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# 6

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This article is about the mathematical number. For other uses, see 6 (disambiguation).
 ← 5 6 7 →
Cardinal six
Ordinal 6th
(sixth)
Numeral system senary
Factorization 2 × 3
Divisors 1, 2, 3, 6
Roman numeral VI
Roman numeral (unicode) Ⅵ, ⅵ, ↅ
Greek prefix hexa-/hex-
Latin prefix sexa-/sex-
Binary 1102
Ternary 203
Quaternary 124
Quinary 115
Senary 106
Octal 68
Duodecimal 612
Hexadecimal 616
Vigesimal 620
Base 36 636
Greek στ (or ΣΤ or ς)
Arabic & Kurdish ٦
Persian ۶
Urdu
Amharic
Bengali
Chinese numeral 六，陆
Devanāgarī
Hebrew ו (Vav)
Khmer
Thai
Telugu
Tamil
Saraiki ٦

6 (six /ˈsɪxs/) is the natural number following 5 and preceding 7.

The SI prefix for 10006 is exa- (E), and for its reciprocal atto- (a).

## In mathematics

6 is the smallest positive integer which is neither a square number nor a prime number. Six is the second smallest composite number; its proper divisors are 1, 2 and 3.

Since six equals the sum of its proper divisors, six is the smallest perfect number, Granville number, and ${\displaystyle {\mathcal {S}}}$-perfect number.[1][2]

As a perfect number:

• 6 is related to the Mersenne prime 3, since 21(22 − 1) = 6. (The next perfect number is 28.)
• 6 is the only even perfect number that is not the sum of successive odd cubes.[3]
• As a perfect number, 6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one number; the square number, 25.

Six is the only number that is both the sum and the product of three consecutive positive numbers.[4]

Unrelated to 6 being a perfect number, a Golomb ruler of length 6 is a "perfect ruler."[5] Six is a congruent number.[6]

Six is the first discrete biprime (2 × 3) and the first member of the (2 × q) discrete biprime family.

Six is the smallest natural number that can be written as the sum of two positive rational cubes which are not integers: ${\displaystyle 6=\left({\frac {17}{21}}\right)^{3}+\left({\frac {37}{21}}\right)^{3}.}$ Others up to 100 are: 7, 9, 12, 13, 15, 17, 19, 20, 22, 26, 28, 30, 31, 33, 34, 35, 37, 42, 43, 48, 49, 50, 51, 53, 56, 58, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 75, 78, 79, 84, 85, 86, 87, 89, 90, 91, 92, 94, 96, 97, 98. (sequence A228499 in the OEIS)

Six is a unitary perfect number,[7] a harmonic divisor number[8] and a superior highly composite number, the last to also be a primorial. The next superior highly composite number is 12. The next primorial is 30.

5 and 6 form a Ruth-Aaron pair under either definition.

There are no Graeco-Latin squares with order 6. If n is a natural number that is not 2 or 6, then there is a Graeco-Latin square with order n.

The smallest non-abelian group is the symmetric group S3 which has 3! = 6 elements.

S6, with 720 elements, is the only finite symmetric group which has an outer automorphism. This automorphism allows us to construct a number of exceptional mathematical objects such as the S(5,6,12) Steiner system, the projective plane of order 4 and the Hoffman-Singleton graph. A closely related result is the following theorem: 6 is the only natural number n for which there is a construction of n isomorphic objects on an n-set A, invariant under all permutations of A, but not naturally in one-to-one correspondence with the elements of A. This can also be expressed category theoretically: consider the category whose objects are the n element sets and whose arrows are the bijections between the sets. This category has a non-trivial functor to itself only for n = 6.

6 similar coins can be arranged around a central coin of the same radius so that each coin makes contact with the central one (and touches both its neighbors without a gap), but seven cannot be so arranged. This makes 6 the answer to the two-dimensional kissing number problem. The densest sphere packing of the plane is obtained by extending this pattern to the hexagonal lattice in which each circle touches just six others.

A cube has 6 faces

6 is the largest of the four all-Harshad numbers.

A six-sided polygon is a hexagon, one of the three regular polygons capable of tiling the plane. Figurate numbers representing hexagons (including six) are called hexagonal numbers. Because 6 is the product of a power of 2 (namely 21) with nothing but distinct Fermat primes (specifically 3), a regular hexagon is a constructible polygon.

Six is also an octahedral number.[9] It is a triangular number and so is its square (36).

There are six basic trigonometric functions.

There are six convex regular polytopes in four dimensions.

Six is the four-bit binary complement of number nine (6 = 01102 and 9 = 10012).

The six exponentials theorem guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.

All primes above 3 are of the form 6n ± 1 for n ≥ 1.

### In numeral systems

Base Numeral system Representation
2 binary 110
3 ternary 20
4 quaternary 12
5 quinary 11
6 senary 10
over 6 (decimal, duodecimal, hexadecimal, etc.) 6

In bases 10, 15 and 30, 6 is a 1-automorphic number.

### List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
6 × x 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 300 600 6000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6 ÷ x 6 3 2 1.5 1.2 1 0.857142 0.75 0.6 0.6 0.54 0.5 0.461538 0.428571 0.4
x ÷ 6 0.16 0.3 0.5 0.6 0.83 1 1.16 1.3 1.5 1.6 1.83 2 2.16 2.3 2.5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
6x 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
x6 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809

## Greek and Latin word parts

### Hexa

Hexa is classical Greek for "six". Thus:

### The prefix sex-

Sex- is a Latin prefix meaning "six". Thus:

• Senary is the ordinal adjective meaning "sixth"
• People with sexdactyly have six fingers on each hand
• The measuring instrument called a sextant got its name because its shape forms one-sixth of a whole circle
• A group of six musicians is called a sextet
• Six babies delivered in one birth are sextuplets
• Sexy prime pairs - Prime pairs differing by six are sexy, because sex is the Latin word for six.[10]

## Evolution of the glyph

The evolution of our modern glyph for 6 appears rather simple when compared with that for the other numerals. Our modern 6 can be traced back to the Brahmins of India, who wrote it in one stroke like a cursive lowercase e rotated 90 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Ghubar Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.[11]

On the seven-segment displays of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a 'b' is not practical.

Just as in most modern typefaces, in typefaces with text figures the 6 character usually has an ascender, as, for example, in .

This numeral resembles an inverted 9. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.

## In music

A standard guitar has 6 strings

### In instruments

• A standard guitar has 6 strings
• Most woodwind instruments have 6 basic holes or keys (e.g., bassoon, clarinet, pennywhistle, saxophone); these holes or keys are usually not given numbers or letters in the fingering charts

### In music theory

• There are 6 whole tones in an octave.
• There are 6 semitones in a tritone.

### In works

• "Six geese a-laying" were given as a present on the sixth day in the popular Christmas carol, "The Twelve Days of Christmas."
• Divided in six arias, Hexachordum Apollinis is generally regarded as one of the pinnacles of Johann Pachelbel's oeuvre.
• The theme of the sixth album by Dream Theater, Six Degrees Of Inner Turbulence, was the number six: the album has six songs, and the sixth song — that is, the complete second disc — explores the stories of six individuals suffering from various mental illnesses.
• Aristotle gave six elements of tragedy, the first of which is Mythos.

See also 666.

## In science

### Chemistry

The cells of a beehive are 6-sided

### Medicine

• There are 6 tastes in traditional Indian Medicine called Ayurveda: sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body
• Phase 6 is one of six pandemic influenza phases

### Physics

In the Standard Model of particle physics, there are 6 types of quarks and 6 types of leptons
• In the Standard Model of particle physics, there are 6 types of quarks and 6 types of leptons
• In statistical mechanics, the six-vertex model has 6 possible configurations of arrows at each vertex
• There are six colors in the RGB color wheel: (primary) red, blue, green, (secondary) cyan, magenta, and yellow. (See Tertiary color)

## References

1. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 11. ISBN 978-1-84800-000-1.
2. ^ "Granville number". OeisWiki. The Online Encyclopedia of Integer Sequences. Archived from the original on 29 March 2011. Retrieved 27 March 2011.
3. ^ David Wells, The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books (1987): 67
4. ^ Peter Higgins, Number Story. London: Copernicus Books (2008): 12
5. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 72
6. ^ "Sloane's A003273 : Congruent numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
7. ^ "Sloane's A002827 : Unitary perfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
8. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
9. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
10. ^ Chris K. Caldwell; G. L. Honaker Jr. (2009). Prime Curios!: The Dictionary of Prime Number Trivia. CreateSpace Independent Publishing Platform. p. 11. ISBN 978-1448651702.
11. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.66
12. ^ Mason, Robert (1983). Chickenhawk. London: Corgi Books. p. 141. ISBN 978-0-552-12419-5.
• The Odd Number 6, JA Todd, Math. Proc. Camb. Phil. Soc. 41 (1945) 66—68
• A Property of the Number Six, Chapter 6, P Cameron, JH v. Lint, Designs, Graphs, Codes and their Links ISBN 0-521-42385-6
• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 67 - 69


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### Two Dice

Find all the numbers that can be made by adding the dots on two dice.

### Biscuit Decorations

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

### Writing Digits

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

# Number Lines

##### Stage: 1 Challenge Level:

It might help to have a number line of your own to work with.

You could print off this sheet of number lines.

If Leah did a jump of five to get to $9$, where did she start?
How could you find out?
So how big was the jump she had to do to get there from zero?

format: plain


text:
《1　前言》

1　前言

《2　无线信号室内传播对部署模型的影响》

2　无线信号室内传播对部署模型的影响

《图1》

Fig.1　Ichnography of the testing room

《表1》

Table 1　Test results

《图2》

Fig.2　Variance of received signal strength with T-R distance in different antenna height

《图3》

Fig.3　Relation between boundary coverage probability and T-R distance

《3　室内无线传感器网络部署方案》

3　室内无线传感器网络部署方案

1）尽可能实现全部范围内的完全覆盖；

2）在保证节点通信连通的前提下，尽可能减少节点数目，以降低成本，减少不必要的数据采集量。

《图4》

Fig.4　Relation between effective communication area and sensing area

《图5》

Fig.5　Sensing collapsar (a) ＆ Modification of Sensing Collapsar (b)

《4　计算与实验结果》

4　计算与实验结果

《表2》

Table 2　Parameter of simulation

《表3》

Table 3　Effective communication range

《图6》

Fig.6　Performance comparisons of different approaches

《图7》

Fig.7　Variance of sensing parameter with awful coverage area

《5　结语》

5　结语


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# Liters to Pints(US,liq)

Not Reviewed
"Pints" =
Tags:
Rating
ID
JustinLiller.Liters to Pints(US,liq)
UUID
66c1b79f-53c7-11e4-a9fb-bc764e2038f2

The Liters to Pints utility computes the number of pints in any quantity of liters. In 1 pint, there is about 1/2 of a liter.

INPUTS:

The following describes the inputs to this equation:

• Liters = amount of volume in liters

EXAMPLES:

3 Liters = (3) * 2.113436 = 6.34013 Pints


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## The algebra of fuzzy logic

12Citations

#### Abstract

In the following, human thinking based on premises with no complete truth value is reviewed for controlling the algebra of fuzzy sets operations. Assuming a system may be developed in this sphere, it should be considered as the algebra of fuzzy sets, as the same algebra is satisfied by classical logic and sets. As will be proved, this algebra is not a lattice and consequently the Zadeh definitions do not constitute an adequate representation. The binary operations of my algebra are "interactive" types. An axiom system is given that, in my opinion, is the foundation of the conception, adequately and without redundancy. The agreement of the theorems deduced from the axiom system with the intuitive expectations is shown. A special arithmetical structure satisfying this algebra is given, and the relation between this structure and the theory of probability is analyzed. Adapting a process of classical logics, fuzzy quantifiers are defined on the basis of the operations of propositional algebra. A "qualifier" is also defined. The qualifier is functional; applying it to Ax we get the statement "usually Ax" s a middle cource between the statements "at least once Ax" and "always Ax". The concept of entailment of fuzzy logics is introduced. This concept is an innovative generalization of the classical deduction theory, opposite to the concept of entailment of classical multi-valued logics. An important error of the abbreviated system of notation of the fuzzy theory [e.g. m(x, A v B)] appears: the functional type operations (e.g. quantifiers) cannot be interpreted in propositional calculus. Therefore a new system of symbols is proposed in this paper. ?? 1978.

#### Cite

CITATION STYLE

APA

Albert, P. (1978). The algebra of fuzzy logic. Fuzzy Sets and Systems, 1(3), 203–230. https://doi.org/10.1016/0165-0114(78)90005-2

Save time finding and organizing research with Mendeley


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# CS+X at Caltech: Disrupting science and engineering with computational thinking

It seems like I’ve been waiting forever to make this post!  Back in the fall, I helped to organize an Alumni College at Caltech centered around the theme of “CS+X”.  Now, I’m very excited to announce that the videos from the event are up!

What is an alumni college you ask?  Well, instead a homecoming game or something like that, we get alumni back to Caltech by promising a day of research talks, well really thinks like TED talks!  So, Alumni College focuses on a different theme each year, and then does a day of provocative talks on that topic.  This year the theme was “Disrupting Science and Engineering with computational thinking” i.e., the disruptive power of CS+X.

As I’ve written about before, we view “CS+X” as what makes Caltech’s approach to computer science so distinctive compared to other schools.  We pride ourselves on inventing fields and then leaving them for others once they’re popular so that we can invent the next field.  So, “seeding fields and then ceding them”…

In any case, the alumni college was a day filled with talks on CS+X from researchers at Caltech that are leading new fields…  We covered CS+Astronomy, CS+Physics, CS+Biology, CS+Economics, CS+Chemistry, CS+Energy, and so on…

# Beyond worst-case analysis

Well, last week was the final workshop in the semester-long “Algorithms & Uncertainty” program that I helped to organize at the Simons institute.  There are a few weeks of reading groups / seminars / etc. left, but the workshop marks the last “big” event.  It’s sad to see the program wrapping up, though I’m definitely happy that I will be spending a lot less time on planes pretty soon — I’ve been flying back and forth every week!

The last workshop was on “Beyond worst-case analysis” and the organizers (Avrim Blum, Nir Ailon, Nina Balcan, Ravi Kumar, Kevin Leyton-Brown, Tim Roughgarden) did a great job of putting together a really unique program.  Since there’s not “one way” to go beyond worst-case, the week included a huge array of interesting ways to get results beyond what is possible from worst-case analysis, whether it be learning commonalities of different types of instances, semi-random / smoothed analysis models, or extracting features that enable learning what algorithmic approach to use.

If you’re interested in getting a broad overview of the approaches, I highly recommend watching Avrim’s introductory talk, which gave a survey of a ton of different approaches for going “beyond worst-case” that have received attention recently.  Tim also has a great course on the topic that is worth checking out…

My own contribution was the final talk of the week, which gave an overview of our work on how to use properties of prediction noise to help design better online optimization algorithms.  The idea is that predictions are crucial to almost all online problems, but we don’t really understand how properties of prediction error should influence algorithm design.  Over the last few years we’ve developed some models and results that allow initial insights into, e.g., how correlation structure in prediction errors changes the “optimal” algorithm form.  Check out the video for more details!

# Algorithms in the Field

One of the great new NSF programs in recent years is the introduction of the “Algorithms in the Field” program, which is a joint initiative from the CCF, CNS, and IIS divisions in CISE.  It’s goal is almost a direct match with what I try to do with my research:  it “encourages closer collaboration between (i) theoretical computer science researchers [..] and (ii) other computing and information researchers [..] very broadly construed”.  The projects it funds are meant to push the boundaries of theoretical tools and apply them in a application domain.

Of course this is perfectly suited to what we do in RSRG at Caltech!  We missed the first year of the call due to bad timing, but we submitted this year and I’m happy to say it was funded (over the summer when I wasn’t blogging)!

The project is joint with Steven Low, Venkat Chandrasekaran, and Yisong Yue and has the (somewhat generic) title “Algorithmic Challenges in Smart Grids: Control, Optimization, and Learning.

For those who are curious, here’s the quick and dirty summary of the goal…taken directly from the proposal.

# Data Markets in the Cloud

Over the last year, while I haven’t been blogging, one of the new directions that we’ve started to look at in RSRG is “data markets”.

“Data Markets” is one of those phrases that means lots of different things to lots of different people.  At its simplest, the idea is that data is a commodity these days — data is bought and sold constantly. The challenge is that we don’t actually understand too much about data as an economic good.  In fact, it’s a very strange economic good and traditional economic theory doesn’t apply…

# Finding Any Nontrivial Coarse Correlated Equilibrium Is Hard

One of the things one might hope to get from an equilibrium concept in a game is that it might plausibly describe or predict behavior in the real world. That’s one reason negative results suggesting that certain equilibria can’t be computed efficiently are so interesting—they call those equilibrium concepts into question. Of course, there’s much more to it than that, but the existence of efficient algorithms (or, even better, simple, distributed dynamics) for computing equilibria is a big selling point for a solution concept.

In that sense, correlated equilibria (CE) and coarse correlated equilibria (CCE) are much more promising than Nash equilibria (NE). Even in games with many players, there exist a number of natural dynamics that quickly converge to these solution concepts. In particular, these dynamics induce efficient computation of approximate CE and CCE in multiplayer games; by contrast, computation of approximate Nash equilibria is computationally hard in multiplayer games.

If you aren’t so familiar with CEs and CCEs, you can think of them as very similar to Nash equilibria, in that they also consist of a distribution over players’ action profiles at which no player can benefit by unilateral deviation, and hence represent stable choices of distributions over player actions. The big difference is that, whereas a Nash equilibrium is defined to be a product of independent distributions over actions (one for each player); correlated and coarse correlated equilibria are general (joint) probability distributions—CEs and CCEs allow players to correlate their choices of actions. For the purposes of this blog post, let’s not worry too much about the distinction between CEs and CCEs. Notice that CE and CCE are more general than NE—every NE is a CE (CCE), but the converse is not true. So it makes sense that one might be able to compute a CE efficiently, even in settings where computing a NE is hard.

Beyond computation of equilibria, another significant thread of research in algorithmic game theory has been the study of the quality of equilibria, often as measured by the social welfare of the equilibrium or its ratio to the social welfare of the socially optimal outcome (c.f. the extensive literature on the price of anarchy (PoA)). Given that we know it is possible to efficiently compute CE and CCE, it is natural to ask how good are the equilibria we can efficiently compute? For example, do existing efficient dynamics find the best such equilibria, or at least ones that approximately optimize the social welfare? Since the gap between the worst and the best equilibria (CE or CCE), in terms of social welfare, can be large in natural games, it is interesting to understand if there exist efficient dynamics or algorithms that avoid—at least to some extent—the bad outcomes.

In their notable work, Papadimitriou and Roughgarden [PR] show that determining a socially optimal CE is NP-hard, in a number of succinct multiplayer games*. (What’s socially optimal? The equilibrium that maximizes the total (or average) welfare of the players.) This result intuitively follows from the fact that determining an action profile with maximum welfare—i.e., solving the problem of welfare optimization even without equilibrium constraints—is NP-hard in general. The hardness result of [PR]  leaves open the question of computing near-optimal CE/CCE, i.e., whether there exist efficient algorithms that compute CE/CCE with welfare at least, say, alpha times the optimal, for a nontrivial approximation ratio alpha < 1.

In recent work with Sid Barman, a postdoc at Caltech, we consider exactly this question. We establish that, unless P=NP, there does not exist any efficient algorithm that computes a CCE with welfare better than the worst possible CCE, in succinct multiplayer games*. We also establish similar hardness results for computing equilibria under the egalitarian objective or Pareto-optimality.

Analogous hardness results hold for CE. A classical interpretation of a CE is in terms of a mediator who has access to the players’ payoff functions and who draws outcomes from a correlated equilibrium’s joint distribution over player actions and privately recommends the corresponding actions to each player. The equilibrium conditions ensure that no player can benefit in expectation by unilaterally deviating from the recommended actions. Therefore, the problem we study here is exactly the computational complexity of the problem that a mediator faces if she wishes to maximize social welfare.

We also extend the hardness result to approximate CE and CCE. Therefore, while one can efficiently compute an approximate CE/CCE in succinct multiplayer games, one cannot provide any nontrivial welfare guarantees for the resulting equilibrium (unless P=NP).

In addition, we show that this hardness result also holds specifically for potential games (generally considered to be a very tractable class of games), and persists even in settings where the gap between the best and worst equilibrium is large.

We also have some positive results, but I think the negative ones are the most interesting—this says that those appealing dynamics that compute CE/CCE can’t be guaranteed to be finding anything other than the worst equilibrium. To me, that’s some surprising bad news. One silver lining is that this provides new motivation for studying the price of anarchy (the quality of the worst equilibrium) for CE/CCE, since generally that’s the best thing we can hope to compute.

*Technical Aside (succinct games): In general multiplayer games the size of the normal form representation, $N$, is exponentially large in the number of players; one can compute a CE/CCE that optimizes a linear objective by solving a linear program of size polynomial in $N$, and hence the computational complexity of equilibrium computation is not interesting for general games. However, most games of interest—such as graphical games, polymatrix games, congestion games, local effect games, network design games, anonymous games, and scheduling games—admit a succinct representation (wherein the above-mentioned linear program can be exponentially large in the size of the representation), and hence it is such succinctly representable games that we (and previous works) study.

[PR] PAPADIMITRIOU, C. H. AND ROUGHGARDEN, T. 2008. Computing correlated equilibria in multi-player games. Journal of the ACM (JACM) 55, 3, 14.

# Solution to puzzle: produce or learn?

This post is a solution to the puzzle in the last post.

The optimal strategy has a very simple form: there is a time ${t^* \in \{1, \dots, T\}}$ such that (${^*}$ denotes optimal quantities)

• only learn (${l^*(t)=1}$) before time ${t^*}$;
• only produce (${p^*(t)=1}$) from time ${t^*}$ on.

# Another puzzle: produce or learn?

When our kids were small, they were in sports teams (basketballs, baseball, soccer, …).  Their teams would focus on drills early in the season, and tournaments late in the season.  In violin, one studies techniques (scales, etudes, theory, etc.) as well as musicality (interpretation, performance, etc).   In (engineering) research, we spend a lot of time learning the fundamentals (coursework, mathematical tools, analysis/systems/experimental skills, etc.) as well as solving problems in specific applications (research). What is the optimal allocation of one’s effort in these two kinds of activities?

This is a complex and domain-dependent problem.  I suppose there is a lot of serious empirical and modeling research done in social sciences (I’d appreciate pointers if you know any).  But let’s formulate a ridiculously simple model to make a fun puzzle.

1. Consider a finite horizon t = 1, 2, …, T.   The time period t can be a day or a year.  The horizon T can be a project duration or a career.
2. Suppose there are only two kinds of activities, and let’s call them production and learning.  Our task is to decide for each t, the amount of effort we devote to produce and to learn.  Call these amounts p(t) and l(t) respectively.
3. These activities build two kinds of capabilities.  The fundamental capability L(t) at time t depends on the amount of learning we have done up to time t-1, L(t) := L(l(s), s=1, …, t-1).  The production capability P(t) at time t depends on the amount of effort we have devoted to production up to time t-1, P(t) := P(p(s), s=1, …, t-1).   We assume the functions L(l(s), s=1, …, t-1) and P(p(s), s=1, …, t-1) are increasing and time invariant (i.e., they depend only on the amount of effort already devoted, but not on time t).
4. The value/output we create in each period t is proportional to the time p(t) we spend on production multiplied by our overall capability at time t.   Our overall capability is a weighted sum P(t) + mL(t) of fundamental and production capabilities, with m>1.

Goal: choose nonnegative (p(t), l(t), t=1, …, T) so as to maximize the total value ${\sum_{t=1}^T\ p(t) (P(t) + m L(t))}$ subject to ${p(t) + l(t) \leq 1}$ for all t=1, …, T.

The assumption m>1 means that the fundamentals (quality) are more important than mere quantity of production.  The constraint ${p(t) + l(t) \leq 1}$ says that in each period t, we only have a finite amount of energy (assume a total of 1 unit) that can be devoted to produce and learn.  On the one hand, we want to choose a large p(t) because it not only produces value, but also increases future production capabilities P(s), s=t+1, …, T.  On the other hand, since m>1, choosing a large l(t) increases our overall capability more rapidly, enhancing value.  What is the optimal tradeoff?

We pause to comment on our assumptions, some of which can be addressed without complicating our model too much.

Caveats.  On the outset, our model assumes every activity can be cleanly classified as building either the fundamental capability or the production capability.  In reality, many activities contribute to both.  Moreover, the interaction between these two activities is completely ignored, except that they sum to no more than 1 unit.  For example, production (games, performance, research and publication, etc) often provides important incentives and contexts for learning and influences strongly the effectiveness of learning, but our function L is independent of  p(s).  The time invariance assumption in 3 above implies that we retain our capabilities forever after they are built; in reality, we may lose some of them if we don’t continue to practice.  If we think of P(t)+mL(t) as a measure of quality, then our objective function assumes that there is always positive value in production, regardless of its quality.  In reality, production of poor quality may incur negative value, even fatal.

A puzzle

A simple puzzle is the special case where the capabilities depend on (are) the total amounts of effort devoted, i.e.,

${L(t)\ := \ \sum_{s=1}^{t-1} l(s), \ \ \ P(t) \ :=\ \sum_{s=1}^{t-1} p(t) }$

Despite its nonconvexity, the problem can be explicitly solved and the optimal strategy turns out to have a very simple structure.  I will explain the solution in the next post and discuss whether it agrees, to first order, with our intuition and how some of the disagreements can be traced back to our simplifying assumptions.


text:
Is it possible to pass command line arguments to python script in snakemake?
1
0
Entering edit mode
14 months ago

Hello all,

When I am executing my snakemake pipeline I am trying to pass command line arguments with the --config flag in a python script.

rule assembly:
input:
"trim/{sample}_1.fastq.gz",
"trim/{sample}_2.fastq.gz",
output:
"assembly/{sample}.fa"
params:
fastq1 = "trim/{sample}_1.fastq.gz",
fastq2 = "trim/{sample}_2.fastq.gz",
conda: "environment.yaml"
script:
"assembly.py"

The Python script

import argparse
parser = argparse.ArgumentParser()
args = parser.parse_args()

if args.config["assembly"] == "megahit":
shell ("megahit .........")

I am executing the pipeline like this:

snakemake --cores 5 --config assembly="megahit"

or

snakemake --cores 5 --config assembly="metaspades"

When I do that I am getting the following error:

error: the following arguments are required: --config

1. Is there a way to make this work?
2. Am I completely wrong by choosing this option? (I did because when I used the snakemake run directive I was getting the "conda environments are only allowed with shell script notebook or wrapper directives (not with run)" error.

snakemake python • 2.4k views
0
Entering edit mode

i don't think you need to add the addparse stuff, just use a generic configfile with a default value and your inline arguments should work

0
Entering edit mode

So, you suggest instead of --config use the --configfile and specify the different params in this one?

0
Entering edit mode

all this is unnecessary:

import argparse
parser = argparse.ArgumentParser()
args = parser.parse_args()

0
Entering edit mode

When i have the following code in the script :

if config["assembly"] == "megahit":
shell ("megahit .........")

I am getting the following error:

if config["assembly"] == "megahit": NameError: name "config" is not defined

and I execute my pipeline like this

snakemake --cores 5 --config assembly="megahit"

0
Entering edit mode

config won't exist unless you have a configfile. do you have one?

0
Entering edit mode

May be gb 's answer to your earlier post is useful to you: Snakemake command line arguments.

0
Entering edit mode

By using the run directive, you cannot use conda environments... I need to load my programs from conda

0
Entering edit mode

You could do something like (unstested and quickly typed so only for inspiration):

rule assembly:
input:
"trim/{sample}_1.fastq.gz",
"trim/{sample}_2.fastq.gz",
output:
"assembly/{sample}.fa"
params:
method = config["assembly"]
conda: "environment.yaml"
script:
"assembly.py"

And in the script:

if snakemake.params.method == "megahit":
shell ("megahit .........")

But I personally prefer something you are already doing:

rule assembly:
input:
"trim/{sample}_1.fastq.gz",
"trim/{sample}_2.fastq.gz",
output:
"assembly/{sample}.fa"
params:
fastq1 = "trim/{sample}_1.fastq.gz",
fastq2 = "trim/{sample}_2.fastq.gz",
conda: "environment.yaml"
script:
'assembly.py --assembly config["assembly"]'

and

import argparse
parser = argparse.ArgumentParser()
args = parser.parse_args()

if args.assembly== "megahit":
#guess you want subprocess.Popen
shell ("megahit .........")

The above is just to push you in the right direction. If you can't figure it out I can make a working example. Also the shell line in the python script looks weird but for now I assume it is just a example or not real code.

0
Entering edit mode

Hello!

Thank you for the reply. Yes, the shell directive is an example and not the real code.

I will try your suggestion and I will get back to you.

0
Entering edit mode
14 months ago
Eric Lim ★ 2.0k

argparse is not needed.

(base) [~/Downloads/scratch/biostar/tmp]$cat Snakefile rule: params: test = config['test'] script: 'test.py'  You can access config or params in your script with the snakemake object. (base) [~/Downloads/scratch/biostar/tmp]$ cat test.py
print(snakemake.config)

print(snakemake.params)

This works for config or configfile.

(base) [~/Downloads/scratch/biostar/tmp]\$ snakemake -j1 --config test=hello
Building DAG of jobs...
Using shell: /bin/bash
Provided cores: 1 (use --cores to define parallelism)
Rules claiming more threads will be scaled down.
Job stats:
-----  -------  -------------  -------------
1            1              1              1
total        1              1              1

Select jobs to execute...

[Tue Jan 18 13:24:23 2022]
rule 1:
jobid: 0
resources: tmpdir=/var/folders/q4/cwjcyc851ldgbw2v28txzxbh0000gn/T

{'test': 'hello'}
hello
[Tue Jan 18 13:24:25 2022]
Finished job 0.
1 of 1 steps (100%) done

0
Entering edit mode

I wouldn't agree that you never need to pass arguments to a python script in a snakemake workflow.

What if the python script you're trying to run is actually a published program and you just want to run it with certain parameters? Would I then have to run it from the shell directive?


text:
# Compactness in a Nutshell

Compactness is an important topological property – A property that when seen in a certain perspective can make an infinite string become a ring, that you will give it to your girlfriend while proposing her for marriage. Therefore, compactness really intrigues me.

Let’s make our way to mathematics, without further adieu.

A space A is called Compact under an ambient space X if any open cover of A has a finite subcover.

Theorem 1: A closed set of a compact set is compact.

Theorem 2: The continuous image of a compact space is compact.

Theorem 3: A compact subset of a Hausdorff Space ( eg: Metric Space ) is closed.

Theorem 4: A bijective continuous map from a compact space X to a Hausdorff space Y is a homeomorphism.

Theorem 5 ( Heine Borel Theorem ): X $$\in R^{n}$$ is compact <=> X is closed and bounded.

Theorem 6: X is compact <=> X is complete and totally bounded.

Theorem 7: A continuous real-valued function defined on a compact space is bounded and attains its bounded. (Theorem 2 + Theorem 5)

A space X is called Sequentially Compact (SC) if every sequence in X has a convergent subsequence.

A space X is called Totally Bounded (TB) if, for every $$\epsilon > 0$$, there are finite open balls of radius $$\epsilon$$, that cover X.

A Space X satisfies Bolzano Weierstrass Property (BWP) if every infinite subset of X has a limit point in X.

A Space X is called Separable if X has a countable dense subset.

A Space X is called Complete if every Cauchy sequence in X has a limit point in X.

Super Theorem 8:

Theorem 9: X is Sequentially Compact Metric Space <=> X is a Compact Metric Space.

Theorem 10: For a Sequentially Compact Space, Lesbegue Covering Lemma holds.

#### Topological Algebraic Properties of Compact Sets

Theorem 1: A is compact, B is compact, then $$A \cup B$$ is compact.

Theorem 2: A is compact, B is closed then $$A \cap B$$ is compact.

Note: In general, A is compact, B is compact, then $$A \cap B$$ is not compact. But for metric spaces, this is true due to Theorem 3.

Counterexample 1: A is compact, B is compact, then $$A \cap B$$ may not compact.

X = N∪{−∞,∞}. A=N∪{∞}; B=N∪{−∞}. A∩B=N has the discrete topology and is not compact.

Counterexample 2: In X, A is compact, then $$\overline{X}$$ may not be compact.

In Hausdorff Space, obviously, it is true. Hence, we have to take a non-Hausdorff Space.

X = Z, where the open sets are precisely the sets containing 0. Then $$\overline{0}$$ = Z, which is not compact (why?).

Theorem 3: X x Y is compact <=> X and Y are compact.

More to come!

Stay Tuned!

Go Top


text:
# Basis for vector space

Here is the question...

"Either find a basis for the vector space M2×2 of 2 × 2 matrices that includes the vectors

$$\begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix}$$ $$\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$$ $$\begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}$$

or else explain why this is not possible. [4 marks]"

Do i need to find the reduced row echelon form of these 3 matrices? I know how to find the basis if I was given something like this "v1=(1,1),v2=(2,−1)" but not this style of question. Just an insight on how to start to answer this question would be much appreciated.

• First, a basis of $M(2,K)$ is composite by matrices. Second, do you want include $(0,0)$ in a base? – Rafael Holanda Aug 23 '16 at 7:55
• I think you will have to figure out how to properly convey your ideas here (the easiest way: learn the easy directions to properly write mathematics with MathJaX in this site), or else it is going to be very hard to understand you. Where you wrote "MATRIX" there are three pairs of numbers: how are we to turn this into a $\;2\times2\;$ matrix?? – DonAntonio Aug 23 '16 at 8:03
• Well, the correct way to format a matrix is to write $$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}$$ to get $$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}$$ – celtschk Aug 23 '16 at 8:04
• BTW, even if you were not able to do it in MathJax, you could at least have written it as preformatted text. As is, I have no idea what your matrix looks like. – celtschk Aug 23 '16 at 8:06

Hint: There isn't anything particularly special about the structure of how each of the entries are arranged in each $2 \times 2$ matrix, as long as we're consistent. In fact, since we're more comfortable with working with $m \times 1$ vectors in $\mathbb R^m$ instead of $n \times n$ vectors in $M_{n \times n}$, we can imagine unfolding each square matrix into a column vector in some arbitrary (but fixed) order, say: $$\begin{bmatrix} b & c \\ a & d \end{bmatrix} \iff \begin{bmatrix} a \\ b \\ c \\ d \end{bmatrix}$$ So what we can do is:
• Convert each $2 \times 2$ matrix into a $4 \times 1$ column vector.
• Convert each $4 \times 1$ column vector in your basis back to a $2 \times 2$ matrix.


text:
You are currently offline. Some features of the site may not work correctly.

# Plug-in principle

In statistics, the plug-in principle is the method of estimation of functionals of a population distribution by evaluating the same functionals at… Expand
Wikipedia

## Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2018
2018
• 2018
• Corpus ID: 88523055
We consider the problem of estimating smooth integrated functionals of a monotone nonincreasing density $f$ on $[0,\infty)$ using… Expand
2017
2017
• 2017
• Corpus ID: 88514800
This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and… Expand
2017
2017
• International Conference on Information and…
• 2017
• Corpus ID: 39946826
The topical information security problem of development of statistical tests for hypotheses on the discrete uniform distribution… Expand
2016
2016
• 2016
• Corpus ID: 55746522
The R package quantreg.nonpar implements nonparametric quantile regression methods to estimate and make inference on partially… Expand
2016
2016
• Entropy
• 2016
• Corpus ID: 10589966
Several reproducibility probability (RP)-estimators for the binomial, sign, Wilcoxon signed rank and Kendall tests are studied… Expand
2013
2013
• 2013
• Corpus ID: 12651401
A new Bayesian multi-chain Markov Switching GARCH model for dynamic hedging in energy futures markets is developed by… Expand
Review
2011
Review
2011
• 2011
• Corpus ID: 62763717
Psychologists estimate the precision of their statistics both to conduct hypothesis tests and to construct confidence intervals… Expand
2009
2009
• 2009
• Corpus ID: 46415696
We propose a new approach to conditional quantile function estimation that combines both parametric and nonparametric techniques… Expand
2005
2005
We consider the Gaussian ARFIMA(j,d,l) model, with spectral density and an unknown mean . For this class of models, the n−1… Expand


text:
# Getting the Information

In order to actually get the information on the action campaigns that I needed, I needed to use nokogiri to parse the information, create new actions and clients, and then map that information. I started with this code:
# def self.fetch   #Nokogiri::XML(SalsaLabs::Client.new.request_data('/api/getObjects.sjs', object: 'Action')).css('item').map do |attributes|   #SalsaLabs::Action.new({title: atributes.css('Title').text)})   #end#end
And then used that code to break it into smaller, more transparent methods. I broke the code into five separate methods. First, I created a new class for it called ActionFetch. Then I initialized (or set up) that class setting an instance variable for  api_client
def initialize(api_client)  @api_client = api_clientend
Then, starting from the meat of the class, I created this method:
def data_request  return @data if @data   body = @api_client.fetch('/api/getObjects.sjs', object: 'Action')   doc = Nokogiri::XML(body)   @data = doc.css('item')   @dataend
The data request method starts by saying if there is anything already in the @data instance variable, then just return, if not, then go through the rest of the method’s steps. This is also called Memoizing which basically means storing a value for future use so that you don’t have to run the call over again which saves you time.

The next line says that take the api client (which is the actual http request, set up with faraday, using credentials, etc., set up in a different api client class) and get the stuff that is located at that api endpoint with the params of the object which is named Action. Then, use nokogiri to parse the information that is in the body string (set above). Finally, look at the doc (which is the result of the nokogiri parsing and is now an xml doc) and use the css selector to find all the items. Finally, return the value.

Then, I took those results and fed them into the get_results method.
def get_results  data_request.map do |attribute_set|     new_action(extract_attributes(attribute_set))   endend
This method takes the results from data_request and for each one (each attribute set), it extracts them into a hash and then makes each of them a new action (it wraps each of the attributes sets in an action class). It does this by using the extract_attributes method which looks like this:
def extract_attributes(action_data)  action_data.children.inject({}) do |memo, node|    memo[node.name.downcase] = node.text     memo  endend
and takes each of the item nodes (action_data is the Nokogiri item tag) and makes them into a hash. And finally, wrapping it in an action class is done by using the new_action method which looks like this:
def new_action(params)  SalsaLabs::Action.new(params)end
It just stick each of the params into an object called action which gives the attributes pretty names.
Phew!

Okay, so then, what do I mean by pretty names? Well, in order to see that, I look at the Action class which I’ll cover in the next post.


text:
# Math Help - Solving a quartic equation

1. ## Solving a quartic equation

This problem seems a bit out of the ordinary. s^4+ s^2-6 =0

2. Originally Posted by sgonzalez90
This problem seems a bit out of the ordinary. s^4+ s^2 -6 =0
This is a quadratic in $s^2$. Let $w = s^2$:

$w^2 + w - 6 = 0$.

Solve for $w$. Hence solve for $s$.

3. Oh my gosh I'm so sorry, i typed it wrong again. I'm sorry im really tired and had a long day. I'm just trying to brush up on my algebra before i begin my calculus course in two weeks.

s^4+ 3s^2 -6 =0
this is the correct problem i promise, thank you.

4. Originally Posted by sgonzalez90
Oh my gosh I'm so sorry, i typed it wrong again. I'm sorry im really tired and had a long day. I'm just trying to brush up on my algebra before i begin my calculus course in two weeks.

s^4+ 3s^2 -6 =0
this is the correct problem i promise, thank you.
Just change the appropriate numbers in post #2.

5. Originally Posted by sgonzalez90
s^4+ 3s^2 -6 =0
this is the correct problem i promise, thank you.
This one won't factor, so apply the Quadratic Formula:

$x^2\, =\, \frac{-(3)\, \pm\, \sqrt{(3)^2\, -\, 4(1)(-6)}}{2(1)}$

$x^2\, =\, \frac{-3\, \pm\, \sqrt{9\, +\, 24}}{2}$

$x^2\, =\, \frac{-3\, \pm\, \sqrt{33}}{2}$

Then take the square root of either side to solve for "x=". Yes, you'll have some nested radicals.


text:
# RevolutionPlot3D: axis of revolution that doesn't pass through the origin

This is a follow up question to RevolutionPlot3D: but NOT revolving about the z axis so please check that for the context.

It seems that RevolutionAxis requires the axis of revolution to pass thru the origin. Suppose I want to use an axis of revolution that does not pass through the origin, e.g., the line $y=-1$ in the example above. What is a good way to accomplish this?

I do realize that RegionPlot3D may be appropriate here, but even with seemingly simple examples such as the one above, it can struggle:

Show[
RegionPlot3D[1 <= Sqrt[(y + 1)^2 + z^2] <= 1 + x^2, {x, 0, 1},
{y, -3, 3}, {z, -3, 3}, PlotRange -> All, PerformanceGoal -> "Quality",
Mesh -> False, AxesLabel -> {x, y, z}, PlotPoints -> 100,
ViewPoint -> {0.87, 0.44, 1.76}, ViewVertical -> {0.32, 0.67, 0.67}],
Graphics3D[{Thickness[.01], Black, Line[{{0, -1, 0}, {1.15, -1, 0}}]}]
]

Bumping PlotPoints up to 200, 300, 400 doesn't alleviate the problem and gets really slow.

-


text:
# Convex sets in infinite dimensional Banach spaces

I am reviewing functional analysis and getting stuck in this question.

Let $X$ be an infinite dimensional Banach space. Show that there exist convex sets $K_1, K_2$ such that $K_1\cap K_2=\emptyset, K_1\cup K_2=X, cl(K_1)=cl(K_2)=X$ where $cl(E)$ is the closure of $E$.

I have no idea about where to start. Could anyone give me some hints ? Thank you very much.

Hint: There is $f : X \to \mathbb{R}$ which is linear and unbounded.

• But the complement of the kernel is not convex. – Martin Argerami Jun 11 '16 at 16:56
• @MartinArgerami Obviously. And I never said something about the kernel ;) But starting from the kernel you can develop some idea to get desired $K_1$ and $K_2$. – gerw Jun 11 '16 at 18:34
• Can you be more explicit? – user99914 Jun 11 '16 at 19:53
• What can you say about the kernel of $f$? It has some very nice properties. Similarly, which properties does the set $\{x \in X \mid f(x) = 1\}$ have? This can be used to construct $K_1$ and $K_2$. – gerw Jun 11 '16 at 20:37
• I think I got it. You have that $\{x: f(x)=1\}$ is also dense in $X$. Now, let $K_1=\{x: f(x)\le 0\}$, $K_2=\{x: f(x)>0\}$, then $K_1,K_2$ solve our problem. – Omega Jun 12 '16 at 1:00

I have some approach, but I don't know much about Banach spaces, so I don't know if it works.

We define the sequence of convex and disjoint sets $A_k$ and $B_k$, where $A_k \cup B_k$ is a $k$-dimensional subspace, as follows:

• $A_0 = \{0\}$ and $B_0 = \emptyset$
• For every $n$, let $S_n = A_n \cup B_n$, and let $x_n \in X$ be an arbitrary vector that is not in $S_n$. Then we let $$A_{n+1} = A_n \cup \{s + \lambda x_n : s \in S_n, \lambda > 0\},\\ B_{n+1} = B_n \cup \{s - \lambda x_n : s \in S_n, \lambda > 0\}.$$

The cool part of this construction is that for every $n$, we have $A_n \in \text{cl } B_{n+1}$ and $B_n \in \text{cl } A_{n+1}$!

Now, let $A = \bigcup_n A_n$ and $B = \bigcup_n B_n$. If $X$ is countably dimensional, we should have $X = A \cup B$ (at least if we choose the $x_n$ nicely). Then, we should also have $\text{cl } A = \text{cl } B = X$.

But if $X$ is uncountably dimensional, this doesn't work that well. My idea would be to make the sequence of $A_n$ "even longer" using transfinite induction, but I'm not sure if this works.


text:
• The calculation of active Raman modes of 𝛼-quartz crystal via density functional theory based on B3LYP Hamiltonian in $6–311+$G(2d) basis set

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/078/05/0803-0810

• # Keywords

Density functional theory; Raman; cluster models; normal modes; Hessian matrix; quartz.

• # Abstract

We obtained an approximation of the force ﬁeld of 𝛼-quartz crystal using a new idea of applying density functional theory [J Purton, R Jones, C R A Catlow and M Leslie, Phys. Chem. Minerals 19, 392 (1993)]. Our calculations were based on B3LYP Hamiltonian [A N Lazarev and A P Mirgorodsky, Phys. Chem. Minerals 18, 231 (1991)] in $6−311+$G(2d) basis set for H\$_{16}Si7O6 cluster and included a unit cell of the lattice. The advantage of our method is the increase in the speed of calculations and the better adaption of simulation results with the experimental data.

• # Author Affiliations

1. Physics Department, Faculty of Science, Urmia University-Urmia, P.O. Box 165, Iran

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


text:
# How do I get normal-sized fractions in my matrices?

I would like to write something like the definition of a gradient operator in cartesian coordinates.

\usepackage{amsmath}
$$\nabla \Phi = \begin{pmatrix} \frac{\partial \Phi}{\partial x} \\ \frac{\partial \Phi}{\partial y} \\ \frac{\partial \Phi}{\partial z} \\ \end{pmatrix}$$

The fractions are rendered small, as when they are rendered inline, but I don't like it in that particular instance.

I knew this would happen since it is documented there: http://en.wikibooks.org/wiki/LaTeX/Mathematics#Matrices_and_arrays

Even if I increase the spacing by adding [0.5em] after the double-backslash, it still doesn't look very good. I have a lot of space so I'd like the content of the matrix not to squeeze itself.

How can I make the content of a matrix using its normal size and not its inline size?

-

The \dfrac macro renders fractions as those in displayed math, even if it is part of an inline equation, fraction, or other setting where LaTeX prefers to typeset an inline version.

Conversely, I frequently find myself using \tfrac, which renders fractions in an inline (or "text mode") fashion even if the setting is display mode, because I often find the large fractions distracting from what is important in my equations.

As with most useful but basic macros for mathematics, these are provided by the amsmath package.

Example code:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Some fractions in inline math:
$$\dfrac{\sqrt 2}{2} \bigg/ \frac{\sqrt 2}{2} \bigg/ \tfrac{\sqrt 2}{2}$$

\vspace{1ex}
Some fractions in displayed math (in and outside of some environments):
\begin{gather*}
\begin{split}
\dfrac{\sqrt 2}{2} \bigg/ \frac{\sqrt 2}{2} \bigg/ \tfrac{\sqrt 2}{2}           \\
\begin{bmatrix}
\dfrac{\sqrt 2}{2} & \frac{\sqrt 2}{2} & \tfrac{\sqrt 2}{2}
\end{bmatrix}
\end{split}

Adding to Niel de Beaudrap’s answer, you might find display-style fractions run against each other in matrices. Use \renewcommand{\arraystretch}{1.25} after \begin{pmatrix} if you need to expand the matrix. 1.25 is just a suggested stretch value; play around with it to find what looks best in your document. – AstroPig7 Aug 15 '12 at 14:46
@AstroPig7: See also Using display style fraction in a matrix environment. Note that although \arraystretch is an excellent suggestion, it doesn't quite do what one would expect. – Hendrik Vogt Aug 15 '12 at 19:24
Sometimes I astound myself with my blockheadedness- I've been writing things like $a \cdot \begin{LARGE}\frac{b}{c}\end{LARGE}$ for years... – Andrew Feb 4 at 3:14


text:
# Monthly Archives: December 2018

Where: Barrister’s Hall at the ground floor of the BU Law School. The address is 765 Comm Ave but it’s better to enter the building from the back entrance on Bay State Road, and then turn right.

Organizers: Ran Canetti, Yael Kalai, Vinod Vaikuntanathan and Daniel Wichs.

When:Friday, Dec 14 at BU.

Thanks: NSF MACS Project for their generous support.

### Program:

 9:30 – 10:00. Coffee/Breakfast 10:00 – 11:00. Sandro Coretti, NYU The Double Ratchet: Security Notions, Proofs, and Modularization for the Signal Protocol (video) 11:15 – 12:15. Omer Paneth, Northeastern and MIT Weak Zero-Knowledge Beyond the Black-Box Barrier (video) 12:15 – 1:30. Lunch 1:30 – 2:30. Lisa Yang, MIT Publicly Verifiable Delegation from Standard Assumptions (video) 2:45 – 3:45. Alex Lombardi, MIT Fiat-Shamir from Simpler Assumptions (video) 3:45 – 4:30. Reception

### Abstracts:

Speaker: Sandro Coretti, NYU
Title: The Double Ratchet: Security Notions, Proofs, and Modularization for the Signal Protocol

Abstract:

Signal is a famous secure messaging protocol used by billions of
people, by virtue of many secure text messaging applications including
Signal itself, WhatsApp, Facebook Messenger, Skype, and Google Allo.
At its core it uses the concept of double ratcheting, where every
message is encrypted and authenticated using a fresh symmetric key; it
has many attractive properties, such as forward security,
post-compromise security, and immediate (no-delay) decryption, which
had never been achieved in combination by prior messaging protocols.While the formal analysis of the Signal protocol, and ratcheting in
general, has attracted a lot of recent attention, we argue that none
of the existing analyses is fully satisfactory. To address this
problem, we give a clean and general definition of secure messaging,
which clearly indicates the types of security we expect, including
forward security, post-compromise security, and immediate decryption.
We are the first to explicitly formalize and model the immediate
decryption property, which implies (among other things) that parties
seamlessly recover if a given message is permanently lost—a property
not achieved by any of the recent provably secure alternatives to
Signal. We build a modular generalized Signal protocol from the
following components: (a) continuous key agreement (CKA), a clean
primitive we introduce and which can be easily and generically built
from public-key encryption (not just Diffie-Hellman as is done in the
current Signal protocol) and roughly models so-called public-key
ratchets; (b) forward-secure authenticated encryption with associated
data (FS-AEAD), which roughly captures so-called symmetric-key
ratchets; and (c) a two-input hash function that is a pseudorandom
function (resp. generator with input) in its first (resp. second)
input, which we term PRF-PRNG. As a result, in addition to
instantiating our framework in a way resulting in the existing, widely
used Diffie-Hellman based Signal protocol, we can easily get
post-quantum security and not rely on random oracles in the analysis.We further show that our design can be elegantly extended to include
forms of fine-grained state compromise recently studied at CRYPTO’18,
but without sacrificing the immediate decryption property. However, we
argue that the additional security offered by these modifications is
unlikely to justify the efficiency hit of using much heavier
public-key cryptography in place of symmetric-key cryptography.

Speaker: Omer Paneth, Northeastern and MIT
Title: Weak Zero-Knowledge Beyond the Black-Box Barrier

Abstract: The round complexity of zero-knowledge protocols is a long-standing open question, yet to be settled under standard assumptions. So far, the question has appeared equally challenging for relaxations such as weak zero-knowledge and witness hiding. Protocols satisfying these relaxed notions under standard assumptions have at least four messages, just like full-fledged zero knowledge. The difficulty in improving round complexity stems from a fundamental barrier: none of these notions can be achieved in three messages via reductions (or simulators) that treat the verifier as a black box.

We introduce a new non-black-box technique and use it to obtain the first protocols that cross this barrier under standard assumptions. Our main results are:

– Weak zero-knowledge for $\NP$ in two messages, assuming quasipolynomially-secure fully-homomorphic encryption and other standard primitives (known from quasipolynomial hardness of Learning with Errors), as well as subexponentially-secure one-way functions.

– Weak zero-knowledge for $\NP$ in three messages under standard polynomial assumptions (following for example from fully-homomorphic encryption and factoring).

We also give, under polynomial assumptions, a two-message witness-hiding protocol for any language L \in NP that has a witness encryption scheme. This protocol is also publicly verifiable.

Our technique is based on a new homomorphic trapdoor paradigm, which can be seen as a non-black-box analog of the classic Feige-Lapidot-Shamir trapdoor paradigm.

Joint work with Nir Bitansky and Dakshita Khurana.

Speaker: Lisa Yang, MIT
Title: Publicly Verifiable Delegation from Standard Assumptions

Abstract: We construct a delegation scheme for all polynomial time computations. Our scheme is publicly verifiable and completely non-interactive in the common reference string (CRS) model.

Our scheme is based on an efficiently falsifiable decisional assumption on groups with bilinear maps. Prior to this work, publicly verifiable non-interactive delegation schemes were only known under knowledge assumptions (or in the Random Oracle model), or under non-standard assumptions related to obfuscation or multilinear maps.

We obtain our result in two steps. First, we construct a scheme with a long CRS (polynomial in the running time of the computation) by following the blueprint of Paneth and Rothblum (TCC 2017). Then we show how to bootstrap this scheme to obtain a short CRS. Our bootstrapping theorem exploits the fact that our scheme can securely delegate certain classes of nondeterministic computations.

Speaker: Alex Lombardi
Title: Fiat-Shamir from Simpler Assumptions

Abstract: We present two new protocols:

(1) A succinct publicly verifiable non-interactive argument system for log-space uniform NC computations, under the assumption that any one of a broad class of fully homomorphic encryption (FHE) schemes has almost optimal security against polynomial-time adversaries. The class includes all FHE schemes in the literature that are based on the learning with errors (LWE) problem.

(2) A non-interactive zero-knowledge argument system for NP in the common random string model, assuming almost optimal hardness of search-LWE against polynomial-time adversaries.

Both results are obtained by applying the Fiat-Shamir transform with explicit, efficiently computable functions to certain classes of interactive proofs. We improve over prior work by reducing the security of these protocols to qualitatively weaker computational hardness assumptions. Along the way, we also show that the Fiat-Shamir transform can be soundly applied (in the plain model) to a richer class of protocols than was previously known.

Joint work with Ran Canetti, Yilei Chen, Justin Holmgren, Guy Rothblum, and Ron Rothblum


text:
# 1)x^2=10^(lgx+1) 2)F(x)=7^(-cosx)    F'(x)? 3)49^(1+sqrt(x-2)) -344*7^(sqrt(x-2))=-7

1) You need to solve for x the equation `x^2 = 10^(lg x + 1)`

Notice that the variable x is present as exponent of base 10, to the right side, hence you should take logarithms of both sides such that:

`lg x^2 = lg 10^(lg x + 1)`

You need to use power property of logarithms such that:

`2 lg x = (lg x + 1)*lg 10`

You need to remember that `lg 10 = ` 1, hence you should substitute 1 for lg 10 in equation such that:

`2 lg x = lg x + 1`

You need to isolate the terms containing x to the left side such that:

`2 lg x - lg x = 1 =gt lg x = 1 =gt x = 10^1`

Hence, evaluating solution to equation yields x=10.

2) You need to find derivative of function `f(x) = 7^(-cos x), ` hence you should use the formula:

`(a^x)' = a^x*ln a`

`(7^(-cos x))' = 7^(-cos x)*(ln 7)*(-cos x)'`

`(7^(-cos x))' = 7^(-cos x)*(ln 7)*(sin x)`

Hence, evaluating f'(x) yields `f'(x) = 7^(-cos x)*(ln 7)*(sin x)`

3)You need to solve the equation `49^(1+sqrt(x-2)) -344*7^(sqrt(x-2))=-7` You should use the properties of exponentials such that:

`49^(1+sqrt(x-2))=49*49^(sqrt(x-2))`

You need to write `49^(sqrt(x-2)) = 7^(2(sqrt(x-2)))`

Hence, you should write the equation such that:

`49*7^(2(sqrt(x-2))) - 344*7^(sqrt(x-2)) + 7 = 0`

You should come up with the substitution `7^(sqrt(x-2)) = ` y such that:

`49y^2 - 344y + 7 = 0`

You should use quadratic formula such that:

`y_(1,2) = (344 +- sqrt(118336 - 1372))/(2*49)`

`y_(1,2) = (344 +-sqrt(116964))/(98)`

`y_(1,2) = (344 +-342)/98`

`y_1 = 2/98 =gt y_1 = 1/49`

`y_2 = 686/98 =gt y_2 = 7`

You need to solve for x equations `7^(sqrt(x-2)) = 1/49 ` and `7^(sqrt(x-2)) = 7`  such that:

`7^(sqrt(x-2)) = 1/49 =gt7^(sqrt(x-2)) = 7^(-2)`

Equating exponents yields:

`sqrt(x-2) = -2`  contradiction since `sqrt(x-2) gt=0`

`7^(sqrt(x-2)) = 7 =gt sqrt(x-2) = 1`

You need to raise to square both sides such that:

`x - 2 = 1 =gt x = 3`

Hence, evaluating solution to equation yields x = 3.

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text:
Browse Questions

# Which of the following is primary pollutant?

$(a)\;H_2SO_4\qquad(b)\;acrolein\qquad(c)\;formaldehyde\qquad(d)\;CO$

$CO$ is a primary pollutant.
Hence (d) is the correct answer.


text:
2019
Том 71
№ 11

# Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series

Konyushkov A. A.

Abstract

We study restrictions that should be imposed on the numbers sequences $\{α_n\}$ and $\{Β_n\}$ in order to guarantee that the series $\sum\nolimits_{n = 1}^\infty {a_n } \cos nx$ and $\sum\nolimits_{n = 1}^\infty {b_n } \sin nx$ do not belong to the classes $B$ or $C$ for any {a n } and {b n } such that $a_n ≥ α_n, b_n ≥ Β_n,\; n = 1, 2$.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1636-1643.

Citation Example: Konyushkov A. A. Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1455–1460.

Full text


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Tag Info

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$$\renewcommand{\AA}{\text{Å}}$$

# dihedral_style charmm command¶

Accelerator Variants: charmm/intel, charmm/kk, charmm/omp

# dihedral_style charmmfsw command¶

## Syntax¶

dihedral_style style

• style = charmm or charmmfsw

## Examples¶

dihedral_style charmm
dihedral_style charmmfsw
dihedral_coeff  1 0.2 1 180 1.0
dihedral_coeff  2 1.8 1   0 1.0
dihedral_coeff  1 3.1 2 180 0.5

## Description¶

The charmm and charmmfsw dihedral styles use the potential

$E = K [ 1 + \cos (n \phi - d) ]$

See (MacKerell) for a description of the CHARMM force field. This dihedral style can also be used for the AMBER force field (see comment on weighting factors below). See (Cornell) for a description of the AMBER force field.

Note

The newer charmmfsw style was released in March 2017. We recommend it be used instead of the older charmm style when running a simulation with the CHARMM force field, either with long-range Coulombics or a Coulombic cutoff, via the pair_style lj/charmmfsw/coul/long and pair_style lj/charmmfsw/coul/charmmfsh commands respectively. Otherwise the older charmm style is fine to use. See the discussion below and more details on the pair_style charmm doc page.

The following coefficients must be defined for each dihedral type via the dihedral_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart commands:

• $$K$$ (energy)

• $$n$$ (integer >= 0)

• $$d$$ (integer value of degrees)

• weighting factor (1.0, 0.5, or 0.0)

The weighting factor is required to correct for double counting pairwise non-bonded Lennard-Jones interactions in cyclic systems or when using the CHARMM dihedral style with non-CHARMM force fields. With the CHARMM dihedral style, interactions between the first and fourth atoms in a dihedral are skipped during the normal non-bonded force computation and instead evaluated as part of the dihedral using special epsilon and sigma values specified with the pair_coeff command of pair styles that contain “lj/charmm” (e.g. pair_style lj/charmm/coul/long) In 6-membered rings, the same 1-4 interaction would be computed twice (once for the clockwise 1-4 pair in dihedral 1-2-3-4 and once in the counterclockwise dihedral 1-6-5-4) and thus the weighting factor has to be 0.5 in this case. In 4-membered or 5-membered rings, the 1-4 dihedral also is counted as a 1-2 or 1-3 interaction when going around the ring in the opposite direction and thus the weighting factor is 0.0, as the 1-2 and 1-3 exclusions take precedence.

Note that this dihedral weighting factor is unrelated to the scaling factor specified by the special bonds command which applies to all 1-4 interactions in the system. For CHARMM force fields, the special_bonds 1-4 interaction scaling factor should be set to 0.0. Since the corresponding 1-4 non-bonded interactions are computed with the dihedral. This means that if any of the weighting factors defined as dihedral coefficients (fourth coeff above) are non-zero, then you must use a pair style with “lj/charmm” and set the special_bonds 1-4 scaling factor to 0.0 (which is the default). Otherwise 1-4 non-bonded interactions in dihedrals will be computed twice.

For simulations using the CHARMM force field with a Coulombic cutoff, the difference between the charmm and charmmfsw styles is in the computation of the 1-4 non-bond interactions, though only if the distance between the two atoms is within the switching region of the pairwise potential defined by the corresponding CHARMM pair style, i.e. within the outer cutoff specified for the pair style. The charmmfsw style should only be used when using the corresponding pair_style lj/charmmfsw/coul/charmmfsw or pair_style lj/charmmfsw/coul/long commands. Use the charmm style with the older pair_style commands that have just “charmm” in their style name. See the discussion on the CHARMM pair_style page for details.

Note that for AMBER force fields, which use pair styles with “lj/cut”, the special_bonds 1-4 scaling factor should be set to the AMBER defaults (1/2 and 5/6) and all the dihedral weighting factors (fourth coeff above) must be set to 0.0. In this case, you can use any pair style you wish, since the dihedral does not need any Lennard-Jones parameter information and will not compute any 1-4 non-bonded interactions. Likewise the charmm or charmmfsw styles are identical in this case since no 1-4 non-bonded interactions are computed.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Restrictions¶

When using run_style respa, these dihedral styles must be assigned to the same r-RESPA level as pair or outer.

When used in combination with CHARMM pair styles, the 1-4 special_bonds scaling factors must be set to 0.0. Otherwise non-bonded contributions for these 1-4 pairs will be computed multiple times.

These dihedral styles can only be used if LAMMPS was built with the MOLECULE package. See the Build package doc page for more info.

## Default¶

none

(Cornell) Cornell, Cieplak, Bayly, Gould, Merz, Ferguson, Spellmeyer, Fox, Caldwell, Kollman, JACS 117, 5179-5197 (1995).

(MacKerell) MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field, Fischer, Gao, Guo, Ha, et al, J Phys Chem B, 102, 3586 (1998).


text:
Year: 1973

Authors: G.allavotti, C. Marchioro

Title On the calculation of an integral: Journal of Mathematical Analysis and Applications, 44, 661--675, 1973,

Abstract: The integral over $R^n$ $$I_n(g,\omega)=\int dq_1\ldots dq_n \exp\{-\frac12\sum_{i\ne j}^{1,n} \frac{g^2}{(q_i-q_j)^2}-\frac12\sum_{i=1}^n \omega^2 q_i^2\}$$ is exactly computed and shown to be $$I_n(g,\omega)=I_n(0,\omega) \exp\{-\omega g \frac{n(n-1)}2\}$$ In Sec. 5 we conjecture that the related Hamiltonian mechanical system is exactly integral and propose the form it would take in action-angle variables.

A Follow Up: The conjecture in Sec.5 has been proved partially (integrability) in "J. Moser, Three integrable Hamiltonian systems connected with isospectral deformations Advances in Mathematics, 16:197--220, 1975", and completed (action-angle variables found) in "J.P. Francoise. Canonical partition functions of Hamiltonian systems and the stationary phase formula, Communications in Mathematical Physics, 117: 37--47, 1988".

Key words:  Statistical Mechanics, Path Integral, Brwonian Motion, FEynman-Kac Formula

Giovanni Gallavotti
Fisica, Universita' di Roma 1
P.le Moro 2
00185 Roma, Italia
tel +39-06-4991-4370
fax +39-06-4957697

em: giovanni.gallavotti@roma1.infn.it
http://ipparco.roma1.infn.it


text:
# Tag Info

## Hot answers tagged natbib

13

The natbib option for biblatex causes the blx-natbib.def file to be loaded and not much else. There may be some styles that do different things depending on if the natbib option has been used, but the authoryear style does not seem to care. The blx-natbib.def file defines a handful of macros to recreate natbib citation commands, but it does not disable any ...

8

If you don't need to have natbib=true then the command \citeauthor* does exactly that. \documentclass{article} \usepackage[style=authoryear-comp, backend=biber, sorting=nyt, autolang=hyphen]{biblatex} \begin{filecontents}{literature.bib} @ARTICLE{ref1, AUTHOR = {AuthorA, A. and AuthorB, B.}, JOURNALTITLE = {{Journal of Testing}}, PAGES = {1--2}, ...

5

There are two errors in your MWE. \bibliography{mybib.bib} should be \bibliography{mybib} otherwise BibTeX looks for the file mybib.bib.bib instead of mybib.bib. \bibliographystyle{apa} should be \bibliographystyle{apalike}. The bibliography style apa.bst is not compatible with bibentry. So, delete your .aux and .bbl file, and retry with the following ...

5

The way described in Ingmar's answer is the preferred one, but you don't get a separating comma between authors when you have only two of them. I would follow that way, but if you really want a comma to separate them, you have to enclose the comma in braces, so that BibTeX considers it as normal text, i.e. @Book{williamson, author={David P Williamson{,} ...

4

The conjunctions used between author names are defined by the bibliography style in use -- in your case, plainnat. Fortunately, changing "and" to "&" (or "en") isn't too difficult: Locate the file plainnat.bst in your TeX distribution and make a copy of that file. Call this copy, say, myplainnat.bst. (Don't edit an original file of the TeX distribution ...

4

With biblatex and its natbib compatibility option, you may use \citep for "standard" citations in parentheses. For the case specified in your question, you have to resort to \parencites. See section 3.7.3 of the biblatex manual for details. \documentclass{article} \usepackage[style=authoryear,natbib=true]{biblatex} \usepackage{filecontents} ...

3

The revtex class loads the natbib package with sort&compress option, that is for numerical citations. If you want an author-year citation in a revtex document, you need to set the citation style for natbib, this can be done adding \setcitestyle{authoryear}, using this command also you can set the whole style of a citation. ...

2

I originally thought you could change the formatting by patching the \NAT@split macro where the \NAT@date macro is set. The problem with this is that the \NAT@date macro is used in conditionals so it doesn't have the right form if you patch it. This means you need to patch where the \NAT@date macro is used. the \NAT@date macro is used in a number of places ...

1

You seem to be having trouble in compiling a latex file with bibliography using natbib. IF this is the real issue, then please note the following: 1) With your current MWE example, please keep the file myrefbibfile.bib in the same folder as your manuscript .tex file 2) To compile, follow this sequence: Run latex, the run bibtex and then run latex twice. So ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# wave amplitude, frequency,wavelength,energy

1. While understanding mechanical wave, if i just sit in front of the pond and throw a stone, there is a ripple formed. I want to understand the ripple in terms of the sine wave depicted in text books. Is the sine wave form in text books depicts the movement of a point (The point where the stone hits the water) in the wave(up and down or horizontal movement of water?). What is the wavelength of the ripple? Is it same as saying when one point goes up down in the ripple how long it takes for the next particle to start the up-down movement? I know wave form depicts the energy transfer. I want to know the physical meaning of the amplitude and frequency. Is it the water particle vibration?

2. In electromagnetic wave there is no physical movement of matter. In this case how should i understand the frequency and wavelength. Is it vibration of the source electron only. Since EM travels at light speed, we need not worry about what is the shape?

• In case 1) there isn't any movement of matter, only its oscillation. What dissipates is the energy. In case 2) there is the movement of photons, emitted from accelerated electrons. Depending from the acceleration value the photon has different energy content-for visible light (say from an fire) - from red (lower energy photons) to blue. Since in double slit experiments photons of different energy content produce different distances between fringes this was related to wavelengths and frequencies. – HolgerFiedler Oct 2 '16 at 8:59
• Mechanical simple harmonic waves - physicskey.com/34/waves-and-mechanical-simple-harmonic-waves – Saral Dec 29 '18 at 6:52

What is the wavelength of the ripple?

If you look at the pond, you can see the wavelength with your eyes: It is the distance between two crests of the wave.

Is it same as saying when one point goes up down in the ripple how long it takes for the next particle to start the up-down movement?

Yes, you need the propagation speed of the wave in order to convert the wavelength to a period $T$ for one oscillation. This period is the inverse of the frequency: $T = 1/f$.

Is the sine wave form in text books depicts the movement of a point (The point where the stone hits the water) in the wave (up and down or horizontal movement of water?)

The sine wave in the book depicts the surface shape of the water. From your question I'd say it is the horizontal movement, but there is a slight catch. In a water wave, the water actually only moves up-down! You can easily check this by putting something on the water (leaves, pollen, sawdust) and create some waves. You will see that the waves travels through the stuff on the surface, the swimming thing will move mostly up and down and does not travel with the wave.

I want to know the physical meaning of the amplitude and frequency.

The amplitude is the height that the water gets lifted above the normal height when the wave passes by.

The frequency is the number of up-down movements of a particular point within one time period.

Is it the water particle vibration?

I wouldn't call it vibration as it happens on a larger scale. But otherwise I think you can say that.

In electromagnetic wave there is no physical movement of matter. In this case how should i understand the frequency and wavelength.

There is movement of matter if that matter is charged. Actually you need some charged matter (electrons) in order to detect the field in the first place; you need an antenna.

The EM wave will take the electrons in the antenna and move them along. The stronger the wave, the higher the voltage you can pick up from the antenna.

The frequency here is again the number of times that the electrons get shaken up-down in a period of time. The wavelength is the distance between to crests of the wave. You can measure this by taking two antennas and spacing them apart. If the electrons in both antennas get pulled up at the same time, the antennas are a wavelength (or a multiple of that) apart. If one antenna has a positive voltage while the other one has a negative one, and vice versa, they are half a wavelength (or $n + 1/2$ wavelengths) apart.


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• In a post discussing the kind the of answer one would like: rigorous or heuristic, the need to attach a diagram with a solution was felt.

• The other day, I was trying to tell the bijection between $$\mathbb{N}$$ and $$\mathbb{Q}$$ in a discussion and it would have been very easy had there been a diagram.

• Again the new feature of "Contribute", (which I liked very much, for it is much easier than email, which doesn't even allow $$\LaTeX$$), we see David always giving problems with diagrams, but again we cannot submit diagrams.

Thanks.

A.De

Note by Abhishek De
4 years, 11 months ago

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We are looking into it. You are very right that a diagram would make many things, much easier, on many aspects of the site. For now, though it is not ideal, we encourage people to feel free to use services like imgur to host their pictures and to provide links in their comments, solutions, and problems for others to view them.

We will eventually have the ability to submit your own image or diagram, inline with your discourse, however it won't happen immediately.

Staff - 4 years, 11 months ago


text:
How can I have a sequential model inside Keras' functional model?

I'm trying to build a architecture that takes in multiple inputs and has a smaller neural network inside a larger architecture. For me to keep track of of the smaller netowrk's loss, I need to compile the sub-network as a Sequential, but it still needs to be part of the functional model as a whole for the architecture. Is this possible in Keras?

I managed to trial and error through this.

x = Sequential()
# add some layers...
inputs = [Input(...), Input(...), ...]
outputs = ... #some layers stacked together via the functional model
result = Model(inputs=inputs, x(outputs))

If you want the sequential in the middle of the outputs up there for some reason:

output1 = Layer(input)
output2 = x(layer1)
outputs = Layer(output2)


text:
# How much?

This topic is 4504 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

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Hello to everybody. I'm doing with a friend a business plan. We have chosen to sell our projects to a publisher. We have the idea of doing all the development in our study, but we don't know how much the publishers pay for a complete game. We know that it depends on the quality of the game, so please give us an idea being realist. We also know that it depends on the development platform too. We know it's not an easy question, but we would be very pleased if you help us. Thanks in advance.

Being realistic: Expect $0. If you find a publisher willing to publish it at your expense, expect that you will have pay thousand dollars for the work they are going to do. Selling game ideas to a game publisher is not a realistic business plan. Read this. According to the very rough but realistic numbers, you have less than a 7% chance of selling a completed, polished, ready-to-ship game to a publisher. Selling completed games to a publisher is almost certainly not going to happen unless you have a proven track record and an excellent game. Read this, the first six publication methods (a-f) probably apply to you. A publisher will only buy a game if they can anticipate sales in the hundreds-of-thousands, or perhaps tens-of-thousands in the mobile market. But if you could sell that many copies with your completed game, you'd probably be better off financially doing it yourself. #### Share this post ##### Link to post ##### Share on other sites OK!! That has been so realistic; but now, being less realistic, let's say that we are a important developer studio, that has finished a really good game (FFX level more or less, for example). Of course, we don't have this kind of level, but we need the numbers of the possible game sell, because we have to obtain a business plan that's viable. We hope that now you can be a little more "fantastic". By the wat, thanks for your opinion. Thanks in advance. P.S: I know that the project it's not viable, but we need to do the finance results and we need some benefits for it. #### Share this post ##### Link to post ##### Share on other sites This smells of homework. Though in this case we could likely help. Most of the info you're asking for would be private and never released, so most numbers you get here will be out of thin air and you could likely make them up yourself. Best of luck. #### Share this post ##### Link to post ##### Share on other sites Of course, it doesn't smell, it stinks -LOL-. I have read my previous posts, and you're right, I've forgot to tell it. It's a "serious" business plan, but it's not going to be put on practice, so we have to "make-up" it to make it viable. We agree with you, we can imagine the numbers ourselves, but the problem is that we are really lost, because we don't know how much is expensive, and how much is cheap. Because of that, we only need a estimated number. Thanks in advance again, and thanks mike2343 for your attention #### Share this post ##### Link to post ##### Share on other sites Quote:  Original post by sagoga69We know that it depends on the quality of the game, so please give us an idea being realist. We also know that it depends on the development platform too. You know this information is important but you haven't given it to us so how can we answer. Even if it is for homework you still need to tell us what type of game and on what format. Will the publisher fund the game or will the developer self fund? #### Share this post ##### Link to post ##### Share on other sites Quote:  Original post by sagoga69OK!! That has been so realistic; but now, being less realistic, let's say that we are a important developer studio, that has finished a really good game (FFX level more or less, for example). The Final Fantasy games are major works. FFIX had a stated cost of over$30M USD. FFX has a stated cost of a little under \$40M USD.

I suppose if you self-financed the development cost of that kind of "really good game", finding a publisher would be a trivial thing.
Quote:
 Original post by sagoga69Of course, we don't have this kind of level, but we need the numbers of the possible game sell, because we have to obtain a business plan that's viable.We hope that now you can be a little more "fantastic".

The number of SKUs sold is anybody's guess. It depends on the platform for the game, the quality of the game, the reputation of the companies, branding, popularity of releated titles, the amount and quality of marketing, media coverage, hype, distribution channels, the ESRB game rating, the day you release and events near it, other titles released around the same time, the economy, and thousands of other factors.

For comparison, FFX was one of the most successful PS2 games out there. It sold about 8 million copies worldwide.

There is no simple formula.
Quote:
 Original post by sagoga69P.S: I know that the project it's not viable, but we need to do the finance results and we need some benefits for it.

I agree with the above -- smells like homework. Real ventures don't need to come up with finance results when they know up front that the project is not viable. They will instead look at more viable plans rather than persuing a known dead-end.

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Quote:
 Original post by sagoga69 we can imagine the numbers ourselves, but the problem is that we are really lost, because we don't know how much is expensive, and how much is cheap. Because of that, we only need a estimated number.

You can get some numbers here and here - did you read the other articles frob pointed you to before?

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Thanks a lot tsloper.
Yes, we had read the documents, but there are so many lines to read, so we only had read the ones that Frod pointed to.
Now, we have read the ones that you have pointed and they are exactly what we are looking for.

For the moment, we have are doubts solved, so thanks a lot frod, mike2343 and tsloper for your help. You have been very fast and very kind.

By the way, frod, logically, if the project it's not viable, there's no reason to do it, and if we have money to develope a 30M USD we don't need a publisher, but the situation is that we need to convince a business teacher that the project is viable, and she doesn't know anything about game business.

Edit 1: tsloper, my congratulations for your complete document. It's a really good web.

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I can't actually answer what you're asking, since you gave no info, but your response about "so many lines to read" made me want to respond. Whether this is for your homework or whether you are honestly writing a real business plan with a publisher calling you for it, the way to success is paved with "many lines to read."

The business plan is also "many lines to write", so studying Expository Writing really pays off in this case. ;)

Now, if you don't read many lines, the publisher will be paying you nothing. Based on the paragraph of info you gave, I'd suggest you and your friend make the game, publish it on the internet yourselves and have a PayPal Donate button and CafePress Shop with your game merchandise (provided none of it is someone else's copyright). If it's a decent enough game, you begin to build a following, and maybe some of the sales/donations can go to Game #2.

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