nigeria Secondary Schools. A Teaching Perspective. Lagos: Anachuna Educational Books.
[22] O’dwyer, A. (2012). Identification of the Difficulties in Teaching and learning of Introductory Organic Chemistry in Ireland and the Development of a second-level Intervention Programme to
Address These. Ollscoil Luimnigh: University of Limerick
[23] Paideya, V. (2010). Exploring the use of supplemental instruction: Supporting deep Understanding and higher-order thinking in chemistry. South African Journal of Higher Education, 24(5),
pp758-770. Retrieved from http://www.sabinet.co
[24] Reid, N. A. (2009). Scientiï¬ c Approach to the Teaching of Chemistry. In Chem-Ed Conference National Centre of Excellence in Mathematics and Science Teaching and Learning. University of
[25] Sherri (2012) Research Methods and Statistics: A critical Thinking Approach.
[26] Silberberg, M, S (2013) Principals of General Chemistry, 3rd ed; McGraw-Hill, New York.
[27] Spicer, J. (2004). Resources to combat math anxiety. Eisenhower National Clearinghouse Focus 12(12).
[28] Staver, J.R. & Lumpe, A.T. (1995). Two Investigations of students’ understanding of the mole concept and its use in problem solving. Journal of Research in Science Teaching, 32, 177-193.
[29] Staver, J. R. & Lumpe, A. T. (1993). A content analysis of the presentation of the mole concept in chemistry textbooks. Journal of Research in Science Teaching, 30(4), 321-337.
[30] Steiner, R.P. (1986). Teaching stoichiometry. Journal of Chemical Education, 63, 1048.
[31] Strömdahl, H., Tulberg, A. & Lybeck, L. (1994). The qualitatively different conceptions of 1 mol.International Journal of Science Education, 16, 17-26.
[32] Talanguar, V. (2015). Threshold Concept in Chemistry- The critical Role of Implicit Schemas. University of Arizona, USA.
[33] Tobias, S. (1993) Overcoming Maths Anxiety.Newyork:ww.Nortorn
[34] Uce, M. (2009). Teaching the mole concept using a conceptual change method at college level. Education, 129(4), 683-691. Retrieved from http://www.eric.ed.gov
[35] Webster, G.H. (2009) Attitude Counts. Self-Concept and Success in General Chemistry. Journal of Chemical Education
[36] Zumdahl, S. (2002). Chemistry. Boston, MA: Houghton Mifflin | {"url":"http://www.ijarp.org/paper-details.php?ref_number=RP0919-2731","timestamp":"2024-11-01T19:10:37Z","content_type":"text/html","content_length":"14089","record_id":"<urn:uuid:ad6afb06-8f8b-48fe-8861-93b159b7cba6>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00464.warc.gz"} |
Exercise for Session 1... | Filo
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Exercise for Session 1
a. The difference between two acute angles of a right angle triangle is rad. Find the angles in degree.
b. Find the length of an arc of a circle of radius subtending an angle of at the centre.
c. A horse is tied to post by a rope. If the horse moves along circular path always keeping the tight and describes , when it has traced out at centre, find the length of rope.
d. Find the angle between the minute hand and hour hand of a clock, when the time is .
e. If makes 4 revolutions in , find the angular velocity in radians per second.
f. If a train is moving on the circular path of radius at the rate of , find the angle in radian, if it has in 10 second.
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Class Class 11
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Corrections: Page One
Washington Post article
"Five myths about the U.S. Postal Service" (February 28th, 2010)
is riddled with errors and questionable statements. The article by the Postmaster General has further convinced Corrections that the United States Postal Service should undoubtedly be privatized. No
economic reason was given for the continued subsidizing of the United States Postal Service by laws banning private services from delivering mail. Below, Corrections offers responses to three of the
editorial's most ludicrous points.
Otherwise, we have not received taxpayer funds to support postal operations since 1982; in fact, though we're often described as "quasi-governmental," we're required by law to cover our costs.
The Post Office is in debt by $2.8 billion dollars. It does not appear to be paying for its costs in a manner that will not explode.
Ten years ago, it took 70 employees one hour to sort 35,000 letters. Today, in that same hour, two employees process that same volume of mail. Though the number of addresses in the nation has
grown by nearly 18 million in the past decade, the number of employees who handle the increased delivery load has decreased by more than 200,000.
The question is not whether or not the Post Office has become more efficient, it is whether or not it is more efficient than potential competitors like FedEx or UPS.
According to the U.N.-affiliated Universal Postal Union, we deliver nearly half of the world's mail.
It's not clear to Corrections that size is equivalent to efficiency given the fact that the Post Office is losing money. It appears that their prices are too low, and that less mail should be being
spent--there is no such thing as a free lunch, and taxpayers pay for the "extra" service they're getting "free."
Philadelphia Inquirer article "Half Empty: A little shopping trip of huge proportions" (February 28th, 2010) makes an argument that doesn't quite add up for Corrections. The Inquirer argues that
Costco has a clever marketing concept because once in the store, customers are unable to resist buying things they do not desire.
The prices are remarkable, or at least they seem remarkable since you have to buy everything in very large multiples. The marketing concept is pure genius, since the Costco folks know that
beginners will go down every row looking for deals, inevitably buying something of no use.
If this was the case, Corrections would expect that customers would choose to avoid the store if they had addictive or dynamically inconsistent behavior. Furthermore, that new customers would have
heard of the addictive shopping and would avoid the store just as old customers do.
In reality, Corrections expects that Costco could possibly make its money by bundling a good, forcing a consumer to buy a little more than he would have preferred, sacrificing some of his consumer
surplus for a higher quality good (equivalent here to a larger pack of goods).
Real Clear Markets article "The Health Care Number You Didn't Hear" (February 26th, 2010) makes the argument that American workers do not pay for their health care because their employers pay. This
is incorrect. While the article's point is quite correct, when people don't have to pay for services they will demand more of them, its point about employers paying for health care is wrong.
American health care fuses these two systems, but with a common economic flaw: people are overinsured, paying pennies directly on every dollar of health service they receive.
The end result: for every dollar spent on health care in the United States, just 12 cents comes out of the individuals' pockets. Imagine what food costs might be if your employer paid 88% of your
grocery bill or what a trip to Saks might be like if your company covered the vast majority of the costs of the shopping spree.
Were employers to pay 88% of one's grocery bill, then one would expect one's wage to go down. The incidence of this tax on employers that refunds benefits to is likely to fall almost entirely on the
individual. We could similarly imagine a world in which the government takes 50% of every person's paycheck and sends it back to them. Take-home wages would go down by half (and we would get a check
from the government for 50%). Equilibrium wages would not change, and employers would not be paying for anything.
New York Times editorial "Tyler Perry's Crack Mothers" (February 26th, 2010) confuses level of drug rates with per capita crack consumption. Specifically, it claims that depictions of black women as
crack-addicted are improper because the total number of blacks admitted to clinics for addiction is now less than the total number of whites.
Furthermore, data from the Substance Abuse and Mental Health Services Administration revealed that of the total admissions to treatment services for crack use, blacks outpaced whites in 1996, but
whites outpaced blacks in 2005 for those under 30 years old.
There are six whites in the U.S. for every black. If blacks used crack cocaine less than whites, as the Times appears to attempt to suggest, one should see black admissions to clinics being one sixth
that of whites, rather than approximately the same.
This piece of evidence that the Times gives is simply ludicrous. If movies are to be ethnically fair, then they would show (approximately) six times as many black crack addicts as white.
One might add that a priori we expect that whites, who are on average weathier, are over-represented in the data the Times provides.
LA Times editorial "A registry of animal abusers is a bad idea" (February 25th, 2010) correctly notes the reasons why an animal-abusers registry would be poor policy in California, Corrections would
only add one consideration: such a registry disproportionately affects the difficulty of obtaining work in fields other than animal abuse.
California already prohibits their cruel behavior, and a registry, however tempting, won't help them to learn compassion.
As Amanda Agan notes in an upcoming paper (available here), sex offender registries do not impact recidivism. There is little reason that we would expect presumably weaker animal registries to have
such an effect. In addition, animal abusers often exploit animals for profit, knowing the illegality of their actions. Presumably, they only work with other animal exploiters and try very hard to
keep their abuse a secret from those who support animal rights. A registry would not change the circumstances of this line of work. However, a registry may make legitimate sector employment more
difficult to obtain, so that work promoting animal abuse becomes only more attractive to offenders. An animal registry may make recidivism more likely, and for this reason alone, it should not be
New York Times Editorial "Clueless in Kentucky" (February 26th, 2010) provides no evidence that unemployment benefits will help Kentucky's jobless recovery, but implies that senators have made a
mistake by not extending benefits.
Kentucky has lost about 60,000 jobs since the end of 2008. In December, its unemployment rate stood at 10.7 percent, the highest since 1983. So what exactly is going on in the minds of Kentucky’s
two Republican senators, Mitch McConnell and Jim Bunning? This week, Mr. Bunning single-handedly shot down a one-month extension of unemployment benefits, along with a federal subsidy for the
unemployed to maintain health coverage.
Unemployment benefits are meant to cover search costs for those looking for relatively high-wage jobs. It is possible that Kentucky has to adjust to a lower demand for labor, and the it has become
optimal for workers to accept lower wages than those they previously earned. In this rather likely case, extending unemployment benefits would only result in a net loss to society.
In addition, it may be optimal for Kentucky citizens to move to a new state in order to match with new employers. For example, if industrial work moves from Kentucky to Minnesota, Kentucky industrial
workers should move to Minnesota. However, unemployment benefits distort their choice set and keep workers in Kentucky inefficiently.
Wall Street Journal article "Why Won't Anyone Clean Me?" (February 24th, 2010) misses a fundamental insight into incentives. It speaks on firm incentives to attempt to clean up fridges by educating
consumers, and putting reminder cards in fridges on how to store items and clean the fridge. However, it also describes Whirlpool's efforts to make a messy fridge less impactful.
For its new refrigerator, Whirlpool Corp. spent months inventing a shelf with microscopic etching so it can hold a can of spilled soda.
The technology is just one weapon against a dirty kitchen secret: Most Americans clean their fridges only once or twice a year.
Whirlpool hopes that increasing the amount of storage space might help. The company's new shelves—to be released later this year—are 25% roomier than previous models. And the microscopic etching
creates surface tension, causing liquids to bubble up around the perimeter instead of spilling over, it says. Currently, shelves in Whirlpool's refrigerators have a plastic rim to help contain
spills. Unfortunately, the rims have "the side effect of crud getting stuck in there," says Carolyn Kelley, brand manager of Whirlpool refrigeration. The new shelves—available on new Whirlpool
models that cost from $1,199 to $1,499—would eliminate that problem because they don't require a rim to stop leaks.
It is important to note that when one makes a fridge that lowers the cost of it being in a messy state (such as microscopic etching), individuals will substitute time away from cleaning and to other
activities. Messiness is less costly, so we invest fewer resource into avoiding messiness (cleaning).
This same issue is a common mistake made by doctors who become frustrated when individuals smoke more after there are medical advances in cancer treatment, or when quitting cigarettes is made easier.
The mistake is understanding the end goal of consumers: it is not to minimize dirtiness or maximize life, but to maximize a weighting of both quality and quantity of life.
The article reads as though technology lowering the cost of messiness and education to have consumers clean the fridge have a common thread: a more clean fridge. Corrections suggests that both are
working against one another when it comes to a more clean fridge, but work together to make life easier for the consumer.
The New York Times OpEd "The Narcissus Society" (February 22nd, 2010), though beautifully written, claims that
Pooling the risk among everybody is the most efficient way to forge a healthier society.
This is true, however it is also true that the government is extraordinarily inefficient, and that the taxes necessary to provide a free lunch for some create a deadweight loss. The efficiency of the
public healthcare is uncertain.
The article also makes the point that
When it comes to health it makes sense to involve government, which is accountable to the people, rather than corporations, which are accountable to shareholders.
Corrections would argue that private health insurers are in fact motivated by profit (maybe not enough--a case for deregulation). They make money by insuring well! If the health care companies
provide a quality good for a low price then they will be able to maintain a high demand. If they create a poor product, consumers will find out and demand will fall, eventually causing their prices
to fall below their cost. Competition will cause the most efficient health companies to stay in the market and the least efficient ones to leave the market.
Finally, the article claims that
Government, through Medicare and Medicaid, is already administering almost half of American health care and doing so with less waste than the private sector.
Likely, the article concocted their notion of "waste" outside of the realm of economics--the deadweight loss from the taxation needed to provide Medicaid may well outweigh any administrative gains
the article reports.
New York Times Editorial "Failing Grade" (February 21st, 2010) argues that New York state should take measures to increase the pass rate on the GED, but makes two mistakes:
New York would do well to emulate Iowa’s highly successful preparation program. In 2008, 99 percent of test takers there passed the arduous exam.
The article compares New York State to Iowa, without informing readers that different states have different standards for passing. Students in different states can take the same test, pass in one
state, but not in the other. Such differences are exploited to measure the gains to a GED degree in studies Tyler, Murnain, and Willett (2000)
In addition, the article fails to explain how the gains to those who pass a difficult GED and provide a strong signal to employers are outweighed by the gains to others from test with a higher pass
rate. Ultimately, if the test is difficult enough to keep many from passing, it is more worthwhile (in terms of labor market signaling) to those who do pass. The article should consider both the
winners and losers from a change in the test pass rate before suggests any overhauls.
New York Times editorial "Who Can Relax This Way?" (February 19th, 2010) flaunts its ignorance and gives no data for its contentious claim. Specifically, the Times claims that the practice of open
carry is dangerous. Open carry is the practice of wielding a firearm in an open and unconcealed manner, such as a waist holster.
Open Carry, which last year invited its members to holster up outside President Obama’s speaking sites, said it would not be deterred. Unfortunately, more than two dozen states also have allowed
themselves to be bullied by the gun lobby into adopting similarly dangerous law.
Under normal circumstances, the New York Times is sophisticated enough to use data, while providing phenomenally poor analysis to make its point. In this article, it fails to do even amateurish
statistical analysis. Corrections notes that there is no evidence of any increase in crime due to open carry, though legal in half of the United States.
Indeed, given that it is not a topic in academia, while being widespread as a potential practice, one might bayesian update that it has little effect (otherwise it would be a topic). This gives
further evidence of partisan malpractice at the Times.
New York Times article Looking for a Date? A Site Suggests You Check the Data (February 12th, 2010) mistakes a correlation between profile pictures on dating websites and interest in the profile for
a causation, and then advises readers to adjust their profiles to maximize readership based on these results. Whether the relationship is truly causal or correlational, the article should note that
after its publication, the magnitude of the effects it reports should diminish.
If you’re a man, don’t smile in your profile picture, and don’t look into the camera. If you’re a woman, skip photos that focus on your physical assets and pick one that shows you vacationing in
Brazil or strumming a guitar.
Those are some of the insights that OkCupid, a free dating site based in New York, has gleaned by using statistical tools to analyze how the mating game plays out on its site.
There are two possible worlds: one in which the relationships the article reports (the effects of pictures on interest in a profile) are causal, likely guided by a signaling model, or they are
correlations and the article has falsely suggested causality. In the second case, choosing photos that don't focus on physical assets may be caused by a good education, or a modest upbringing. These
factors may be what draws interest to the profile. Then, we should not expect an uneducated person to draw a larger crowd simply by covering up.
In the first case, however, profile picture choice may causally draw interest to the profile. This would be the case if profile picture choice signaled unobservable traits, such as creativity,
self-confidence, etc. Those who are not creative would not realize that turning away from the camera may signal artistic flair. Similarly, those who are not self-confident will not realize that they
can attract men without showing off their physical assets. Such signaling, however, is only valuable as long as it accurately predicts personality. Once the trade secrets of the artistic and
confident are revealed, they become worthless. So, after the article's publication, Corrections expects the value of such signals to diminish.
Consider the example below (click to enlarge):
We see people who are creative are much more likely to look away from the camera for their picture than those who are uncreative. After the signal is made public, and those who want to fake
creativity do so, the signal becomes almost meaningless.
Notably, if OkCupid were to succeed in predicting the "perfect" picture, their business would become worthless. The company's product is the ability to learn about the personality of others through
their conscious (or subconscious) profile signals. When these signals become worthless, so too does the company.
New York Times Opinion Editorial "Do We Really Want the Status Quo on Health Care?" (February 18th, 2010) bemoans the quality of health care in the United States, but does not adequately consider the
possibility that America may be better off with less "free" healthcare than more.
Skeptics suggest that America’s poor health statistics are a result of social inequities and a large underclass. There’s something to that. But despite these problems, the population over age 65
manages to enjoy above-average health statistics — because it enjoyed health care reform back in 1965 with Medicare.
In fact, a hugely expensive, tax-payer funded Medicare plan may be sub-optimal. Perhaps, without such a plan, the elderly would save their money throughout life, anticipating medical problems as they
age. Certainly, if they pay the full cost of their own healthcare, they will purchase less healthcare than if other Americans pay the full cost of their healthcare, but this doesn't imply that
America, as a whole, is worse off. For example, because they pay such high taxes to fund Medicare, a middle-class family may choose not to purchase their own health insurance, causing their daughter
not to go to the hospital when she develops a rash, and later to die of meningitis. What makes her health worth more to the author than that of the elderly woman's whose life was saved by Medicare?
Economists do not make such judgment calls because they are difficult to defend. Rather, they choose the surplus maximizing level of care to provide. Though there may be positive externalities to
increased healthcare for all, one could easily see such gains outweighed by the huge inefficiencies of an unmotivated, incompetent government. There's no such thing as free healthcare.
Acknowledging the inefficiencies generated by the current system, the author continues:
At the present rate, by my calculations, in the year 2303 every penny of our G.D.P. will go to health care. At that time, we’ll probably get daily M.R.I.’s and CAT scans, even as we starve naked
in caves.
Imagine what the author's calculations would deduce if people who could not afford M.R.I.'s were getting them too!
Washington Post editorial "Virginia's immaculate reductions" (February 17th, 2010) criticizes Virginia Governor Robert McDonnell for his failure to shrink the state's budget. McDonnell halted the
selling of the state's liquor stores to private owners. The Post conjectures the reason is because of the money the stores bring in each year in revenue.
The governor said he would raise hundreds of millions of dollars to build roads by selling off state-run liquor stores. But at his urging, a bill in the legislature to do just that was killed
last week. The probable reason? Profits from such liquor stores go directly into the state's coffers, to the tune of about $100 million a year.
This reasoning does not make sense to Corrections. If one holds a bond whose coupons yield $100 per year every year for ten years, then one is able to sell that bond for its net present value. There
is little difference between cashing it out and holding it (if there were, then individuals would buy or sell it until no arbitrage was possible.
Similarly, the sale of the state's liquor stores should represent the net present value of the business's worth. Let us ignore any potential for increased efficiency when individual businesses take
over, as it only helps Corrections's point. A possible objection to our statement might be "but what if the state is charging as a monopolist but in selling its businesses individually it creates a
competitive industry that no longer has the monopolistic rents it previously did?" However, it is within the state's capacity to tax liquor stores until the deadweight loss, consumer surplus, and
state revenue is exactly the same. This is depicted graphically below (click to enlarge). A government monopoly (left) can be the same as a taxed industry (right).
Chicago Tribune article "Growing poverty rate for Ill. children" (February 11th, 2010) speaks on high child poverty rates in Illinois without asking why that might be the case. Corrections suggests
that the reason a place like Illinois might have many individuals below the poverty line is because they do good things for the poor, rather than neglect them.
"Now is not the time to pull back on ensuring that our children have the basic education and health care they need to develop to their full potential," Ryg said.
This may "exacerbate" Illinois's problem. Corrections suggests, as Ed Glazer and Josh Gottlieb did in their NBER Working Paper "The Wealth of Cities: Agglomeration Economies and Spatial Equilibrium,"
(2009), that the reason cities might have many poor people is because they are good places for poor people to be, not bad, as one might intuitively suggest. The reasoning is simple: poor people move
to places where they can get the most assistance, the best living standards.
Imagine a world in which there are four cities. One large one and several small. Before time t, the large city and smaller cities have the same poverty programs. At time t, the large city enacts a
welfare program to help the poor. The poor from other cities will move to the large city, and the impact of welfare by a city may be to increase the number of poor while perhaps decreasing the total
number of poor people. The increase comes from having more poor people move to the city than the program eradicates.
Three 3-D graphics, where the x and y axes are spatial coordinates of cities, and the z axis is level of poverty, are displayed. The center city is the city that enacts the welfare program.The first
diagram represents poverty levels in the cities before the welfare program was enacted (click to enlarge).
The second diagram represents poverty levels in the cities after the welfare program was enacted (click to enlarge). Note the z-axis increases slightly, which hides the increase in the central city
(but displays more prominently the decrease in outside cities.
The third diagram represents the difference in poverty rates (click to enlarge). The poverty program reduced total poverty, but the gain was seen by the outer cities.
Corrections concludes that local, city, or state poverty levels tell us little about whether or not the poor are better off in a location. Indeed, our modeling suggests that areas with more poor
people are perhaps doing more for the poor--that is why they are there. Finally, and as a side note, Corrections could forego the above exercise and note that applying the Law of Demand indicates
that good welfare programs encourage high poverty rates. (Though we note they also have a direct effect).
Washington Post article "The hidden cost of Senate gridlock: Obama can't fire anyone" (February 14th, 2010) entertains an interesting but possibly incorrect point. It notes that due to political
obstructions, nominations are more difficult to pass through the Senate, President Obama's ability to fire his ill-performing Cabinet-level personnel has suffered. The Post gives the example of
Treasury Secretary Timothy Geithner, under fire for cheating on his taxes, among other things:
The problem gets worse as it goes deeper. It's not just that Geithner can't be fired. It's that he, in turn, can't fire anybody. Treasury is understaffed, and there's little reason to believe
that the Senate will consider its nominees anytime soon. If Geithner is displeased with the performance of an appointed subordinate, he can't ponder whether America would be better off with
another individual in that office. Instead, he must decide whether America would be better off if that office were empty.
This has a couple of effects. For one thing, it makes the bureaucracy less accountable, and over the long run, it makes it less effective.
While this may be correct, it isn't immediately apparent. There is no doubt that incentives and accountability matter as the Post suggests, and ease of restructuring a cabinet facilitates the
structuring of proper incentives. However, it may be that an increased chance of rejection has differential effects given candidate skill quality--in this case, then the Post could be wrong, and
candidate quality could increase.
Let us imagine a world in which the Presidency suffers from an empty seat, and has to pay a price for attempting to fill the seat with a candidate of a certain quality. The candidate may then be
accepted or rejected, with differing probabilities based on candidate quality. Furthermore, if the candidate is accepted, then they give a stream of benefits to the Presidency if they stay, with a
chance of leaving an empty seat in every period. If a candidate is rejected, then the seat remains empty (to be attempted to be filled or not next period). Therefore we have three states--empty seat
(with cost), a seat in the process of being filled (with cost and probability of rejection), and a filled seat (with a stream of benefits so long as the candidate is in the seat, and a probability of
a candidate leaving).
Finally, let us say that the President pays a cost to attract candidates of high or low skill. What is the impact of a change in rejection probability on the relative values of low-skilled and
high-skilled candidates? Setting the problem up as a Bellman equation with generic coefficients and solving recursively, we see that the relative value of high-skilled candidates increases more when
the probability of rejection is increased. We graph the relative value of low-skilled and high-skilled candidates crossed with low and high chance of rejection over time. (All approach zero as the
time in which one is in office and accrues benefits from their being in office decreases). The relevant comparison is to compare the value gap between high and low skilled candidates in low chance of
rejection against the value gap between high and low skilled candidates in a high chance of rejection regime. We see that the relative value of high skilled candidates increases as the chance of
rejection increases at any given moment in time. (Click to enlarge). Note that we don't necessarily care about the level of value, we care about the difference between the two blue lines and the two
red lines. Even though the red lines (low chance of rejection) are higher than their counterparts in levels, the difference between them is smaller than the difference between the blue lines (high
chance of rejection). Therefore, in a high chance of rejection regime, high-skilled candidates are worth more.
Observing the diagram above, we can see that if there is a cost to choosing candidates of a certain skill level, then our comparative statics suggest increasing the probability of rejection will
increase the skill level of a candidate. The motivating factor behind this is the idea that skill level and probability of leaving are linked traits. As an empty seat "hurts" more, the President
chooses higher-skilled candidates, as they are worth relatively more because they (perhaps due to high job performance) presumably leave less frequently.
This is not a disproof of what the Post is saying, but it does offer the possibility that a higher chance of rejection leads to higher quality candidates, not lower.
New York Times Op-Ed "Watching China Run" (February 13th, 2010) very misguidedly suggests that the U.S. should be as heavily invested in environmental technologies of the future as China, whose rapid
industrialization has also come with rapid increases in pollution.
China also has become the world’s largest manufacturer of solar panels and is pushing hard on other clean energy advances.
The article continues:
We’re in the throes of an awful and seemingly endless employment crisis, and China is the country moving full speed ahead on the development of the world’s most important new industries. I’d like
one of the Washington suits to step away from the photo-op and explain the logic of that to me.
Though not Washington suits, Corrections will happily explain. There are two reasons that a country like China, whose air pollution is the stuff of legends, would be expected to invest more in energy
than the stable United States.
First, the price of using old energy technologies is higher for China than the US, so by the law of demand, they use fewer of these technologies. While a slight increase in air pollution would go
unnoticed in Chicago, the same increase would decrease the quality of life in Chongqing, China--the city with the fifth worst air pollution in the world, according to the World Bank. (Note that China
has 12 of the top 20 most polluted cities--the United States has none!) Such a decrease in the quality of life is a price that this city would have to pay, in addition to its direct costs, for using
"old energy." Eventually, that price is too high and the city will prefer more directly expensive but cleaner technologies. Chicago can get away with producing the same amount of pollution without
having to pay for the inconvenience of foggy air.
In addition, an environmental Kuznets curve would explain why China should be first to invest in cleaner energy. The environmental Kuznets curve gives an inverted U-shape for the relationship between
national income per capita and environmental health indicators, as depicted below (click here to enlarge). This would suggest that a clean environment is a luxury good. As China's income per capita
grows, so too does its environmental investment.
New York Times editorial "How Not to Write a Jobs Bill" (February 11th, 2010) makes a reflexive claim about jobs and tax cuts that may not be valid. Specifically, the Times argues that tax cuts are
unconnected to jobs. Further, it appears to support creation and maintenance of governmental jobs.
An $85 billion proposal put forward Thursday morning by Max Baucus, the chairman of the Finance Committee, and by Charles Grassley, the committee’s top Republican, scarcely began to grapple with
the $266 billion in provisions for jobs and stimulus that President Obama proposed in his budget. It was not even in the same league as the modest House-passed $154 billion jobs bill.
Worse, about half of the proposal had nothing to do with new jobs. The single largest chunk, about $31 billion, went to renew expiring tax breaks that are generally useful but unrelated to jobs.
Another $10 billion would renew an expiring Medicare payment formula so doctors wouldn’t face a pay cut
Harald Uhlig's 2010 Working Paper "Some Fiscal Calculus" suggests that in the long run, a discounted $2.60 is lost for every dollar the government spends, while tax cuts on labor offer up to $1.7 in
gain. The relevant idea is that removal of distortionary taxes improve outcomes, while short-run multiplier benefits are temporary and small.
While time Times mentions tax cuts on labor, it focuses on fiscal aid to states and increasing the supply of government jobs. The Times demands more government jobs:
What senators don’t understand or choose to ignore is that state budget cuts mean layoffs. State and local governments are among the nation’s largest employers, responsible for 15 percent of the
labor force, about the same share as the health care sector and far larger than manufacturing or the financial sector. Since August 2008, states and localities have eliminated 151,000 jobs.
From the perspective of Corrections, this may be good news for the economy. In "The Current Financial Crisis: What Should We Learn from the Great Depressions of the Twentieth Century?" (March 2009)
Federal Reserve Bank of Minneapolis Working Paper, Gonzalo Fernández de Córdoba and Timothy Kehoe, reporting that sharp productivity drops are a main contributer to depressions, write:
With banks and other financial institutions in crisis, the government needs to focus on providing liquidity so that banks can provide credit at market interest rates, and using the market
mechanism, to productive firms. Unproductive firms need to die. This is as true for the automobile industry as it is for the banking system. Bailouts and other financial efforts to keep
unproductive firms in operation depress productivity. These firms absorb labor and capital that are better used by productive firms. The market makes better decisions than does the government on
which firms should survive and which should die.
Corrections suggests the same goes for one of the few employers whose labor productivity appears fundamentally disconnected from wages, and whose labor allocation is distorted by a labor force that
is 36.8% unionized, a figure that is approximately the highest private sector union density ever reached, in the mid 1950's. Government job shrinkage appears to serve a double purpose: increase
productivity in the long run as well as serve as a (Ricardian) tax cut in the short.
San Diego Times article "Insight is a good thing" (February 9th, 2010) appears to cast a weak comment against the practice of "ability-grouping." Corrections does not understand why.
As long as teachers approach students with different expectations and rely on dangerous practices such as ability-grouping – blue birds, red birds etc. – in order to make those classrooms more
manageable, then we shouldn’t be surprised that students continue to perform at different levels.
The sentence appears quite correct, save for the phrase "dangerous." Ability-grouping is the tactic of putting groups of students at similar skill levels together. If other-student knowledge is
complementary to student learning, then putting groups of students together is a good idea. Students help one another learn. Everyone would be better off with a higher-achieving individual in their
reading group. However, in terms of efficiency, it may be better to match high individuals with high individuals if higher knowledge individuals help other individuals with higher knowledge more than
they help lower knowledge individuals.
That is to say, if a sixth-grade reading level individual boosts another sixth-grade reading level individual's reading level up two grades, and would only boost a fourth-grade reading level up one,
then we might say that it creates more total learning to match the two highest--a concept called positive assortative matching in economics. This is more easily seen in the table below (click to
enlarge). The table displays the joint returns to schooling. We see that higher reading level individuals create more surplus when matched with higher reading level individuals than they would with
lower reading level individuals.
In matching theory, our graph displays supermodularity. Corrections displays this graph in colored 2-d and from two perspectives in 3-d to give an idea of why we might want to positively assort
individuals. Click to enlarge 2-d. Click to enlarge 3-D #1. Click to enlarge 3-D #2. Note that colors match between the two 3-D graphs, but not between these graphs and our 2-D contour graph. In all
cases, the "surplus" might be imagined to be total extra points on reading tests created from a combination. It ranges from zero to twenty-five (without loss of generality).
While the article is correct that this practice will cause more inequity, it may also cause a higher total amount of learning.
Time Magazine article "Lay Off the Layoffs" (February 5th, 2010) concludes that Southwest's decision not enact mass layoffs post September 11th was a cause of their success, comparing them against
their rivals that did lay off employees. Not only is Time weakly using a single example, but it's missing a more obvious answer: firms that lay off employees are less healthy.
On Sept. 12, 2001, there were no commercial flights in the United States. It was uncertain when airlines would be permitted to start flying again—or how many customers would be on them. Airlines
faced not only the tragedy of 9/11 but the fact that economy was entering a recession. So almost immediately, all the U.S. airlines, save one, did what so many U.S. corporations are particularly
skilled at doing: they began announcing tens of thousands of layoffs. Today the one airline that didn't cut staff, Southwest, still has never had an involuntary layoff in its almost 40-year
history. It's now the largest domestic U.S. airline and has a market capitalization bigger than all its domestic competitors combined. As its former head of human resources once told me: "If
people are your most important assets, why would you get rid of them?"
It's an attitude that's all too rare in executive suites these days.
Corrections suggests that organizational/firm-specific capital or search costs can certainly be a reason for labor-hoarding. However, concluding that firms should not lay workers off because firms
that don't lay off workers are successful is like concluding that firms that don't declare bankruptcy are the most successful firms--therefore they shouldn't declare bankruptcy. The rest of the
article provides nothing but economic sound and fury, signifying nothing.
Jerusalem Post opinion "Viral irrationalism" (February 8th, 2010) reports on the failure of Jews to inoculate their children against basic diseases. It recommends required immunization, while
Corrections remains uncertain as to whether or not such a requirement would be welfare-enhancing.
The Jewish community, here and in the Diaspora, is not immune to such irrationalism. Some people have been instructed by their clerics not to immunize; some have been swept up in the quagmire of
medical quackery, while still others are convinced profiteering pharmaceutical companies are conspiring to promote unnecessary vaccines.
After establishing that Hasidic Jews have experienced outbreaks of mumps, the article urges required inoculation.
We urge the Health Ministry to consider requiring parents to provide a child’s pinkas hisunim – immunization record – when they register their youngsters for school. The enforcement tool would be
simple: Any municipality or stream, including most of the haredi sector, which is found to admit unimmunized children, would face loss of funding from the national government.
The only reason Corrections can see that a government might get involved in required inoculation is that it represents a positive externality through herd immunity. Herd immunity is a concept in
epidemiology that allows for the protection of non-inoculated individuals because enough of the herd is immune. In brief, the concept is as follows: if one person has the disease, and they give it to
(on average) less than one other individual, then there will be no outbreaks. The herd is largely "immune." If they give it to (on average) more than one other individual, then there will be
exponential growth in a disease and outbreaks will ensue.
So long as a society is past herd immunity thresholds, they have decreasing returns to further inoculation, in terms of herd immunity. In such a case, required inoculation can easily be seen as
welfare-decreasing, especially as all other individuals have the option of becoming inoculated.
The threshold for herd immunity in mumps is approximately 80%. Israel passed that threshold in 1990. Corrections notes that among humanity's most valuable accomplishments has been the eradication of
smallpox through vaccination. Vaccination has great value. However, given that the critical herd immunity threshold has been passed, allowing Jewish parents to make their own decisions about the
risks of their children dying is much cheaper.
Christian Science Monitor opinion "When athletes praise God at the Super Bowl and other sports" (February 9th, 2010) ignores possible utilitarian concerns in its invective against Drew Brees praise
of god on national television.
'God is great.'
So said Drew Brees, the most valuable player in last Sunday’s Super Bowl, after leading the New Orleans Saints to an upset victory over the Indianapolis Colts.
Such comments have become commonplace on American television, where athletes routinely thank God in postgame prayers and interviews.
Is this a problem? I think it is. And to see why, try to imagine if Brees had made a slightly different statement: 'Allah is great.'
It is worth noting that approximately 76% of the United States are Christians. Corrections imagines that among Super Bowl watchers, and American sports fans, it's likely higher (and more intense).
In a purely felicific calculus, average gain that individuals who watch may get from hearing a praise of their chosen deity multiplied by their number is likely greater than the average loss from
individuals who watch and don't like hearing praise of god. The author's comparison would make the transition from somewhere between a 3-to-1 and 9-to-1 christian-to-other watcher, to a very small
minority-to-a large majority, if an Islamic prayer were said.
The author's comparison is false, if we examined it on Benthamian felicific calculus, or any reasonable weighting to achieve a comparison between aggregate benefit and aggregate cost.
In the Chicago Tribune Opinion "Supreme Court sets bad public policy" (February 8th, 2010) describes the consequences of striking down an Illinois law prohibiting exorbitantly high awards for
malpractice lawsuits:
The law ended ridiculously high noneconomic (e.g. pain, suffering and loss of consortium or society) awards handed out in Illinois malpractice suits, especially in downstate Madison County, the
malpractice lawyer's mecca. The law was effective, helping reduce medical costs and stemming the departure of Illinois health care providers because of excessively high malpractice insurance
The article forgets one additional effect of such a law: it made bad doctors stay in the state. When the punishment for malpractice increases, so too does the cost of practicing medicine, especially
for the worst (most likely to get sued) doctors. Of course, higher malpractice payouts should all get passed to consumers in the form of higher doctor's fees, because in the long run doctor location
is elastic.
LA Time's Opinion Editorial "L.A.'s blueprint for job creation" (February 7th, 2010) puts forth a "cost" figure for trade, without considering the incredible benefits of trade:
Buy local: In 2009, L.A. city government spent roughly $1.7 billion for various goods and services. Unfortunately, companies in L.A. received only 15% of it. More than half of the total went to
firms outside the region, and some of it left the state entirely. The city's procurement guidelines should give preference to local manufacturers and service companies.
Economists have long known that trade benefits both trading partners. To analyze California's situation properly, we would need to know the benefits that Californian buyers receive from non-locally
produced food and clothing purchases. "Buy local" may be the prescription of many, until they are faced with a price-tag of $50 per cup of coffee.
It is also worth noting that even if companies in L.A. received only 15% of total food purchases from L.A. city government, these companies could still be receiving a great deal of revenue from
around the world. The discrepancy would be natural if the companies were specializing--making only what they make most efficiently. For example, if L.A. companies are only good at making carrots,
then we would expect that they service very little of L.A.'s total food demand. However, these companies are still better off than they would be if forced to give up their natural advantage for
carrot-growing to grow the coffee beans that the government now refuses to buy from Columbia.
Both the carrot farmers and L.A. consumers are better off if L.A. doesn't adopt a "Buy local" policy--all inefficiencies created by L.A. city government are passed on to consumers. Subsidizing
production that food companies wouldn't make without such a subsidy only hurts the city.
New York Times article "A Recovery That’s Factory-Built and Gaining Speed" (February 5th, 2010) points out that increased manufacturing output may be a sign of quick economic recovery:
The sharpness of the rebound, reflected in the indexes created by the Institute for Supply Management in the United States, and recreated in many other countries by Markit, could indicate that
the American economy is not in line for another slow recovery
Likely, this is a sign of recovery. An interesting economic possibility, however, is that increased manufacturing output is actually a sign that the economy is headed only further into recession. We
imagine a world in which individuals can either consume with their income or invest it. If the economy is only headed further down, they want to invest less, meaning they must consume more, until
captial has depreciated to its new steady state, as depicted below (click to enlarge). Investment trends would need to be analyzed in order to dismiss this possibility.
Wall Street Journal opinion editorial "The Necessity of Obamanomics" (February 4th, 2010)
You don't have to be an orthodox Keynesian to understand that as long as the private sector is deleveraging the public sector has to borrow and spend in order to keep the economy moving forward.
Spending on the original stimulus will peak soon; spending for additional unemployment insurance and the jobs bill will add about $90 billion.
You may not have to be an "orthodox Keynesian," to believe that the government can stimulate aggregate demand as a pareto-improving (or some "aggregate" utility improving) government intervention,
but if you aren't an orthodox Keyesian (whatever that means), you might find yourself as a hydraulic Keynesian or neo-Keynesian. Perhaps familiarity with economics breeds an inability to understand
when a non-economist such as Robert Reich makes contentious claims seem ordinary.
Corrections disputes Reich's point, and suggests that even if you don't have to be an "orthodox Keynesian," to understand government intervention is currently necessary for some reason, you have
apparently heard of some secret consensus that has evaded Correction's ears.
The LA Times recently ran an editorial called "Backing down on climate change" (February 5th, 2010) that claimed
No one really knows what would happen if average temperatures hit 5 C higher than 1850 -- a level we could easily reach within a century under a business-as-usual scenario -- but changes to the
physical geography of the planet become probable: land masses would vanish; ecosystems would collapse. Human civilization would change, and not for the better.
Corrections would urge the author to credit the human race with some modicum of intelligence. It is unclear that a global climate change would harm civilization, as a whole. Afterall, the flood urged
Noah to build the world's largest boat. Rational human beings will begin to invest increasingly in technology that will prevent serious climate change as soon a such change becomes worrisome. In
fact, many have done so already. Assuming people discount the future, they may be willing, for some time, to put off trying to solve the global warming problem in favor of leisure activities or other
types of invention. When demand for a solution becomes large enough, individuals will certainly shift their production toward climate innovation. Just because we currently see no social investment in
the problem of global warming (beyond shopping in a special "organic" aisle at the grocery store), does not imply that such investment will not take place. Warning readers that "human civilization
will change, and not for the better" is contingent on the same, ageless refrain "if current trends continue..."
By its title at least, a recent New York Times editorial--"Jim Crow Policing" (February 1st 2010)--suggests that the New York City police department is racist:
An overwhelming 84 percent of the stops in the first three-quarters of 2009 were of black or Hispanic New Yorkers. It is incredible how few of the stops yielded any law enforcement benefit.
Contraband, which usually means drugs, was found in only 1.6 percent of the stops of black New Yorkers. For Hispanics, it was just 1.5 percent. For whites, who are stopped far less frequently,
contraband was found 2.2 percent of the time.
In this analysis lies a fundamental mistake. We have not been provided with the correct statistic to determine whether the department is actually racist. Suppose, as in the figure below (click to
enlarge), that minority members of the population and majority members of the population factually have a different distribution of "suspiciousness."
For example, the x-axis could represent the level of "suspicious dress" (let's suppose that this is not endogenous). The top chart represents the distribution of the majority population, while the
bottom chart represents the distribution of the minority population. In this example, there is little signaling differentiation among the minority population. However, there is a great deal among the
majority population. In this sense, although the population averages are the same, and although the "level of suspiciousness" trigger is the same, a much larger proportion of the minority population
appears suspicious.
If suspiciousness is correlated with commission of crimes, the New York Police would not be discriminating by stopping more black men. Moreover, if suspiciousness in the majority population is so
rare that it strongly signals criminal behavior, we would expect a larger proportion of police stops of majorities to lead to arrest.
Ultimately, what determines discrimination is not the average number of police stops that lead to arrest of minorities vs. majorities. The proportion of marginal stops that lead to arrest , which we
do not observe, determine the level of discrimination on the police force. If the marginal (last) stop of a minority is less likely to lead to arrest than the marginal (last) stop of a majority, then
the police department would be discriminating by stopping the minority. The only way the statistics we are given could actually lead us to the conclusion that the New York Police Department is racist
is if they were the results of marginal, not average stops. This is not the case; the Times is mistaken.
Reuter's article titled "Some 600,000 jobs tied to Obama stimulus plan in 4Q" (January 31st, 2010) reports improvements in the job-generation counting mechanism of the stimulus plan, but neglects to
mention those jobs that this government has taken away from future generations:
That would mean a total of a little more than 1.2 million jobs were created or saved in 2009, versus the Council's forecast of 1.5 million to 2 million jobs, though comparisons are difficult.
Comparisons are made even more difficult by the deadweight loss associated with any subsidy. In the picture below, the deadweight loss in the job market is given by the red shaded area (click here to
It is important to specify that the government has taken money from people to "create" jobs, redistributed it, and claimed victory, likely at the cost of future jobs. If the government had not
decided to push forward with a stimulus, the money they no longer needed could be re-invested by consumers in more productive activities--hopefully, in spending that does not generate deadweight
loss. Natural investments, which spur industrial growth, may create many more jobs in the future than the government has burdened tax-payers with now.
It is also important to note, as Kevin Murphy has, that the effect of government spending depends largely on how efficient the government is at employing the resources it has. If we believe that the
government is largely inefficient (so for every tax dollar it raises, it entirely wastes fifty cents), this makes it more likely that the net value of the stimulus is negative. If we notice that the
stimulus plan is not devoted to making use of "idle" resources, but rather to transferring funds from productive taxpayers to less productive citizens, this also makes it more likely that the net
value of the stimulus is negative. Finally, if we believe that even "idle" resources, such as the unemployed, are able to become productive with relative ease, such as by taking a college course or
moving, the case that the stimulus has net negative value becomes quite compelling. | {"url":"https://correctionspageone.blogspot.com/2010/02/","timestamp":"2024-11-10T12:45:52Z","content_type":"text/html","content_length":"221701","record_id":"<urn:uuid:f2a27a6d-4fc6-4970-8416-29e5a8eafa43>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00735.warc.gz"} |
Discrete Mathematics
Explore this modern realm of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and "mathemagician"
who has designed a course that is mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra. | {"url":"https://www.thegreatcoursesplus.com/discrete-mathematics","timestamp":"2024-11-11T09:29:42Z","content_type":"text/html","content_length":"225352","record_id":"<urn:uuid:7bdc23c8-9604-4dc3-a7cd-50a65c84b1db>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00427.warc.gz"} |
Virginia Regulatory Town Hall View Comments
Action Comprehensive Revision of the Licensure Regulations for School Personnel
Stage Proposed
Comment Period Ended on 11/6/2015
Commenter: Ann Wallace, James Madison University
Mathematics Specialist Endorsement
I concur 100% with the comment posted by the Virginia Council of Mathematics Specialists regarding the proposal change requiring 6-8 mathematics specialists to have a 6-12 mathematics endorsement.
Having a secondary mathematics degree (meaning a BS in mathematics) has not necessarily ensured candidates have a strong command of the middle grades curriculum (especially in terms of depth). The 5
graduate-level mathematics content courses taken by candidates pursuing a K-8 Mathematics Specialist Degree provide opportunities to understand deeply the mathematics that reinforces the middle
school mathematics curriculum.
I hope the VBOE will strongly consider the position taken by the VACMS regarding this proposal. | {"url":"https://townhall.virginia.gov/L/ViewComments.cfm?CommentID=42232","timestamp":"2024-11-13T14:28:14Z","content_type":"text/html","content_length":"12252","record_id":"<urn:uuid:66e76de9-206e-4f98-ad82-4f6432b0d9bf>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00824.warc.gz"} |
NeurIPS 2019
Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
Reviewer 1
This is a very good paper. I really enjoyed reading the paper. The result is very strong and the paper is very readable. I strongly recommend accepting the paper, if the proof is correct. (I could
not check the supplementary material due to time constraints.) This paper solves an important open problem in robust estimation. The open problem is described in the beginning: "Is it possible to
attain optimal rates of estimation in outlier-robust sparse regression using penalized empirical risk minimization (PERM) with convex loss and convex penalties?" The answer was negative in the past
researches, but the present paper gives the answer "YES". The estimate is very simple, because it is obtained from the minimization of the simple Huber-loss with the $l_1$ penalty with some devised
tuning parameter $\lambda_o$, which is an interesting point. To show the optimal convergence rate, we need some additional assumptions that the authors honestly mention on l.26-27. However, they are
not strong. The introduction is very clear. The authors give a clear history of the study of convergence rate in robust estimation. The key sentences are: "this result (which means the result
obtained in this paper) is not valid in the most general situation, but we demonstrate its validity under the assumptions that the design matrix satisfies some incoherence condition and only the
response is subject to contamination." and "The main goal of the present paper is to show that this sub-optimality is not an intrinsic property of the estimator (3), but rather an artefact of
previous proof techniques. By using a refined argument, we prove that $\hat{\beta}$ defined by (3) does attain the optimal rate under very mild assumptions." Section 2 gives a key theorem. In
particular, the authors illustrate why some complicated assumptions are necessary in the first paragraph with interesting examples, and they also give the main point of the proof which is to treat
the extra parameter $\theta$ as a nuisance parameter when we obtain the bound, but not in the past. Section 3 focuses on the Gaussian design. Section 4 gives a very clear survey on prior work. The
authors give future works very clearly in Section 5, including technical details amazingly. Section 6 is a numerical experiment, which verifies the order of $o/n$. This is a very small experiment,
but this is enough, because the main purpose of this paper is a theoretical one. Major Comment I have only one comment. I think the largest feature is that the tuning parameter $\lambda_o$ is
incorporated into the Huber loss in a different way. The usual $l_1$ penalized Huber loss function with $\lambda_o=1$ will not give the optimal convergence rate. What is the role of $\lambda_o$ on
eq.(5)? (although the role is clear on eq.(3).) $\Phi(u)=(1/2)u^2 \cap (|u|-1/2)$. The effect of $\lambda_o$ vanishes for $u^2$, but it remains for (|u|-1/2), which gives the loss function $\lambda_o
\sqrt{n} ( (1/n)\sum_{i=1}^n |y_i-X_i^\top \beta| -1/2 )$. When $\lambda_o$ has the order used in Theorem 3, the factor $\lambda_o\sqrt{n}$ has the order $(\log(n))^(1/2)$, which converges to
infinity. This implies that the effect of large error of $|y_i-X_i^\top \beta|$ is not admitted at all. As a result, the main loss is the squared error only. Is this an appropriate point of view? If
you have a clear point of view on the role of $\lambda_o$ on eq.(5), please give related comments. -------------------------------------------- Thank you for your reply.
Reviewer 2
I thank the authors for their detailed response. There is another NeuIPS submission whose results supersedes this one (this paper's result is only a corollary of that submission), and I will leave
the decision to the AC. ===== - originality This paper only deals with the setting where response variables (y), and has to assume that x are sub-Gaussian, and similar results were already
established in (Bhatia et al., 2017). However, (Liu et al., 2019) can handle corruptions in both x and y, although the bound is slightly worse. - quality The proofs are sound. - clarity The paper is
well written. - significance There are many papers in this area, and this work has not differentiated itself from other papers.
Reviewer 3
I enjoyed reading this paper and support its publication in NeurIPS. The primary contribution of this work is technical and theoretical, but it provides a sharpened analysis of a very practical
algorithm for robust regression. This work shows that under certain natural conditions, ell-1 penalized least-squares achieves the minimax rate of convergence for this problem, up to a logarithmic
factor. I am not an expert in this area, but according to the authors, previous analyses of this same algorithm failed to show this sharp rate, and previous algorithms achieving this rate were
complicated and difficult to use in practice. The technical innovation applies the KKT condition for beta, at the estimated outlier-contamination vector theta, to derive a recursive bound for the
squared-error of the beta estimate. A main term of this bound is v'X'u for (u,v) the errors in (theta,beta), and a main technical insight is that this can be controlled by ||u||_2*||v||_1/sqrt(n) + |
|u||_1*||v||_2/sqrt(n), rather than the naive operator-norm bound ||v||_2*||u||_2, when the design X satisfies an incoherence property with the standard basis. The improved bound then applies this
insight and an a priori bound on (u,v) from a more standard Lasso-regression analysis. The authors demonstrate that the required incoherence property holds for (correlated) multivariate Gaussian
designs, using a Gaussian-process and peeling argument. In my view, this insight is non-trivial, and both the paper and proof are also well-written. A few comments/minor typos: (1) I think some more
explanation is needed after Definition 1, to explain how this captures the notions of restricted invertibility and incoherence in the previous paragraph. In particular, the role of the transfer
principles in restricted invertibility is a bit confusing, as the RE condition for Sigma is only discussed later on the page. Explaining why (ii) captures some notion of incoherence would also be
helpful. (2) It took me a while to find where X^{(n)} and \xi^{(n)} are defined---perhaps this can be clarified more explicitly. (3) Line 101, p-th largest should be p-th smallest (4) Line 476, J
should be S and beta_j should be beta_j^* (5) Is there a minus sign missing in the first term on the right of Lemma 1, and its application in line (525)? (6) I'm not sure what trace means above line
564 for W_{b,v}. ------------- Post-rebuttal: Thanks to the authors for the response, clarification, and discussion. | {"url":"https://papers.nips.cc/paper_files/paper/2019/file/f0d7053396e765bf52de12133cf1afe8-Reviews.html","timestamp":"2024-11-12T09:50:23Z","content_type":"text/html","content_length":"8375","record_id":"<urn:uuid:b2e2da83-4365-4108-9e67-ad0afe6c8e04>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00373.warc.gz"} |
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Node2Vec representation learning with Stellargraph components
Node2Vec representation learning with Stellargraph components¶
This example demonstrates how to apply components from the stellargraph library to perform representation learning via Node2Vec. This uses a Keras implementation of Node2Vec available in stellargraph
instead of the reference implementation provided by gensim. This implementation provides flexible interfaces to downstream tasks for end-to-end learning.
[1] Node2Vec: Scalable Feature Learning for Networks. A. Grover, J. Leskovec. ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), 2016. (link)
[2] Distributed representations of words and phrases and their compositionality. T. Mikolov, I. Sutskever, K. Chen, G. S. Corrado, and J. Dean. In Advances in Neural Information Processing Systems
(NIPS), pp. 3111-3119, 2013. (link)
[3] word2vec Parameter Learning Explained. X. Rong. arXiv preprint arXiv:1411.2738. 2014 Nov 11. (link)
Following word2vec [2,3], for each (target,context) node pair \((v_i,v_j)\) collected from random walks, we learn the representation for the target node \(v_i\) by using it to predict the existence
of context node \(v_j\), with the following three-layer neural network.
Node \(v_i\)’s representation in the hidden layer is obtained by multiplying \(v_i\)’s one-hot representation in the input layer with the input-to-hidden weight matrix \(W_{in}\), which is equivalent
to look up the \(i\)th row of input-to-hidden weight matrix \(W_{in}\). The existence probability of each node conditioned on node \(v_i\) is outputted in the output layer, which is obtained by
multiplying \(v_i\)’s hidden-layer representation with the hidden-to-out weight matrix \(W_{out}\) followed by a softmax activation. To capture the target-context relation between \(v_i\) and \(v_j\)
, we need to maximize the probability \(\mathrm{P}(v_j|v_i)\). However, computing \(\mathrm{P}(v_j|v_i)\) is time consuming, which involves the matrix multiplication between \(v_i\)’s hidden-layer
representation and the hidden-to-out weight matrix \(W_{out}\).
To speed up the computing, we adopt the negative sampling strategy [2,3]. For each (target, context) node pair, we sample a negative node \(v_k\), which is not \(v_i\)’s context. To obtain the
output, instead of multiplying \(v_i\)’s hidden-layer representation with the hidden-to-out weight matrix \(W_{out}\) followed by a softmax activation, we only calculate the dot product between \(v_i
\)’s hidden-layer representation and the \(j\)th column as well as the \(k\)th column of the hidden-to-output weight matrix \(W_{out}\) followed by a sigmoid activation respectively. According to
[3], the original objective to maximize \(\mathrm{P}(v_j|v_i)\) can be approximated by minimizing the cross entropy between \(v_j\) and \(v_k\)’s outputs and their ground-truth labels (1 for \(v_j\)
and 0 for \(v_k\)).
Following [2,3], we denote the rows of the input-to-hidden weight matrix \(W_{in}\) as input_embeddings and the columns of the hidden-to-out weight matrix \(W_{out}\) as output_embeddings. To build
the Node2Vec model, we need look up input_embeddings for target nodes and output_embeddings for context nodes and calculate their inner product together with a sigmoid activation.
import matplotlib.pyplot as plt
from sklearn.manifold import TSNE
import os
import networkx as nx
import numpy as np
import pandas as pd
from tensorflow import keras
from stellargraph import StellarGraph
from stellargraph.data import BiasedRandomWalk
from stellargraph.data import UnsupervisedSampler
from stellargraph.data import BiasedRandomWalk
from stellargraph.mapper import Node2VecLinkGenerator, Node2VecNodeGenerator
from stellargraph.layer import Node2Vec, link_classification
from stellargraph import datasets
from IPython.display import display, HTML
%matplotlib inline
For clarity, we use only the largest connected component, ignoring isolated nodes and subgraphs; having these in the data does not prevent the algorithm from running and producing valid results.
dataset = datasets.Cora()
G, subjects = dataset.load(largest_connected_component_only=True)
The Cora dataset consists of 2708 scientific publications classified into one of seven classes. The citation network consists of 5429 links. Each publication in the dataset is described by a 0/
1-valued word vector indicating the absence/presence of the corresponding word from the dictionary. The dictionary consists of 1433 unique words.
StellarGraph: Undirected multigraph
Nodes: 2485, Edges: 5209
Node types:
paper: [2485]
Features: float32 vector, length 1433
Edge types: paper-cites->paper
Edge types:
paper-cites->paper: [5209]
Weights: all 1 (default)
Features: none
The Node2Vec algorithm¶
The Node2Vec algorithm introduced in [1] is a 2-step representation learning algorithm. The two steps are:
1. Use random walks to generate sentences from a graph. A sentence is a list of node ids. The set of all sentences makes a corpus.
2. The corpus is then used to learn an embedding vector for each node in the graph. Each node id is considered a unique word/token in a dictionary that has size equal to the number of nodes in the
graph. The Word2Vec algorithm [2] is used for calculating the embedding vectors.
In this implementation, we train the Node2Vec algorithm in the following two steps:
1. Generate a set of (target, context) node pairs through starting the biased random walk with a fixed length at per node. The starting nodes are taken as the target nodes and the following nodes in
biased random walks are taken as context nodes. For each (target, context) node pair, we generate 1 negative node pair.
2. Train the Node2Vec algorithm through minimizing cross-entropy loss for target-context pair prediction, with the predictive value obtained by performing the dot product of the ‘input embedding’ of
the target node and the ‘output embedding’ of the context node, followed by a sigmoid activation.
Specify the optional parameter values: the number of walks to take per node, the length of each walk. Here, to guarantee the running efficiency, we respectively set walk_number and walk_length to 100
and 5. Larger values can be set to them to achieve better performance.
walk_number = 100
walk_length = 5
Create the biased random walker to perform context node sampling, with the specified parameters.
walker = BiasedRandomWalk(
p=0.5, # defines probability, 1/p, of returning to source node
q=2.0, # defines probability, 1/q, for moving to a node away from the source node
Create the UnsupervisedSampler instance with the biased random walker.
unsupervised_samples = UnsupervisedSampler(G, nodes=list(G.nodes()), walker=walker)
Set the batch size and the number of epochs.
batch_size = 50
epochs = 2
Define an attri2vec training generator, which generates a batch of (index of target node, index of context node, label of node pair) pairs per iteration.
generator = Node2VecLinkGenerator(G, batch_size)
Build the Node2Vec model, with the dimension of learned node representations set to 128.
emb_size = 128
node2vec = Node2Vec(emb_size, generator=generator)
x_inp, x_out = node2vec.in_out_tensors()
Use the link_classification function to generate the prediction, with the ‘dot’ edge embedding generation method and the ‘sigmoid’ activation, which actually performs the dot product of the input
embedding of the target node and the output embedding of the context node followed by a sigmoid activation.
prediction = link_classification(
output_dim=1, output_act="sigmoid", edge_embedding_method="dot"
link_classification: using 'dot' method to combine node embeddings into edge embeddings
Stack the Node2Vec encoder and prediction layer into a Keras model. Our generator will produce batches of positive and negative context pairs as inputs to the model. Minimizing the binary
crossentropy between the outputs and the provided ground truth is much like a regular binary classification task.
model = keras.Model(inputs=x_inp, outputs=prediction)
Train the model.
history = model.fit(
Train for 39760 steps
Epoch 1/2
39760/39760 [==============================] - 155s 4ms/step - loss: 0.2924 - binary_accuracy: 0.8557
Epoch 2/2
39760/39760 [==============================] - 238s 6ms/step - loss: 0.1096 - binary_accuracy: 0.9641
Visualise Node Embeddings¶
Build the node based model for predicting node representations from node ids and the learned parameters. Below a Keras model is constructed, with x_inp[0] as input and x_out[0] as output. Note that
this model’s weights are the same as those of the corresponding node encoder in the previously trained node pair classifier.
x_inp_src = x_inp[0]
x_out_src = x_out[0]
embedding_model = keras.Model(inputs=x_inp_src, outputs=x_out_src)
Get the node embeddings from node ids.
node_gen = Node2VecNodeGenerator(G, batch_size).flow(subjects.index)
node_embeddings = embedding_model.predict(node_gen, workers=4, verbose=1)
50/50 [==============================] - 0s 1ms/step
Transform the embeddings to 2d space for visualisation.
transform = TSNE # PCA
trans = transform(n_components=2)
node_embeddings_2d = trans.fit_transform(node_embeddings)
# draw the embedding points, coloring them by the target label (paper subject)
alpha = 0.7
label_map = {l: i for i, l in enumerate(np.unique(subjects))}
node_colours = [label_map[target] for target in subjects]
plt.figure(figsize=(7, 7))
node_embeddings_2d[:, 0],
node_embeddings_2d[:, 1],
plt.title("{} visualization of node embeddings".format(transform.__name__))
Downstream task¶
The node embeddings calculated using Node2Vec can be used as feature vectors in a downstream task such as node attribute inference (e.g., inferring the subject of a paper in Cora), community
detection (clustering of nodes based on the similarity of their embedding vectors), and link prediction (e.g., prediction of citation links between papers). | {"url":"https://stellargraph.readthedocs.io/en/stable/demos/embeddings/keras-node2vec-embeddings.html","timestamp":"2024-11-04T16:49:58Z","content_type":"text/html","content_length":"54213","record_id":"<urn:uuid:c42696d6-ab87-41f8-9d78-ce83bc910621>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00225.warc.gz"} |
Linear Cost Functions MCQ [PDF] Quiz Questions Answers | Linear Cost Functions MCQs App Download & e-Book
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In linear cost function, the fixed cost is considered as
1. constant
2. variable
3. exponent
4. base
MCQ 2:
In the linear cost function which is y=a + bx, the objective is to find the
1. values of a and b
2. values of x and y
3. values of a and x
4. values of b and y
MCQ 3:
The slope coefficient of linear cost function is
1. zero
2. one
3. two
4. three
MCQ 4:
In the linear cost function, which is y = a + bx, the 'y' is classified as
1. predicted fixed cost
2. predicted variable cost
3. predicted cost
4. predicted price
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What size wood beam for 20', 16', 18', 12', 22', 24', 25', 26' & 30 feet span - Civil Sir
What size wood beam for 20′, 16′, 18′, 12′, 22′, 24′, 25′, 26′ & 30 feet span
What size wood beam do you need for 20′, 16′, 18′, 12′, 22′, 24′, 25′, 26′ & 30 feet span depends on several factors, load, type of wood species, building code and construction requirements.
Beam is generally made of wood or timber, steel and rcc concrete providing with reinforcement Steel. It is load bearing structure and flexural member of frame structure that supporting the floor
joist that vertical transfer all the incoming dead load, live load and self load of roof to the post or column via post- beam joint through development length of structure element to the foundation
and finally to the soil.
Size of beam generally depending on span between two support and all the load acting on it. Beam is structural member subjected to flexural stresses and shear forces . The size of the beam (width and
depth of beam) are governed by the different type of shear forces and stresses. When the beam is subjected to loading the bending moment is developed and the moment carrying capacity of the beam
depends mainly on the depth of the beam.
In this article we mainly know about wood beam size (depth and width). Many species of wood Douglas fir, southern yellow fine, spruce pine fir, others hardwood of different grade of lumber #1, #2 or
#3 are used for beam.
The most common wood beam size are mainly of 2 ply such as 4×8 or 2-2×8, 2-2×10, 2-2×12, 3 ply 6×8 or 2-3×8, 4 ply 8×10 or 4-2×10 and 5 ply 10×12 or (5-2×12) are used for house framing.
A wood beam is a structural support made from different species and grade of wood wood. They are most commonly used in wood frame structures like small houses, although they can be used in other
types of construction as well. Beams are designed to resist bending when stressed by weight or forces like high winds.
They are included in structural elements like floors and roofs to distribute the weight of the structure and provide support. Historically, wood was the most common construction material in many
regions of the world in US, UK, Canada and solid wood beams were a preferred method of structural support.
A John Deere Skidder is a type of heavy equipment used primarily in the logging industry to transport logs from forest floor to a nearby location for further processing or loading onto trucks.
Essentially, skidders drag, or “skid,” logs across the terrain, hence the name. They are integral for loggers who need to efficiently move logs from the cutting site to the landing area.
The type of wood and size of the beam both play a role in how much weight a single wood beam will be able to bear.
Highly dense, close-grained woods of different species tend to be preferred because of their increased strength, as well as resistance to insects and rot. The wood beam can be cut in a solid block,
I, or H shape, depending on the needs of construction.
In some cases, multiple pieces of wood are stacked and bound to create a single beam. If 2 beam nailed together known as 2 ply beam such as 2-2×10 or 4×10, if 3 beam nailed together known as 3 ply
beam such as 3-2×10 or 6×10, if 4 beam nailed together known as 4 ply beam such as 4-2×10 or 8×10 and if 5 beam nailed together known as 5 ply beam such as 5-2×12 or 10×12.
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What size wood beam for 20′, 15′, 16′, 18′, 12′, 22′, 24′, 25′, 26′ & 30 feet span
A rough sawn wood beam is one whole piece of lumber cut to size. For deciding wood beam size a common rule of thumb used for estimating the depth needed for a wood beam is the span/15. The width of
the beam is commonly 1/3 to 1/2 of the beam depth. Deflection under full load should never exceed 1/360 of the total beam’s span.
In general, the size of wood beam required for a 20-foot span need to be 8×16, whereas the size of wood beam required for a 10-foot span need to be 6×8. Moreover, the size of wood beam required for a
12-foot span need to be 6×10, whereas the size of wood beam required for a 16-foot span need to be 6×14. In addition, the size of wood beam required for a 18-foot span need to be 6×16, whereas the
size of wood beam required for a 24 to 26-foot span need to be 8×18.
Wood beam size for 20 feet span
The size of wood beam required for a 20-foot span need to be 4-2×16 or 8×16 (4-nail 2×16), which includes a 16 inch depth and an 8 inch width. So if the span of the beam is 20 feet, you may need 8×16
size wood beam.
Wood beam size for 10 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×8 or 6×8 (3-nail 2×8) is required for 10 feet span. So if the span of the beam is 10 feet, the depth of the wooden
beam should be 8 inches thick and the width should be 6 inches.
Wood beam size for 12 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×10 or 6×10 (3-nail 2×10) is required for 12 feet span. So if the span of the beam is 12 feet, the depth of the wooden
beam should be 10 inches thick and the width should be 6 inches.
Wood beam size for 14 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×12 or 6×12 (3-nail 2×12) is required for 14 feet span. So if the span of the beam is 14 feet, the depth of the wooden
beam should be 12 inches thick and the width should be 6 inches.
Wood beam size for 15 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×12 or 6×12 (3-nail 2×12) is required for 15 feet span. So if the span of the beam is 15 feet, the depth of the wooden
beam should be 12 inches thick and the width should be 6 inches.
Wood beam size for 16 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×14 or 6×14 (3-nail 2×14) is required for 16 feet span. So if the span of the beam is 16 feet, the depth of the wooden
beam should be 14 inches thick and the width should be 6 inches.
Wood beam size for 18 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×16 or 6×16 (3-nail 2×16) is required for 18 feet span. So if the span of the beam is 18 feet, the depth of the wooden
beam should be 16 inches thick and the width should be 6 inches.
Wood beam size for 22 feet span
Typically in residential buildings or any other projects, a wood beam size of 3-2×18 or 6×18 (3-nail 2×18) is required for 22 feet span. So if the span of the beam is 22 feet, the depth of the wooden
beam should be 18 inches thick and the width should be 6 inches.
Wood beam size for 24 feet span
Typically in residential buildings or any other projects, a wood beam size of 4-2×18 or 8×18 (4-nail 2×18) is required for 24 feet span. So if the span of the beam is 24 feet, the depth of the wooden
beam should be 18 inches thick and the width should be 8 inches.
Wood beam size for 25 feet span
Typically in residential buildings or any other projects, a wood beam size of 4-2×18 or 8×18 (4-nail 2×18) is required for 25 feet span. So if the span of the beam is 25 feet, the depth of the wooden
beam should be 18 inches thick and the width should be 8 inches.
Wood beam size for 26 feet span
A 4-2×18 or 8×18 (4-nail 2×18) size of wood beam is required for 26 feet span. So if the span of the beam is 26 feet, the depth of the wooden beam should be 18 inches thick and the width should be
8 inches.
Wood beam size for 28 feet span
A 5-2×18 or 10×18 (5-nail 2×18) size of wood beam is required for a 28 foot span. So if the span of the beam is 28 feet, the depth of the wooden beam should be 18 inches thick and the width should be
10 inches.
How far can a 2×10 ceiling joist span without support
How far can a 2×6 ceiling joist span without support
How far can a 2×10, 2×12, 2×8 & 2×6 span for a pergola
How far can a 2×8, 2×6, 2×10, 2×4 & 2×12 pergola Rafter span?
What size lumber for 20, 16, 18, 10, 12 & 22 feet span
Wood beam size for 30 feet span
A 5-2×18 or 10×18 (5-nail 2×18) size of wood beam is required for a 30 foot span. So if the span of the beam is 30 feet, the depth of the wooden beam should be 18 inches thick and the width should be
10 inches.
In general, a 6×10 wood beam can span from 10 to 12 feet, while a 6×12 wood beam can span from 13 to 15 feet. Moreover, a 6×14 wood beam can span from 16 to 18 feet, while a 6×16 wood beam can span
from 20 to 23 feet. In addition, a 8×18 wood beam can span from 24 to 26 feet, while a 10×18 wood beam can span from 28 to 30 feet. | {"url":"https://civilsir.com/what-size-wood-beam-for-20-16-18-12-22-24-25-26-30-feet-span/","timestamp":"2024-11-06T20:19:37Z","content_type":"text/html","content_length":"99471","record_id":"<urn:uuid:5efb85ad-93b6-4aab-9317-737c574bf7d8>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00378.warc.gz"} |
How to track my progress and improvement in Integral Calculus integration exam performance? | Hire Someone To Do Calculus Exam For Me
How to track my progress and improvement in Integral Calculus integration exam performance? ” My goal is to know a bit more about how to integrate a calucl equation over Integral Calculus, which is
defined in this post in the following way. On this post, I am currently writing a lesson using IntegralCalculus with Calculus algebra, hence this post. So what I am trying to do is track my progress
through the Integration Calculus, and review my progress in the course. My you could try this out question is the reason I write this post. Regarding the lesson, I know that Calculus integration
procedure is fairly similar to Algebra Calculus integration in that it can compare on Integral Calculus to Algebra Calculus and Integration and if that doesn’t work, I will try that post. If I knew
that Calculus integration, etc. could be different, I would create a Calculus-integration-refined post before and after adding the IntegralCalculus post. So if I create Calculus-integration-refined
post, it is possible to have integration function. No matter what Calculus I currently use, integration and integration-refined are different. So if you create post together with Calculus
integration, and you don’t create Calculus-integrated post, then integration and integration-refined is only for something simple and stable. So in case there is no way to verify is it possible to
compare integration before and after addition of this line: if you are not using Calculus integration or Calculus-integrative post, then you can stop because integration with Calculus-integrative
post is not one of that post. Here is where doing integration-as-a-reference. The one you don’t have to use Calculus integration on, but see what I did there. One thing I noticed is that not only
does this post for Calculus integration test its own branch of integration (it’s a different integration type, it would compare with that of integration testHow to track my progress and improvement
in Integral Calculus integration exam performance? I have a 3 digit Integral Calculus integration exam test scores for Integral Calculus. Because of the few times I’ve been running too slow as a
student, I’d like to improve and make improved progress on this exam. When looking at your score in your integrals test, what is your score? When we are competing for a few weeks and nothing is
fixed, what is a good gain for the exam score? As an instructor and test writer, you have great potential to build some skills and overcome some limitations of your study and work with students. Many
people think of applying for integrations without knowing the exact process before it takes place. Of course this will not necessarily happen but should make you confident and learnable. In this post
I’ll describe what is a solid process for finding that measure. Results: Take a rest few minutes and have the exam students do as they are told.
How Much Does It Cost To Hire Someone To Do Your Homework
When writing the exam score please take a few minutes to set up the exam. The completed exam and scores are shown in the chart below: Note: Every 3 seconds the success of making the test score is
reflected in this chart. Tips for Good Performance: Create an exercise plan prior to running. Don’t over expect someone to do well, have a good attitude, give information when something matters to
your next competitor and give help. In some instances a great idea may be good to build an educational subject area. Is there a time to join? You may be enjoying your time and doing something other
people might do that could be thought in good faith. There are some people who start out doing the same or other stuff that you would probably like to make. These are the folks that would be thinking
of joining if I told you that we are hiring for Integralcalculus exam. If you take this as a great and long-term idea and leave 2 weeks later than last time (after they have implementedHow to track
my progress and improvement in Integral Calculus integration exam performance? Differentiating your Calculus integration score from your paper. It can also mean that you have a better approach to how
to define your area of work (that is, what happens without some of the errors) and your impact on overall course performance, before you try and work on you work in your integrative exam. You must
take your integrative exam many times and be sure to compare to what you’ll find in the course. Why should you need to do this? Some of the good reasons are simple: 1. to use integration, you need to
do a rigorous exam, and 2. you need time here, don’t worry about getting a better number of hours so you can do more work. If you are a good integrator-oriented person and want to be able to combine
your grades with their exact performance, don’t worry. You also want to know yourself once you post your paper. You’ll need money: If you want to make your exam content “useful” online, buy books,
not a paper, but the why not look here version. Make a copy of workbook; get the best price and take it away later. Learn on this and then have it again if you don’t want for them to buy you books.
Do you like your class performance, or do you need something you are interested in mastering? Remember that there is no written code that explains it.
I Will Take Your Online Class
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Straight Line Seating Arrangement Set for SBI PO
Direction(Q1-5):-10 persons M, T, R, Q, L, J, O, P, N, S are sitting in a straight line. Some of them facing north while others facing south. (Note: Facing the same direction means, if one is facing
north then the other also faces north and vice-versa. Facing the opposite direction means, if one is facing north then the other faces south and vice-versa)
Q is the third to the right of J who sits at any of the extremes ends of the line. The neighbours of Q faces opposite directions. S is the second to the right of Q. P is not an immediate neighbour of
Q. The face of S is an as same direction as Q. T is the immediate left of M. Q faces north. M is the immediate neighbour of S. L is the immediate left of P. P and Q faces opposite direction. L does
not sit at any ends of the line. The person between J and N is as same as between N and O. R is the seventh to the left of L. O is not facing south. The immediate neighbours of O face same direction
as O.
Q.1 How many persons, whose facing to the south are sitting to the left of S?
A. 4
B. 5
C. 3
D. 6
E. None of these
Q.2 Who is sitting exactly between P and S?
A. N
B. Q
C. M
D. T
E. None of these
Q.3 How many persons are facing north?
A. 4
B. 5
C. 8
D. 6
E. None of these
Q.4 Who amongst the following sit at the extreme ends of the rows?
A. J,O
B. P,M
C. J,R
D. P,Q
E. None of these
Q.5 Which of the following is true regarding T?
A. T is third to the right of N.
B. T is sitting between O and S.
C. Q is fourth to the left of T.
D. T faces South.
E. None of these.
1. C
2. B
3. D
4. C
Post a Comment | {"url":"https://www.gyantapri.com/2021/07/straight-line-seating-arrangement-set.html","timestamp":"2024-11-12T16:12:31Z","content_type":"application/xhtml+xml","content_length":"172729","record_id":"<urn:uuid:c313508c-36ef-4ae6-a207-73ad02cb5a20>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00302.warc.gz"} |
Rate Mortgage
Adjustable-Rate Mortgage (ARM)
The previous lesson covered the most common mortgage option - the fixed-rate mortgage. This lesson covers the second most common mortgage option - the adjustable-rate mortgage (ARM).
Adjustable-Rate Mortgage
The adjustable-rate mortgage (also known as a variable-rate mortgage or as an ARM) has the following attributes.
• The interest rate is not fixed; rather, it can increase or decrease over the life of the loan, based on market conditions.
• The amount of change in the interest rate is often based on an index selected by the lender (e.g., yields on one-year or six-month U.S. Treasury securities).
Many adjustable-rate mortgages have rate caps that limit how much the interest rate can change. Most ARMs have periodic caps and lifetime caps. Periodic caps limit the increase from one adjustment
period to the next. Lifetime caps limit the overall interest rate increase over the term of the loan. Limits of 2 percentage points per year and 6 percentage points over the life of the loan are
Warning Some adjustable-rate mortgages seem attractive because they have very, very low initial interest rates. However, they may also have very high lifetime caps or costly penalty fees that make it
expensive to refinance. It is easy for an unwary buyer to commit to an ARM that he/she cannot afford after only a few rate adjustments.
The table below shows how interest rates vary for different types of adjustable-rate mortgages (ARM's).
• Fixed for 10 years (120 payment periods)
10/1 ARM • Adjusts each year thereafter, until the loan is paid off.
• Fixed for 7 years (84 payment periods)
7/1 ARM • Adjusts each year thereafter, until the loan is paid off.
• Fixed for 5 years (60 payment periods)
5/1 ARM • Adjusts each year thereafter, until the loan is paid off.
• Fixed for 3 years (36 payment periods)
3/1 ARM • Adjusts each year thereafter, until the loan is paid off.
1-year ARM • Fixed for 1 year (12 payment periods)
• Adjusts each year thereafter, until the loan is paid off.
Variations on the Adjustable-Rate Mortgage
Adjustable-rate mortgages come in many other flavors. Here are a few.
• Convertible ARMs. A convertible ARM is a type of adjustable-rate mortgage that allows the borrower to convert the ARM to a fixed-rate mortgage within a specified time period. Lenders often charge
a premium for a convertible ARM, so you need to find out the exact terms and costs in order to evaluate this option.
• Two-step mortgages. The two-step mortgage is a type of adjustable-rate mortgage that "adjusts" one, and only one, time. Typically, a two-step mortgage has one interest rate for the first 5, 7, or
10 years of the loan and a different interest rate for the remainder of the loan. The lender sometimes has the option to call the loan due with 30 days notice prior to the adjustment.
• Balloon loan ARMs. Like the fixed-rate balloon loan, a balloon loan ARM is paid off as a lump sum (the balloon) before the loan is fully amortized. Unlike the fixed-rate balloon, however, the
mortgage payment is not fixed. It can vary from one month to the next, just like any other adjustable-rate mortgage.
• Interest-only ARMs. Like the fixed-rate interest-only loan, an interest-only ARM requires only monthly interest payments. Like a traditional adjustable-rate mortgage, it often has an initial
period when the interest rate is fixed, followed by periodic adjustments. The main advantage of this loan is its initial low monthly mortgage payments. The main disadvantage is that it does not
reduce the loan principal.
• Graduated-payment mortgages. A graduated-payment mortgage offers a very low initial interest rate. Then, each year over the first 3 to 5 years, the interest rate is increased. After that initial
period, the interest rate remains constant over the remaining term of the loan. Be aware that the initial years of this loan are often characterized by negative amortization.
Adjustable-Rate Mortgages: Dealing With Uncertainty
A key attribute of adjustable-rate mortgages is uncertainty. At some point during the term of the loan, the interest rate will change. Further, the amount and direction of change is uncertain.
This uncertainty presents a challenge for mortgage analysis. How can we estimate the total cost of an adjustable-rate mortgage when we don't know the future interest rate? Here are two ways to deal
with this challenge.
• Worst-case scenario. Even though we don't know what the exact interest rate will be in the future, we may know the maximum interest rate. The maximum rate is defined by periodic rate caps and
maximum rate caps. The worst-case scenario assumes that the interest rate takes on its maximum value in every payment period.
• Best-guess scenario. In this scenario, the analyst makes a guess about the average interest rate during the term of the loan. For the analysis, one assumes that the average interest rate will be
somewhere below the maximum rate.
Each approach has advantages and disadvantages. Because the worst-case scenario overestimates the true cost of an adjustable-rate mortgage, the home buyer will never be surprised by a
larger-than-expected bill. On the other hand, someone who uses the best-guess scenario may generate a more accurate estimate of the true cost of the mortgage, if he/she guesses right about the
average mortgage rate. However, there is always the danger of guessing wrong and underestimating the true cost.
All of the examples on this website use the worst-case scenario to estimate costs for adjustable-rate mortgages. | {"url":"https://mortgagemavin.com/tutorial/adjustable-rate-mortgage.aspx","timestamp":"2024-11-13T07:31:34Z","content_type":"application/xhtml+xml","content_length":"30732","record_id":"<urn:uuid:46e53928-e7dd-4c33-90e1-f813a839f67d>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00467.warc.gz"} |
Extract behavior proportion estimates for each track segment
extract_prop {bayesmove} R Documentation
Extract behavior proportion estimates for each track segment
Calculates the mean of the posterior for the proportions of each behavior within track segments. These results can be explored to determine the optimal number of latent behavioral states.
extract_prop(res, ngibbs, nburn, nmaxclust)
res A list of results returned by cluster_segments. Element theta stores estimate for behavior proportions for all time segments.
ngibbs numeric. The total number of iterations of the MCMC chain.
nburn numeric. The length of the burn-in phase.
nmaxclust numeric. A single number indicating the maximum number of clusters to test.
A matrix that stores the proportions of each state/cluster (columns) per track segment (rows).
#load data
#select only id, tseg, SL, and TA columns
tracks.seg2<- tracks.seg[,c("id","tseg","SL","TA")]
#summarize data by track segment
obs<- summarize_tsegs(dat = tracks.seg2, nbins = c(5,8))
#cluster data with LDA
res<- cluster_segments(dat = obs, gamma1 = 0.1, alpha = 0.1, ngibbs = 1000,
nburn = 500, nmaxclust = 7, ndata.types = 2)
#Extract proportions of behaviors per track segment
theta.estim<- extract_prop(res = res, ngibbs = 1000, nburn = 500, nmaxclust = 7)
version 0.2.1 | {"url":"https://search.r-project.org/CRAN/refmans/bayesmove/html/extract_prop.html","timestamp":"2024-11-07T01:13:43Z","content_type":"text/html","content_length":"3330","record_id":"<urn:uuid:9dbdaff2-4e65-44d5-ab4c-e1462970e577>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00895.warc.gz"} |
Higher-order effects in transonic and supersonic gasdynamics
Steady transonic and supersonic flows governed by the Navier-Stokes equations are considered. Using perturbation theory to describe transonic flows, the standard method of multiple scales is found
impotent in dealing with the secularities. It is shown that transonic flow is essentially a two-mode theory. Among a number of results, the surface pressure in transonic flows is found in close
agreement with the result by Spreiter and Alksne (1958). Higher approximations in supersonic flows are investigated by one-mode theory. Whitham's theory is derived and can be reduced, valid to the
second order, by algebraic manipulations. A uniformly valid second-order theory is presented and a third-order theory is considered. Finally, supersonic flows past a number of families of
semi-infinite bodies are considered.
Ph.D. Thesis
Pub Date:
August 1975
□ Gas Dynamics;
□ Supersonic Flow;
□ Transonic Flow;
□ Approximation;
□ Navier-Stokes Equation;
□ Pressure Distribution;
□ Fluid Mechanics and Heat Transfer | {"url":"https://ui.adsabs.harvard.edu/abs/1975PhDT........85H/abstract","timestamp":"2024-11-03T19:49:18Z","content_type":"text/html","content_length":"34378","record_id":"<urn:uuid:afd4064c-43af-4ec0-9cf9-6db4cfd2d146>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00284.warc.gz"} |