text: Maximal origami flip graphs of flat-foldable vertices: properties and algorithms Thomas C. Hull, Manuel Morales, Sarah Nash, and Natalya Ter-Saakov Vol. 26, no. 4, pp. 503-517, 2022. Regular paper. Abstract Flat origami studies straight line, planar graphs $C=(V,E)$ drawn on a region $R\subset\mathbb{R}^2$ that can act as crease patterns to map, or fold, $R$ into $\mathbb{R}^2$ in a way that is continuous and a piecewise isometry exactly on the faces of $C$. Associated with such crease pattern graphs are valid mountain-valley (MV) assignments $\mu:E\to\{-1,1\}$, indicating which creases can be mountains (convex) or valleys (concave) to allow $R$ to physically fold flat without self-intersecting. In this paper, we initiate the first study of how valid MV assignments of single-vertex crease patterns are related to one another via face-flips, a concept that emerged from applications of origami in engineering and physics, where flipping a face $F$ means switching the MV parity of all creases of $C$ that border $F$. Specifically, we study the origami flip graph $\rm{OFG}(C)$, whose vertices are all valid MV assignments of $C$ and edges connect assignments that differ by only one face flip. We prove that, for the single-vertex crease pattern $A_{2n}$ whose $2n$ sector angles around the vertex are all equal, $\rm{OFG}(A_{2n})$ contains as subgraphs all other origami flip graphs of degree-$2n$ flat origami vertex crease patterns. We also prove that $\rm{OFG}(A_{2n})$ is connected and has diameter $n$ by providing two $O(n^2)$ algorithms to traverse between vertices in the graph, and we enumerate the vertices, edges, and degree sequence of $\rm{OFG}(A_{2n})$. We conclude with open questions on the surprising complexity found in origami flip graphs of this type.  This work is licensed under the terms of the CC-BY license. Submitted: August 2021. Reviewed: June 2022. Revised: July 2022. Accepted: September 2022. Final: September 2022. Published: September 2022. Communicated by Anna Lubiw article (PDF) BibTeX


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# Source on functorial algebraic geometry

I want to understand algebraic geometry from the functorial viewpoint. I've found a set of notes (linked below) that develop algebraic geometry from the elementary beginnings in this framework. They go under the name "Introduction to Functorial Algebraic Geometry" (following a summer course held by Grothendieck), and are in parts in an almost unreadable shape. Is there an available, elementary, and readable source which takes the functorial viewpoint?

http://www.math.jussieu.fr/~leila/grothendieckcircle/FuncAlg.pdf

EDIT: Great answers so far, thanks! I would like to add that if anyone were to have a better scan of the document linked to above, or if anyone has vol. 2 of the notes I would be very interested in aquiring a copy.

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Try Demazure and Gabriel. – Thel Seraphim Jun 27 '11 at 15:34
As Josh already said, Demazure/Gabriel is the definite source. If you can read german, try to contact Marc Nieper-Wißkirchen. He has written lecture notes in which he developes algebraic geometry from the functorial viewpoint. – Martin Brandenburg Jun 27 '11 at 15:42
The question said "available, elementary and readable"... D&G doesn't fit all three points :-) But it's indeed the best answer I know ; the functorial point of view is also mentioned in Eisenbud&Harris "The geometry of schemes" if I remember well, but it isn't the base. – Julien Puydt Jun 27 '11 at 18:08
In my memory, EGA does not qualify -- in EGA the schemes/spaces are defined as ringed spaces and not as sheaves on a site which are locally representable. Knutson's "Algebraic spaces" has more of the functorial approach. FGA (and recent "FGA explained" cf. ncatlab.org/nlab/show/FGA+explained ) are more useful for start, complemened by Demazure-Gabriel. – Zoran Skoda Jun 27 '11 at 20:00
The functor of points approach is written down with great clarity in the Springer edition, and it is used to construct the Grassmannian and flag varieties, among other things. Now, a functorial approach to the basics of schemes is a different matter, but EGA 1 (the Springer edition) is a reference for all the notions mentioned in the accepted answer. – Keerthi Madapusi Pera Jun 28 '11 at 22:22

Dear Eivind, since your question might interest other readers, allow me to expand it.
Given a scheme $T$, you can associate to it the contravariant functor $h_T: \mathcal{ Schemes}^{opp} \to \mathcal{Sets}$. In a nutshell, Eivind's request is for documents showing how you can study the scheme $X$ by studying the functor $h_T$.
Not all functors
$$h: \mathcal{ Schemes}^{opp} \to \mathcal{Sets}$$ come from a scheme $T$ and you have to characterize those that do. A pleasant surprise is that it is enough to look at what your functor does on affine rings, so that in effect you study a functor $$k: \mathcal{ Rings} \to \mathcal{Sets}$$ The characterization is then relatively easy (once Grothendieck has shown us what to do!): the functor must be a sheaf in the Zariski topology and satisfy a condition which translates that a scheme is covered by affines. There is a real aesthetic appeal to the realization that concepts like closed or open immersions, tangent spaces,... can be expressed purely in terms of functors. The appeal is not only aesthetic, but also technical: it is with the functorial method that parameter spaces, like Grassmannians, Hilbert schemes,...are constructed.
And where is all this to be found?

a) In Mumford's Introduction to Algebraic Geometry, affectionately called The Red Book, Chapter Ii, §6: The functor of points of a prescheme. The book has been reprinted by Springer

b) Unfortunately Mumford didn't publish the rest of his course. However there is a set of notes (more than 300 pages) coauthored by Oda, corresponding to Chapters I to VIII, which can be found on-line here

c) Eisenbud and Harris wrote a book on schemes which came out of a common project with Mumford. The last chapter (chapter VI) is called Schemes and Functors and, as the name says, is dedicated to the point of view we are discussing.

d) Brian Osserman has a very pleasant short hand-out here on the use of the functorial point of view to illuminate the construction of the product of two schemes.

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Very nice answer. – Martin Brandenburg Jun 27 '11 at 22:31
Thank you, Martin. – Georges Elencwajg Jun 27 '11 at 22:47

Toen's master course on stacks is awesome and it starts from scratch. Unfortunately it doesn't take matters too far (although I guess the next for him would have been model sites and $\infty$-stacks!). http://ens.math.univ-montp2.fr/~toen/m2.html

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The main reference that I'm aware of is

• Demazure and Gabriel -- Groupes algébriques (1970)

If I remember correctly the first chapter develops the fundamentals of scheme theory from the functorial point of view. Part of the above work (including the relevant first chapter) was translated into English and published as

• Demazure and Gabriel (translated by J. Bell) -- Introduction to algebraic geometry and algebraic groups (1980)

Another source is

• Jantzen -- Representations of algebraic groups (2nd ed., 2003)

Jantzen basically copies the approach of Demazure and Gabriel but his presentation is easier to read. Demazure and Gabriel are pretty rigorous with their foundations and talk a lot about Grothendieck universes and such things, whereas Jantzen doesn't go overboard with these kinds of details.

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If you are group-oriented and functiorially minded, then Sancho de Salas's book "Groupos algebraicos y theoria de invariantes" seems great (although I haven't gone through it yet). (ah, the book's in spanish) librarything.com/work/2781283 – babubba Jun 27 '11 at 21:02

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# Calculate dic manually

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The DIC function calculates the Deviance Information Criterion given the MCMC chains from an estimateMRH routine, using the formula: DIC. ADDED In response to user's comment below: $\operatorname{P}(D\vert\theta)$ depends on the model for the data. Kurtosis is one of the summary statistics; it is used for describing or estimating a distribution’s peakedness and frequency of extreme values.

The DIC function calculates the Deviance Information Criterion given the MCMC chains from an estimateMRH routine, using the formula: DIC. It transforms a sequence of complex numbers into another sequence of complex numbers. As such, you may be required to calculate your RMD for your inherited IRA. Employing human rather than mechanical energy. Jul 21,  · Does anybody know how to calculate pD from the coda files output from R2WinBUGS?. calculator: 1 n a small machine that is used for mathematical calculations Synonyms: calculating machine Types: show 9 types hide 9 types abacus a calculator that performs arithmetic functions by manually sliding counters on rods or in grooves adder a machine that adds numbers adding machine, totaliser, totalizer a calculator that. The left term is non-negative; consequently the intraclass correlation must satisfy ≥ − −.

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This form is usually attributed to Harris. number of iterations to discarded at the beginning for generating [HOST] Define calculator. Return to the top 2.

It's usually analytically simpler and more computationally stable to work with the log-likelihood, and that's what you'll need to calculate the DIC anyway. 1. I am currently fitting a set of 16 models in JAGS. Has anyone ever tried to calculate DIC "manually" from WinBUGS output? Use the Binomial Calculator to compute individual and cumulative binomial probabilities. Generally, age is linked to human beings but if seen on another perspective, it is the calculation of the length of time for anything that has ever existed.

See more. Employing human rather than mechanical energy. By the way, 'set DIC' is greyed out for some reason within WinBUGS, so I can't monitor DIC.

Binomial Probability Calculator. The left term is non-negative; consequently the intraclass correlation must satisfy ≥ − −. Unlike RMD amounts for IRA owners, custodians are not required to calculate RMD amounts for inherited IRAs.

While the term “Age” refers normally to human beings, it can actually be used for the calculation of the length of period that anything has existed. Guidelines for Gathering Optimizer Statistics Manually In most cases, automatic statistics collection is sufficient for database objects modified at a moderate speed.e.

Automatic collection may sometimes be inadequate or unavailable, as shown in the following table. To calculate the present value of receiving $1, at the end of 20 years with a 10% interest rate, insert the factor into the formula: We see that the present value of receiving$1, in 20 years is the equivalent of receiving approximately $today, if the time value of money is 10% per year compounded annually. a.e. Mark off pairs of digits, starting from the decimal point and working left. The formula for Macaulay duration is. Example of how to calculate the check digit of barcode upc-a. With our 44 online dictionaries, conjugation tables and multilingual phrases, the [HOST] language portal will help you translate, learn and practice new languages. In the most recent work week, he worked 50 hours. ymis are treated as extra parameters in the model of missingness, with the model of interest acting as their prior distribution. The DIC score calculator evaluates the following clinical criteria: platelet count, increased fibrin markers, prothrombin time prolongation, and fibrinogen level. Thus pD is the posterior mean of the deviance minus the deviance of the posterior means. Aug 18, · According to the Oxford dictionary, age is defined as the length of time calculate dic manually one person has existed into life or have lived. It is widely used in capital. Department of Veterans Affairs | Vermont Avenue, NW Washington DC Last updated August 21, Define calculator. Manually definition, done, operated, worked, etc. n. Does anybody know how to calculate pD from the coda files output from. Calculation of a square root by hand is a little like long-hand division.. I. To calculate your daily calorie and macro goals, simply fill out the information on my calculator below! adj. First, the DIC deviance is obtained using a discrete calculate dic manually set of samples to the main parameter estimates. c. Viewed times 1. 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Made Easy Free Download PDF Learn woodworking online Expert advice on woodworking and furniture making, with thousands of how-to videos, and project plans designed to take your craft to the next level. Step 1.) and commas (,) mark pairs of digits.The DIC automatically generated by WinBUGS in the presence of missing data is a conditional DIC, and WinBUGS produces DIC values for the model of interest and model of missingness separately. There is more than one way to calculate duration (which we'll get to below), but the Macaulay duration (named after Frederick Macaulay, an economist who developed the concept in ) is the most common. Feb 09, · I've been trying to figure out how JAGS calculates the deviance at each iteration during the sampling process from the posterior. To calculate age manually is a fairly simple arithmetic procedure. How do you calculate DIC from coda files (R2WinBUGS)? Thus pD is the posterior mean of the deviance minus the deviance of the posterior means. If such is the case, it may be wise to work with your tax or retirement calculate dic manually planning professional to ensure the accuracy of the calculation. ADDED In response to user's comment below:$\operatorname{P}(D\vert\theta)$depends on the model for the data. U. However, what I calculate and what JAGS calculates are slightly different. Also, because my model was simultaneously calculating a lot of derived parameters (my outcome variable over a fine-scale gradient of the predictor variable), I couldn't use the documented print() function, because there was too much text and it got. Unlike RMD amounts for IRA owners, custodians are not required to calculate RMD amounts for inherited IRAs. posterior mean deviance minus deviance evaluated at the posterior mean. . To calculate a bond’s yield to call, enter the face value (also known as "par value"), the coupon rate, the number of years to the call date, the frequency of payments, the call premium (if any) and the current price of the bond. 1) run [HOST]s monitoring all the parameters + deviance (this require [HOST]("dic")). Dhat is a point estimate of the deviance obtained by substituting in the posterior means &[HOST]: thus Dhat = - 2 * log(p(y | &[HOST])). Done by, calculate dic manually used by, or operated with the hands. The Discrete Fourier transform formula is derived from the Euler's formula. DIC (Spiegelhalter et al ) is calculated by adding the “effective number of parameters” (pD) to the expected deviance. Dhat is a point estimate of the deviance obtained by substituting in the posterior means &[HOST]: thus Dhat = - 2 * log(p(y | &[HOST])). Compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at. Photo courtesy of Joy Hicks Collection rates help the medical office determine how successful the office is in collecting receivables. (Here the decimal point is a period . The check digit is the last barcode number that makes sure the barcode is correctly composed. This page explains the formula calculate dic manually for kurtosis, excess kurtosis, sample kurtosis, and sample excess kurtosis. Jul 22, · How to Calculate Collection Rate. I tried for the simplest linear model, and could get exact the same calculate dic manually Dbar, but always a bit different Dhat. NCWAM Toolbox (Database for storing manually entered FAF or FAF from a GPS unit): NCWAM Toolbox User Manual. Package ‘R2WinBUGS’ DIC logical; whether DIC should be calculated, see also argument DICOutput and details DICOutput DIC value [HOST] number of total iterations per chain used for generating [HOST] [HOST] length of burn in, i. Calculate definition, to determine or ascertain by calculate dic manually mathematical methods; compute: to calculate the velocity of light. An electronic or mechanical device for the performance of mathematical computations. NCWAM Toolbox Database. calculate dic manually Alfredo Montoya works the evening shift at Electronic Inference Corporation, which adds$1 calculate dic manually of shift differential per hour to his base wage of \$15 calculate dic manually per hour. Net present value (NPV) is a method used to determine the current value of all future cash flows generated by a project, including the initial capital investment. posterior mean deviance minus deviance evaluated at the posterior mean. Use the Normal CDF formula to manually calculate the probability function. manually synonyms, manually pronunciation, manually translation, English dictionary definition of manually. Deviance Information Criterion, DIC = ‘goodness of ﬁt’ calculate dic manually + ‘complexity’ • They measure ﬁt via the calculate dic manually deviance D(θ) = −2logL(data|θ) • Complexity measured by estimate of the ‘eﬀective number of parameters’: pD = Eθ|y[D] − D(Eθ|y[θ]) = D− D(θ); i.

DIC: Deviance Information Criteria DIC (Deviance Information Criterion) is a Bayesian method for model comparison that WinBUGS can calculate for many models. Aug 18,  · According to the Oxford dictionary, age is defined as the length of time one person has existed into life or have lived.


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# Isometric Error: decrement iteration removes tiles [closed]

I am new to isometric and game programming in general.

Just cannot figure out how to iterate the grid from behind. I want to do it so that the tiles overlap properly.

My grid starts at [0][0] which translates into the tile closest to the left edge.

This is how my a smaller version of my map grid looks like:

var map = [
[1, 1, 1],
[1, 0, 0],
[1, 1, 1]
];

I have no trouble displaying it when I loop forward through the arrays:

But when I try to iterate backwards through the Y array, it starts bugging, and does not display all tiles and have no clue why:

I hope the images are large enough, else please "Zoom in" or open them in a new tab.

Cheers

## closed as too localized by MichaelHouse♦, bummzack, Trevor Powell, Josh♦, AnkoApr 8 '13 at 8:31

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

for (var y=map.length-1; y>=0; y--) {

for (var y=map.length; y-->0;) {


text:
## anonymous one year ago The incomplete work of a student to solve an equation is shown below: Step 1: 3x + 12 = 3 Step 2: ? Step 3: x = −9 ÷ 3 Step 4: x = −3 What is the missing Step 2?

1. anonymous

Subtract 12 from both sides

2. marihelenh

They subtracted the 12 over to get 3x=-9

3. anonymous

$\huge~\rm~ 3x + 12-12 = 3-12$

4. anonymous

$$\huge\rm\color{red}{3x=-9}$$

5. anonymous

Thank you so much


text:
20 Answered Questions for the topic Definite Integration

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#### Definite Integral Evaluation

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#### What is ∫-7^-1 f(x)dx?

suppose that f(x) is an even function and let ∫0^1 f(x)dx = 5 and ∫0^7 f(x)dx = 1. What is ∫-7^-1 f(x)dx?   This is my work   I expand ∫-7^-1 f(x)dx to F(-1) - F(-7)   F(-1) - F(-7) is the... more
Definite Integration Math Calculus Integrals

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#### What M value should I use? (how do i find it)

I was asked to calculate the area between two functions, y=e^x and y=x using midpoint riemann sums from 0-2 with n=4. so i found my answer by subtracting the second sum from the first. The second... more
Definite Integration

01/07/17

#### I need help to this problem!!

Integral of tan inverse of x divided by x, limits are from 1/2014 to 2014
Definite Integration Calculus Physics Parabolas

12/26/16

#### If I have a spinning bowl of water...

A spinning liquid of any sort forms a paraboloid; a three dimensional parabolic shape. Therefore, you can apply the physics principles relating to centripetal motion to any mass, m, on the surface... more
Definite Integration Integral Calculus

12/06/16

#### If f' is continuous on [a,b], show that

2∫ab f(x)f'(x)dx=[f(b)]2-[f(a)]2
Definite Integration Calculus Integrals U Substitution

06/23/16

#### Definite Integral with U-Substitution

I have an integral with ∫ (b=0, a=-1) and the inside function is (2t)/[(3+t2)3]dt. The directions tell me to "Evaluate the definite integral by making a u-substitution and integrating from u(a) to... more
Definite Integration Calculus

05/26/16

#### Definite integral question

Calculate the integral of:  cos [2x] π. cos πx dx From 0 to 1.
Definite Integration Calculus Integration

05/25/16

#### Integral limit definition

No limit is visible in integral notation, but integration is defined in terms of a limit.  Give the definition; explain what is being limited, and how this allows an integral to calculate the exact... more
Definite Integration Integral Calculus Integration

04/23/16

#### integration

show that ∫dx/(2+3sinx) [upper limit pi/2, lower limit 0] = ∫dt/((t+ 3/2)2 - (√5/2)2) [ upper limit 1, lower limit 0]     I know that sin(x) = 2t/(t2+1), where t = tan(x/2) but i cannot get the... more
Definite Integration Calculus Integrals Integral Calculus

04/21/16

#### Indefinite/Definite Integrals

I need help solving a couple of indefinite/definite integrals. It seems all of my homework problems have done the less complicated ones so I'm not sure how to do these ones:First problem:... more
Definite Integration Integrals Integral

02/02/16

#### Cubic curve integral - area enclosing curve and x-axis

The curve is x^3-6x^2+11x-6. I have to prove that the two regions enclosed between the x-axis and the curve are equal. Given is, that the curve cuts the x-axis at x=1,x=2 and x=3. I tried finding... more
Definite Integration

11/25/15

#### integrate 0 to pi/2 xsinx/1+ cos2x

definite integral question
Definite Integration Calculus Integrals

07/17/15

#### Express limit as definite integral?

limit as n goes to infinity.   n Σ     i4/n5     on interval [0,1] i=1   Options are:  1             1              1            7          1 ∫  1/x5  , ∫  1/x4    , ∫  x4   ,   ∫  x5  ... more
Definite Integration

06/01/15

#### how do the constants of integration cancel out during definite integration

how do the constants of integration cancel out during definite integration. please answer these.

11/10/14

#### Definite Intergrals

Approximate the area of the region bounded by the graph of f(x)= cos (t/2-7pi/8) and the t-axis on [7pi/8, 15pi/8] with n=4 sub intervals. Use the midpoint of each sub interval to determine the... more
Definite Integration

07/23/14

#### Calculus question

Find each definite integral    top:3 bottom:0 (square root) y+1dy     top:3 bottom:2 1/e^x Dx

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text:
1. ## 2nd derivative

I've done this problem two different ways and have gotten two different answers. It's very long and one simple algebraic mistake messes up everything so i was wondering if someone could find the anwer: find the second derivative of (x^2)(y^2)-2x=3. Can you use the quotient rule to find it so if i did do it wrong i can see where i made the mistake? i got (2x^2y^4-2xy^2-1)/(x^4y^3) the first time and (2x^2+y^2-2xy-1)/(x^4y^3) the second. Also, how do i find the derivative of an equation implicitly. Explicity it's d(f(x),x) but i can't figure it out implicitly. I'd rather check my work that way instead of bothering you. Thanks alot

2. What? isnt the first derivative (-xy^2+1)/(x^2*y)? i put that in the calculator and it gives me the same answer....please reply

3. Originally Posted by jarny
What? isnt the first derivative (-xy^2+1)/(x^2*y)? i put that in the calculator and it gives me the same answer....please reply
yes, that is true

now differentiate again


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# ValueRockets price increase?

### Help Support The Rocketry Forum:

#### dpower

##### Well-Known Member
After weeks of indecision, I went to order some D10 & D21 motors today, and noticed that the 3 pack prices are $17.49. They were$15.90, I think just last week. This is the only place to get these 3 packs, right?

#### MarkII

##### Well-Known Member
After weeks of indecision, I went to order some D10 & D21 motors today, and noticed that the 3 pack prices are $17.49. They were$15.90, I think just last week. This is the only place to get these 3 packs, right?
I haven't noticed this before, but you are right; no one else seems to sell AT 18mm SU motors in 3-packs, and Apogee Components seems to be the only other vendor of 18mm D10's (in their Apogee Medalist line of motors). Still, at \$5.83 per motor. the ValueRockets price is awfully good.

MarkII

#### Davidtmp

##### Well-Known Member
Gary announced a price increase about a week or so ago...Seems the AP is getting scarce in the surplus market. So they are having to buy some of the higher grade, which is a little more expensive.


text:
Paper ID: 782 Title: Online Learning with Adversarial Delays
Current Reviews

Submitted by Assigned_Reviewer_1

Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
Summary: This paper contributes to a growing literature which seeks to weaken

full-feedback assumptions in traditional online learning.

Here, rather than observing feedback immediately, the learner may have to wait an unknown amount of time (the "delay") before observing the results of actions taken on a given round.

The paper derives algorithms for this setting, where the delays are chosen adversarially -- more precisely, the paper shows that in fact existing learning algorithms already offer regret guarantees for this setting with appropriate choices of the learning rate.

Praise: The results are intriguing, as they show once again that the standard online learning algorithms are quite robust to changes in the model.

The proofs are reasonably concise and to the point.

Criticism: The first question I had, given that "adversarial delays" appears in the title, was: how does the adversary behave here?

I was disappointed to see that there was no such discussion on this point.

In particular, are these bounds tight?

The discussion of Langford et al. before the proof of Thm 1 suggests that the optimal delays for the adversary, given a budget of D, is to spread them out evenly, and this should yield a tight bound.

But what does adversarial mean if there is no budget D, which seems to be the setting in question?

Perhaps "unknown delays" would be a better term here.

My second criticism is the lack of intuition given about the results.

In particular, it seems to me that the bounds are saying that additional delays are "equivalent" to playing more rounds of the game -- I would have liked to see some discussion about why this might be the case.

Is the intuition that delays are cumulative in the above sense grounded in the proof?

The proofs are reasonably clean yet obscure this point (to me).

In my opinion at least one of the proofs should move to the appendix to make way for a thorough discussion on the nature of the bounds.

Comments: page 1 (the big-O notation assumes that diameter of K): Typo page 2 (et al): Here and elsewhere, should be "et al." page 2 (for some parameter   R): Positive as well page 6 (For = O(1/  D), Theorem 2 implies a regret bound of O(  D).): Remove first O(), otherwise the statement is false. page 8 (regularized-follow-the-leader): Usually this is follow-the-regularized-leader
The results are nice but not groundbreaking.

Needs more intuition and consideration of the adversary.

Submitted by Assigned_Reviewer_2

Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The authors slightly modify two well known online algorithms, OGD and FTPL, to address the problem of adversarial delays. In this problem, it is assumed that adversary might not reveal the loss functions at end of every round. The modifications to the algorithms are most natural and I appreciate the simplicity.

Since the crux of the paper lies in the analysis of the modified algorithms, I need to be sure about the correctness of the proofs before accepting the paper. While it is of course possible that I have misunderstood a couple of things, I want to be convinced that it is my mistake rather than mistake in the proofs before agreeing that the paper can be accepted to a conference of such prestige.

Originality- Unless someone has already published the ideas before, I cannot question the originality of the work.

Significance- The authors give a few examples in the beginning as to why adversarial feedback might be delayed. I have not encountered this problem before; so I am assuming that this problem is of interest to the online learning community.

Clarity- The introduction and the two (modified) algorithms are certainly clear and simple to understand. However, I have a few issues regarding the presentation of the proofs. Normally, it would not matter, but considering the paper is all about the analysis, and the proofs are in the main paper, I think the presentation is important.

1. Line 033- Why is the game fundamentally unfair? Unfair to whom? Learner or adversary? If the adversary is adaptive, I would say that the adversary is very powerful. Moreover, considering the regret is w.r.t to the best single decision learner could have taken in hindsight, I do not understand the unfairness issue. 2. It is confusing how the proof is going from line 151 to 156. While the inequality in line 156 is correct ( I checked it- simply write ||x_{t+1}- y||^2= ||x_t - \sum_{s \in F_t} \nabla f_s|x_s - y||^2 and open up the expression on the right followed by simple algebra), I find what is written in the paper confusing. First, the authors fix s as max F_t, but then the expression is unrolled over $s$. Is s fixed or variable? 3. Please check the expression for x_{t,s} when it is introduced. I think in the gradient term, it should be \nabla f_r|x_r, not \nabla f_s|x_r.

4. I found it very difficult to understand the proof of Lemma 3.2. Can it be presented in a better way? It is simply the end part of Theorem 1.1 and Lemma 3.2 in Kalai-Vempala FTPL paper. In their paper, it is so simple to understand (the argument of what fraction of two hypercubes overlap followed by the fact that in the fraction they dont overlap, the maximum difference in decision*cost factor is bounded by L_1 norm of decision and L_{infty} norm of cost, which is precisely what is being done in Lemma 3.2 of this paper). I dont see the need to recast Kalai-Vempala's argument in a more complicated way. 5. There are number of notational mistakes in Lemma 3.3. Please check.

Quality- The main questions I have are in the proof of Theorem 1. 1. Why does the inequality in Line 192 hold? Specifically, why is x_{t,s} closer to x'_{s+1} in Euclidean space than to x_{s+1}? I simply could not understand how this came about? As far as as I can see, x_{t,s} is an arbitrarily defined point. Is x_{t,s} inside or outside the convex set K? Either way, why does the inequality hold? 2. I simply could not wrap my head around the argument between Line 200 to line 219. I tried to reason independently but could not. While of course it does not mean the proof is wrong, I would like to talk to other reviewers before being convinced about it.

I liked the paper and was generally happy with the fact that authors maintained simplicity, analyzing (most natural) modifications to two well known online algorithms, OGD and FTPL. The main reason for not accepting the paper is a doubt I have about the proof of Thm.1,

and couple of relatively minor issues which I highlight below. I will surely reconsider after author feedback and discussions.

Submitted by Assigned_Reviewer_3

Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The paper uses the on-line optimisation framework.

Suppose that the feedback (the cost function f_t) comes to us with arbitrary (possibly adversarial) delays. What bounds can we achieve?

The paper takes two algorithms, on-line gradient descent and follow the perturbed leader (in the optimisation context) and makes natural adjustments to them: all modifications to the x_t and to the current choice of the leader are made on the basis of the feedback available so far. New modifications are introduced as soon as feedback becomes available.

The paper provides theoretical bounds for the new algorithms. The change amounts to the introduction of an extra term of the order square root of the sum of delays, which is comparable with the standard \sqrt{T}.

The paper also considers an application to the tree update problem, but the discussion is rather terse.

The paper is lucidly written.

I believe the paper provides an important contribution to the theory of on-line prediction.

Minor issues:

1. Page 5, last displayed equation. I think brackets are needed after argmin for clarity.

2. I would like to point out some previous work concerned with the delays in feedback. See the treatment of weak and lazy teachers in

D. Ryabko. On the Flexibility of Theoretical Models for Pattern Recognition, Ph.D. Thesis; Royal Holloway, University of London. April, 2005
The paper adapts two on-line optimisation algorithms for the scenario where there is delay in the feedback.

Author Feedback
Author Feedback
Q1:Author rebuttal: Please respond to any concerns raised in the reviews. There are no constraints on how you want to argue your case, except for the fact that your text should be limited to a maximum of 5000 characters. Note however, that reviewers and area chairs are busy and may not read long vague rebuttals. It is in your own interest to be concise and to the point.
We thank all the reviewers for their careful reviews. We have generally incorporated all the changes suggested, addressed individually below. These changes have improved the paper and we are grateful for the feedback. Due to space constraints, not all comments can be addressed here. We omit some points that we agree with and have made simple adjustments for.

Assigned_Review_1 (AR1): Thank you for the additional references. They have both been incorporated into the paper. We have given considerable space to your first reference, "Online learning under delayed feedback", explained below in the section addressed to AR5.

AR2: Thank you for your careful review. The term "adversarial" was to imply no assumptions regarding bounded or independent delays, in the some way that we have "adversarial" or "worst-case" inputs in classical algorithms. A better term here may be "arbitrary" or "unbounded", as well as "unknown" as you've suggested. We've slowed the pace and softened our language when introducing the model accordingly. Regarding intuition, our hope was to obtain results clean and transparent enough to wrap one's mind around and extend. At your suggestion, we've tried to improve the commentary surrounding the results.

AR3: Thank you for your encouraging review. Thank you also for the reference to Ryabko's thesis, which is now cited.

AR4: Thank you for your astute review.

(Clarity) (1) We apologize for the confusion caused by our choice of words. The goal here is to gently motivate and introduce the notion of regret to an outside reader. We have softened the language and emphasized that the comment is informal.

(4) Our proof of Lemma 3.2 merely extends the argument of Kalai and Vempala. As authors, we went back and forth between the algebraic argument and the geometric one. In the end, we resolved that the algebraic argument may be more concrete and easy to verify, at the cost of Kalai and Vempala's (very nice) geometric intuition. As per your suggestion, we have provided comments that relate our algebraic version of the proof to the original geometric version.

(Quality) (1) You are correct. We should have written the proof to unroll from the recent rounds (t,t-1,t-2,...) to the oldest rather than the other way around (s,s+1,s+2,...). For example, the first step is use the triangle inequality and Lemma A.1 to obtain

||x_{t,s} - x_s}|| \leq ||x_{t,s} - x_t|| + ||x_t - x_s|| \leq ||x_{t,s} - x_t|| + ||x_t' - x_s||

The second term ||x_t' - x_s|| is similarly bounded by ||x_t' - x_{t-1}|| + ||x_{t-1}' - x_s||, and so on, until arriving at the same sum, and continuing the proof as before.

We are grateful to the reviewer for noting this error, and have corrected our proof accordingly.

AR5: Thank you for the reference to the paper of Joulani etal, also suggested by AR1. We have now included an introduction to this work and other work (such as that of Weinberger and Ordentlich) similar in spirit. As a different approach to a similar problem, these results provide a healthy contrast to our work. Please note the following.

(a) The framework of using a pool of learners, each of which acts as an undelayed learner over a subsequence of rounds, is a qualitatively different algorithm. Maintaining independent instances of learners proportional to the delay is more resource intensive then a single learning algorithm. Furthermore, the pooling framework requires the feedback to be timestamped by its originating round in order to return the feedback to the appropriate learner.

(b) The $\sqrt{D}$ bound is asymptotically sharper then the bounds obtained by the pooling framework. To recap, let $C$ be the maximum number of outstanding feedbacks at any single point of decision. Then the pooling framework has a regret bound of $O(\sqrt{CT})$. (Jensen's inequality can then model $C$ probabilistically.) Clearly, $D \leq CT$ in any scenario. For a simple example to distinguish the two bounds, suppose that the feedback from the first $\sqrt{T}$ rounds is withheld until after round $\sqrt{T} + 1$, and all other feedback is delivered on time. Then the maximum number of outstanding feedbacks is $C = \sqrt{T}$, giving a regret bound on the order of $T^{3/4}$. On the other hand, the total delay is still $D = O(T)$, and our results give a regret bound on the order of $\sqrt{T}$.

AR6: Thank you for your insightful observation. We think it may be correct. As noted in the conclusion, we expect a $\sqrt{D}$ regret bound for mirror descent, and similar bounds for most popular algorithms in online learning. The staying power of this work is the introduction of the quantity $D$, by which one can argue that standard algorithms have been fairly robust to delays all along. The individual proofs for gradient-descent and follow-the-perturbed-leader are experiments that validate the model. We look forward to updating the conclusion once we finalize our verification, very soon.


text:
# Locklin on science

## Cybersyn and Allende’s Semi-Automated Luxury Socialism

Posted in econo-blasphemy by Scott Locklin on February 26, 2019

One of the interesting “what ifs” of history is “what if the 70s-80s commies used computers to do their planned economy.” Men like KantorovichNikolay Fedorenko and Victor Glushkov helped develop some of the mathematical tools and computer systems which would have made this possible.There were abortive attempts to build this in East Germany (pdf link), the Soviet Union and Allende’s Chile. As far as I can tell, the Soviet and German efforts were crushed by old guard party rednecks who feared losing control to technocrats. Oddly, Allende’s attempt at this, which would have been constructed of bone knives and bearskins, seemed to come closest to being deployed.

The visionary behind this was Fernando Flores, who is still alive despite being Allende’s minister of finance and later “General Secretary” back in the early 1970s. Flores was inspired by a sort of futurist “cyberneticist” operations research proponent named Stafford Beer. Operations research is generally now thought of as the field of applied work involving optimization; linear programming and all that. In those days  it was something more general: mathematics applied to the problem of management. Guys like Beer with this sort of training ended up running large parts of the war economy.

It’s difficult for me to characterize what “cybernetics” is, probably because it doesn’t really mean anything. Norbert Wiener, who I respect, coined the phrase, and more or less defined as a hand wavey general study of systems of feedback and control mechanisms. As far as I can tell, “cybernetics” was a complete bullshit field, and what it really meant was “I know futuristic looking words and have Wiener’s book on my shelf; pay me more.”  Stafford Beer was a proponent of “management cybernetics” which, as far as I can tell, meant “using data to make business decisions.”  The books are hysterical; you can go look at them on filesharing sites. They appear to be total horse shit. FWIIW the Soviets more or less agreed with me, at least in 1947; the field of cybernetics was condemned as “a science of obscurantists, a pseudoscience wedded to obscurantist epistomology.”

This looks like it pertains to something real; nope

Flores hired Beer. Beer cut his rates to $500 a day (about$2500 in today’s money) along with unlimited cigars, chocolate and wine; items the Chilean government had a surplus of. Mind you the Chilean government was being starved of dollars at the time as a form of colonial pressure, just as the Venezuelan government is now in 2019. The results were hilarious.

The thing Beer built for the Chilean government is most famous for its control room, so we’ll start there. It had a bunch of cool chairs where powerful human intelligences would examine data on the walls and vote on the cybernetically optimal next steps. The chairs are TOTALLY not based on Captain Kirk’s control chair from Star Trek; every account of the thing makes certain to mention this. I assume Beer got a lot of shit over it, and rightly so, because he totally copied this from Star Trek. Or, if he didn’t, his designer did.

The chairs come equipped with ash trays (men of power always smoked in those days) and a place for a whiskey glass, presumably in case Castro or Beer wanted to relax while making important decisions. There are 7 of the chairs to make sure they can always achieve consensus when they vote. They use ridiculous glowing geometric buttons (like on Star Trek) instead of keyboards. The main reason is because they’re all hardwired to physical mechanisms; the images and graphs on the wall are not computer generated or directly interfaced with a computer at all. They’re slides and viewgraphs that are manually put in there by human helpers behind the walls. The lack of keyboard has also attributed to keyboards being “feminine” or confusing to men, which may be true in some way, but which doesn’t make any sense, as male factory workers used the teletypes to communicate factory data with home base.

The important pieces in the background, besides the workers behind the curtain, were the computer, an antique that they had on hand, and dozens of teletype machines they distributed to factories and control points to relay important metrics and data back to home base. These metrics would be entered into the computer (by hand), which would presumably generate reports (it’s not clear this ever happened) which would be manually turned into viewgraphs and slides by artists. The display of these slides would then be controlled by heavy drinking/smoking men in Captain Kirk Star Trek chairs, just like when they show you their vacation photos on a carousel slide projector. Except it was 7 people controlling the projector and arguing about what it all means.

People go on about how futuristic this was, because … I dunno, muh internet and muh powerpoint is used to make business decisions now. The reality is, Beer built the Allende government the economic equivalent of one of those WW-2 era RAF air defence sector station operation rooms with a little futuristic woo slapped onto it. It has some trappings of high technology with the Star Trek like buttons, but those buttons really didn’t do much of anything. The data allegedly eventually feeding  back to the computer could have been more effectively gathered by people on the telephone with yellow legal pads rather than the teletype, just like it was in a WW-2 era RAF air defence command center. In fact, factory managers ended up routing around the central command center and teletype process by calling up other factory managers and working out potential supply issues.

The one time it was allegedly useful was during a CIA organized truckers strike. You’d expect any central data/controll station to be useful in a crisis situation, more for putting decision makers in a room where all the data is available than anything else. Pretty sure the slides, assuming any were made for the event, and the computer, assuming any data was entered into it, were not helpful here.

It may have eventually been a helpful tool if Pinochet hadn’t taken over, thrown many of those involved out a helicopter, and destroyed the room of socialist power. The fancy appearance of it was almost entirely Potemkin village though. It relied on people entering stuff into the system at the collection end. It relied on “data science” people writing code. And it relied on artists marshalling the data into useful and insightful visual reports. It also relied on people who managed the factories to obey, and in a timely fashion; presumably once you finished your whiskey and cigars, you summoned a telephone to tell the factory workers what to do. All of these things are guaranteed to more or less fail.

Even small design decisions were foolish. The controls; why should everyone in the room be able to control the view? How could everyone in the room control the view? We don’t give everyone a remote when we do powerpoint now. Beyond that, how does the cigar smoking drunk in the chair know what slides are where when he’s pressing his buttons? It changes every meeting, and some boob in the background could screw up the order of the things. Who sets the agenda? I strongly suspect the guys in the chairs would be shouting through the walls to get the secretaries to pull up different slides. Also the voting buttons. Seems very scientific and futuristic to have the seven cigar puffing drunks in the Captain Kirk chairs voting by some kind of electrical secret ballot to make decisions. Why wouldn’t they just say “dude this sucks?” How would it make a difference? And of course, there was no way to actually transmit decisions using all this fancy electronics, besides the telephones they should have used in the first place.

The SAGE system was a real world embodiment of this sort of thing, built 15 years earlier. Unlike Cybersym, it was a real time system, with real time data flowing into a central processing unit, and real time commands being sent out to remote bases. SAGE also had human operators who helped the computer make the right decisions. SAGE worked (we think) because it actually was entirely networked, and the data flowed quickly, and split second decisions were absolutely necessary. SAGE also didn’t have any goofy fake control panels with a place to put your liquor, or LARPY telex stuff where secretaries had to do data entry to put the data into a computer. But, at the time, it was probably fairly difficult to see this, and people who watched a lot of Star Trek were probably impressed.

I’m not sure how the detailed history of this played out. It’s entirely possible American spooks ramped up their efforts to depose Allende in part because of fear of this. US economists and analysts almost always overrated Soviet and communist efficiencies. In part this happened because the Soviets would occasionally surprise people with things like Sputnik. In part it was rice bowl politics; you get a bigger budget for the scary threat rather than the third world threats made of coconuts and rubber band slingshots. But mostly it was because the technocrats and economists who purported to study Soviet economics thought their own farts smelled of roses. Western economists in those days were not the mere bean counters and toadies for capital they are today: they had vast powers to regulate the economy, set prices and so on. They just assumed more regulation of the economy would cause it to run more efficiently. They believed their own bullshit.

The threat of a more efficient civil service is taken very seriously by governments. For examples from history, the late Imperial government of Russia was seen as a great threat by Germany as it had developed an efficient and productive civil service. One which was rapidly industrializing the country and improving its logistics with a fraction of the per capita civil service manpower of Germany. WW-1 may have been partially a result of this fear. I can’t  prove any of this without access to spook internal documents and reports on Cybersyn. But I do have the example of an article in New Scientist who described Cybersyn as potentially “one of the most powerful weapons in history.” I mean, it very obviously wasn’t and probably couldn’t have been with the approach they took. But the CIA had no real way of knowing this.

As a sort of weird coda to all this, apparently Brian Eno and later David Bowie and David Byrne befriended Beer. I kind of wonder what they talked about, or if they just partied. As mountebanks go Beer seemed like a fun guy. Any proto data scientist who puts ashtrays and whiskey cup holders in a Captain Kirk control chair can’t be all bad, even if he was full of shit.

Bones send whiskey and smokes, stat

https://www.newstatesman.com/world/2018/08/project-cybersyn-afterlife-chile-s-socialist-internet

https://www.newyorker.com/magazine/2014/10/13/planning-machine

https://mitpress.mit.edu/books/cybernetic-revolutionaries

https://www.jacobinmag.com/2015/04/allende-chile-beer-medina-cybersyn/

http://www.guardian.co.uk/technology/2003/sep/08/sciencenews.chile

https://en.wikipedia.org/wiki/Project_Cybersyn

## AI is not eliminating jobs

Posted in econo-blasphemy, machine learning by Scott Locklin on February 9, 2019

Midwits keep asserting that “AI” is going to eliminate jobs. They say things like “those jobs aren’t coming back because of AI” (or screws or whatever other dumb excuse: but they’re real sure about those jobs not coming back).  These are not statements of scientific or technological fact, or even a reasonable prediction based on present trends. These are ideological political statements. “AI” is a soundbite/fnord excuse for not doing anything about the policy problems of the present.

The ruling caste of American tech and FIRE lizard people continue to make these statements, not because they are inevitable, but because this is their desired future. Their preferred future is a population consisting of powerless, preferably drugged up serfs on the “universal basic income” dole, ruled over by our present ruling class of grifters, rentiers, pyramid scheme salesmen, watched over by a surveillance hellscape.  The lizard people would like to continue our present policy of de-industrializing the country, breaking what little labor negotiating power US citizens have, and atomizing people to their raw protoplasm. It’s almost like a Freudian slip. Don’t bother agitating for any rights, slave, we soon will have electric Golems and won’t need you!

The most murderous drug dealers who ever existed … Google’s AI dude thinks they’re great! https://twitter.com/JeffDean/status/1093953731756867584

Oh I am sure the Google doofs would like to develop and control some strong AI, and perhaps a robot maid to replace Juanita. I, too, would like to have a magic technology which gives me infinite power, and a robot maid to iron my shirts. If I were a Silicon Valley oligarch rather than a humble nerd, I might develop delusions the pile of C++, Javascript and tech drones which made me rich could become a Golem of infinite power. Personally,  I would build rockets. At least I could get away from lizard people who want to turn the world into a soy dystopia.

If these clowns really believed that “AI” were something actually like an “AI” which could replace humans in general tasks, they’d use it to replace computer programmers. At one point in history, people believed CASE tools would eliminate most programmer jobs. How’s that working out for the AI geniuses at Google? They can’t even automate devops jobs; devops being one of the most automatable roles in tech companies. Devops tasks don’t seem much different from a computer strategy game.

Google’s “AI” team can’t do this useful thing, which, even by my lights, actually seems  achievable. Yet somehow, google boobs think they’re going to violate Moravec’s paradox and replace drivers. Think about that for a minute. It’s becoming clear that autonomous vehicle “technology” as sold to people for the last 10 years is basically fraud, and is still stuck in the 1980s when Ernst Dickmanns was driving around the autobahn with Sun Workstations in his back seat. Demonstrations of this tech always have a human in the loop (remote or in vehicle), because moving automobiles without human control are death machines under most circumstances.

Inside of the UniBwM autonomous experimental vehicle VaMP, at the rear bench where the computing system was installed for easy access and monitoring. This was at the PROMETHEUS demonstration in Paris in October 1994 | Photo by Reinhold Behringer

Even assuming I’m wrong and the media hyperbole is right and full level 5 autonomous vehicles are “right around the corner” Google also has zero business interest in “disrupting” driving. Google is a tech driven advertising company with a  collection of loss leaders. Yet they go after this preposterously difficult, possibly impossible task. Why not disrupt a business they presumably know how to disrupt, like that of the lowly ops engineer? At least this would be good for their bottom line, and it would be a real step forward in “AI” rather than a parlour trick perpetuated by marketing nerds and started by obvious mountebanks.

From a semiotics point of view, this shows astounding hostility to the types of people who drive cars and trucks for a living. Drivers are … ordinary, usually uneducated, salt of the earth people who have a fairly independent lifestyle and make a decent living. Google overlords must really hate such people, since they’re dumping all this skrilla into ruining their lives for no sane business reason. They will almost certainly fail, but man, why would you try to blow up those people’s lives? If this country really wanted to get rid of driving, or considered it a serious problem that there are too many cars on the road, or thought that people now employed as drivers should do something else, we had a solution to this problem invented in the late 1800s.

The other professions  people “think” will be replaced always seem to be low caste irritations or lawyers (lol). You regularly hear “experts” talking about how presently common jobs won’t exist in 20 years because of “AI.”  I’ve said multiple times now that all estimates for delivery of something in 20 years are bullshit. A prediction that a technology will do X in 20 years means “we don’t know how to do this, but we want your money to fool around with anyway.” Controlled nuclear fusion researchers being the most amusing case of the perpetual 20 year rice bowl. 20 years is a magic number, as it’s plenty of time for a technological mountebank to retire; and it’s at least 2-3 generations of tenured academics, which is enough to turn a scam subject like “quantum computing” or “nanotech” into an actual field.

“AI” doesn’t exist. Machine learning is a force multiplier and productivity enhancer for statisticians. If you believe the “automation”=”no more jobs” ding dongs, machine learning should have at least automated away the job of statistician. Yet somehow, the  statistician (aka “data scientist”) jobs are among the best paid and most in-demand jobs out there at present.

The last job category I can think of which was automated away is Flight Engineer on airliners. It mostly went away because of automation of airliners, but it wasn’t even computer related; just normal improvements of systems monitoring and reliability; good old mechanical and systems engineering. Despite 1/3 fewer seats in airliner cockpits, there are now more people with airline flight officer jobs now than ever before. Planes got cheaper and there are more of them servicing vastly more people.

The example of Flight Engineer is how the world works. Technological advances increase human power over nature and makes more things possible. Actual “AI” advances, should any eventually materialize, will work exactly like this.

AI has eliminated exactly zero professions, and essentially no jobs. Since the best prediction tool for a market is generally a random walk, my forecast is, barring giant breakthroughs, this trend of “nothing important actually happened” regarding AI job destruction will continue. If you disagree with me and have an alternate prediction on a normal human (aka 5 or 10 year) timescale, I am happy to entertain any long bets on whatever platform you care to use.

## On beating roulette: part 3

Posted in econo-blasphemy, Gambling systems by Scott Locklin on March 14, 2016

This is third in a four part series. Part 1 here, part 2 here.

To my mind, the most mathematically interesting thing about roulette is the betting system you should use to maximize your wins. Bet sizing systems are important in all probabilistic games, and the types of lessons learned from a winning game of roulette are the same types of lessons you need to learn in betting on other things, like success in trading, or having an edge on the wiener dog races. The nice thing about a game of roulette is it is relatively easy to characterize your edge. Most people’s edge over the roulette wheel is negative, so you should not bet. If you built one of the computer gizmos I went over in part 2, you have a positive edge over the roulette wheel.

We know from results in information theory, that sequential bets in the presence of an edge should be sized according to the Kelly Criterion to maximize bankroll growth rate.

$betsize = \frac{bankroll * edge}{house odds}$

or, in more probabilistic terms;

$betsize = \frac{p * odds + p -1}{odds}$

where $p$ is probability of success.

It’s probably not immediately obvious why this is so, but consider a biased coin toss at even odds ($1 payoff for$1 bet). If your coin’s edge is 100%, you gain money fastest by betting your whole bankroll. If you have 0% edge, you shouldn’t bet anything. If you have a 1% edge, you should bet 1% of your bankroll.

Daniel Bernoulli came up with the same fraction a long time before by maximizing the geometric mean.

Kelly’s original paper figured this out by modeling how a better would place bets assuming he had insider information transmitted over a noisy wire transmitting a binary code; a beautiful way of thinking about predictions in the presence of noise. Kelly is a guy I wish had lived longer. He dropped dead at the young age of 41; in his short life he was a Naval aviator in WW-2, invented computer speech synthesis, made huge contributions to information theory, mentored important mathematicians (Elwyn Berlekamp, who went on to found Axcom/Rentech, based in part on Kelly’s insights) and had the kind of life that would be considered hyperbole if he was in a science fiction novel.  They make big men in Texas. Kelly was a giant.

I’m pretty sure his testicles smoked unfiltered camels

I’ve been known to take sadistic glee in making fun of economists. One of the most mockable economists in American history is (Nobelist -the Swedes have dry humor) Paul Samuelson.  One could write entire books on the ways in which Samuelson was a scoundrel and a numskull who set back human knowledge by decades. One fact will suffice for this essay: Samuelson didn’t believe in Kelly betting. Explaining why he thought this, and why he’s wrong would be pointless; debugging an economist’s faulty thought processes is as pointless as explaining why a crazy lady is breaking dishes in the kitchen. If you’re interested, Ed Thorp is your man here also.

Ed Thorp is the man, period

Following Ed Thorp’s original essay in the Gambling Times, as good little experimental physicists, we need to build up an error budget to figure out our edge.  Thorp breaks down the errors in his and Shannon’s Roulette system into several kinds.

1. E1 Rotor speed measurement error
2. E2 Ball speed measurement error
3. E3 Ball rotor path randomness
4. E4 Ball stator path randomness
5. E5 Fret scatter
6. E6 Rotor tilt (discovered by Shannon and Thorp)

Uncorrelated errors add up as the sum of squares, so the total error budget is

$Error = \sqrt{\sum_{n=1}^{n=6}{E_n^2} }$

The Thorp/Shannon roulette system had a 44% edge on the most favored number; single number payouts in Vegas are 35:1, making the correct bet on one number 0.44/ 35 = 0.01256. Since nobody in 1960s Vegas suspected the mathematical machinators of having a physics edge on the wheel, they were able to place larger bets on parts of the quadrant. While Thorp describes it as “diversification” in his exposition. Another way of thinking about it: he’s just playing more games at once. A friend and former customer explained his trend following method as working in much the same way. The more bets you place, the more likely you’ll hit a winning trend.

Kelly betting isn’t a perfect solution in all cases; fixed fraction betting has certain disadvantages when you can’t exactly characterize your edge, or the payout odds, or you have a limited number of bets before you have to cash in your chips. However, in the case of a machine to beat Roulette, it’s difficult to think of a better technique.

Of course, Kelly betting and things like it figure in other sorts of betting; people do use it in Markets where it is appropriate. Supposedly it was part of Axcom/Rentech’s early secret sauce, and certainly folks who have thought about trading need a bet sizing and risk management strategy that makes sense. Kelly is often a good place to start, depending on your situation. But that’s a topic for another blog post. One more coming on modern techniques to beat Roulette, including the one I came up with in 2010 (which, in case you were holding your breath, didn’t really work, which is why I have to work, and am willing to talk about such things in blogs).

Kelly criterion resources

Kelly’s original paper:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6771227

Thorp’s explanation:

http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/TheKellyMoneyManagementSystem.pdf

Thorp’s website:

http://edwardothorp.com/id10.html

## Bad models and the end of the world

Posted in econo-blasphemy, stats jackass of the month by Scott Locklin on March 23, 2014

I loathe journalism as a profession: a claque of careerist whores, half-educated back-slappers and propagandists for the oligarchical lizard people who are ruining civilization. I loathe “science journalism” particularly, as they’re generally talking about something I know about, and so their numerous impostures are more obvious.

Journalists: they’re mostly like this

Today’s exhibit, the “NASA study predicting the end of Western Civilization.” The actual study can be found in PDF format here. If you read the “journalism” about this in the guardian, cnet, or wherever else, it’s all about our impending doom. Not only do scientists tell us we are doomed, fookin’ NASA scientists tell us we are doomed.

The authors of the study are not NASA scientists. The NASA subcontractor  associated with this paper would like you to know this; probably because NASA was annoyed their name was associated with this paper. The only contribution NASA made was in partially supporting an institution which partially supported one of the three authors for one semester. The author in question,  Safa Motesharrei is a grad student in “public policy” and “mathematics” at U Maryland. The other two authors are also not NASA scientists. One is allegedly a professor of … political science in Minnesota -and more recently some cranky looking outfit called “Institute of Global Environment and Society.” The other one is a professor of the U Maryland department of Oceanic and Atmospheric sciences. Unless you consider the partial ramen noodle stipend one grad student received for one semester to be “funding,” or you consider NASA’s subcontractor to be liars, NASA did not fund or endorse this study in any meaningful way. Journalism 101, failed before even getting to the content of the article.

The three authors of this study

For what it is worth, had I published anything my sophomore year of grad school instead of trying to build a crazy vacuum chamber and catch a venereal disease, I’d have had some words in my paper thanking NASA for their support as well. This is despite the fact that most of my money came from the NSF and the University I was attending. I wasn’t in any way a NASA scientist. My institution wasn’t NASA affiliated. But we did get a NASA grant that paid for at least a month’s salary for me over the course of a year. When you get those grants, you say “thank you.”

Nafeez Ahmed, the imbecile at the Guardian who broke the story, continues to insist that NASA funded this study, despite the fact that they didn’t. I guess when someone Discovers you are a shoddy journalist, the accepted thing to do these days is doltishly double down on your error. Ahmed, of course, works for some preposterous save-the-world outfit, which apparently means he can pretend he is a journalist and doesn’t have to tell the truth about anything.

Journalistic failure is to be expected these days, and NASA scientists say stupid things all the goddamned time. Still, reading the paper itself was informative. Had anybody bothered to do so, the story would have been murdered in infancy. It’s one of the godawful silliest things I have ever read.

There is a fairly standard model from ecology called the “predator prey” model. Predator/prey models were  mostly developed to model exactly what it sounds like: things like wolf and moose populations in a National Park. The model makes assumptions (that predators are always hungry,  the prey will never die of old age, and  there are no other predators or prey available, for just a few examples of the limitations of the model), but if you set these equations up right, and the parameters and conditions are non-degenerate, it can model reality reasonably well. It’s really no good for predicting things, but it’s OK for modeling things and understanding how nature works.  The equations look like this, where $x(t)$ is the predator population, $y(t)$ is the prey population and $a$ is predator birth rate, $b$ is the predator death rate, $c$ is the prey’s birth rate, and $k$ is the predation rate; all rates are constant.

$\frac{dy}{dt} = ay(t)x(t) -bx(t)$

$\frac{dx}{dt} = cy(t) -kx(t)y(t)$

The predator/prey model is elegant, concise, and in some limited circumstances, occasionally maps onto reality. It is, of course, a model; there is no real reason to model things using this set of differential equations, and a lot of reasons not to. But sometimes it is useful. Like most good models, it is simple and doesn’t have too many parameters. Everything can be measured, and interesting dynamics result; dynamics that we can observe in nature.

The authors of this doom-mongering paper  have  transformed that relatively simple set of equations; a set of equations which, mind you, produces some fairly complicated nonlinear dynamics, into this rather un-handy mess, known as HANDY (for “Human And Nature DYnamics”):

$\frac{dx_c}{dt} = \beta_c x_c(t) - \alpha_c x_c(t)$

$\frac{dx_e}{dt} = \beta_e x_e(t) - \alpha_e x_e(t)$

$\frac{dy}{dt} = \gamma (\lambda -y(t)) y(t) - \delta x_c(t) y(t)$

$\frac{d \omega}{dt} = \delta y(t) x_c(t) - C_c(t) - C_e(t)$

In this set of equations, $x_c(t)$ is the productive peasant population, $x_e(t)$ are the population of parasitic elites, $y(t)$ is “natural resources” and $w(t)$ is “wealth.” $\lambda$ is a “saturation of regrowth of nature rate.” $\gamma$ is an “exponential growth of nature rate.” $\delta$ is a “depletion of nature” rate term. $C_c(t), C_e(t)$ are wealth consumption rates.

to make it even more complex: $\alpha_c(t), \alpha_e(t), C_c(t), C_e(t)$ are all functions of $\omega(t), x_c(t), x_e(t)$

$C_c(t) = min(1,\frac{\omega(t)}{poor(t)}) s x_c(t)$

$C_e(t) = min(1,\frac{\omega(t)}{poor(t)}) \kappa x_e(t)$

$poor(t) = \rho x_c(t) + \kappa \rho x_e(t)$

$poor(t)$ is some threshhold wealth function, below which you starve, and allegedly $\rho$ is supposed to be a minimum consumption per capita, but it really makes no sense based on the equations. $s$ is some kind of subsistence level of wealth and $\kappa$ is the multiple of subsistence that elites take.

Instead of contenting themselves with constant predation or death rates, this train-wreck insists on making them the following:

$\alpha_c(t) = \alpha_m + max(0,1-\frac{C_c(t)}{s x_c(t)}) (\alpha_M - \alpha_m)$

$\alpha_e(t) = \alpha_m + max(0,1-\frac{C_e(t)}{s x_e(t)}) (\alpha_M - \alpha_m)$

Where $\alpha_m, \alpha_M$ are constants for a normal death rate and a death rate where you have a high death rate, where, and I quote the paper directly: “when the accumulated wealth has been used up and the population starves.”

It’s worth a look at what they’re implicitly modeling here by adding all this obfuscatory complexity. All of the following assumptions are made by this model. Very few of them are true in reality. Most of these assumptions are designed to get the answer they did.

1. The natural resources of the earth is well modeled by the prey equation
2. The natural resources of the earth regenerate themselves via a logistic function
3. There are two classes of humans
4. There is a thing called “wealth” that is consumed by the two classes of humans at different rates
5. The elite class of humans preys on the peasants and produces nothing
6. The peasant class is all equally productive
7. Wealth comes from peasants exploiting nature
8. Elites all have $\kappa$ times a subsistence income, rather than a smooth distribution of incomes
9. Peasants all have $s$, a subsistence income, rather than a smooth distribution of incomes
10. An extra variable called “wealth” is needed to make sense of these dynamics, and this variable maps onto the thing known in common parlance as “wealth.”
11. The wealth factor could sustain a human society for centuries after ecological collapse (page 18)
12. Death rates increase as natural resources are consumed at a faster rate (everything about modern civilization indicates the exact opposite is true)
13. The peasants get nothing from the elites except population control
14. Technological change is irrelevant (yes, they argue this; page 7)
15. This ridiculous spaghetti of differential equations actually models something corresponding to Human Civilization

There are more assumptions than this, but you get the idea: this model is ridiculous, over parameterized, and designed to get the answers that they did. If you assume parasitic non-productive elites, you get the situation where social stratification can help “cause” collapse. Of course, if you assume parasitic non-productive elites, you’re assuming all kinds of ideological nonsense that doesn’t map well onto reality.

If you assume natural resources also act like prey, you can get situations where the natural resources collapse, then the society collapses. This is no big surprise, and you don’t need these obfuscatory complications to say this: it’s in the predator-prey equations already. Why didn’t they just model humanity and nature as simple “predator/prey” above? I am guessing, because nobody would buy it if you say things that simply, and it wouldn’t be an original paper. It also doesn’t allow them to pontificate on egalitarian societies.

As for the additional “wealth” factor these clowns use to distinguish themselves from an earlier bad model; as far as I can tell, the only purpose served by this degree of freedom is making it easier to mine way more natural resources than we actually need to support a population (something that wouldn’t happen in a standard predator-prey model). It also doesn’t make any sense, modeled in this way, unless you believe grain silos contain centuries worth of corn, or that people can eat skyscrapers. That’s how their wealth equations work; they actually assume you can eat wealth.

Dr. Nafeez Ahmed: Guardian columnist who broke this story

I actually feel a bit sorry for these guys, even though they are unashamed quacks. They didn’t ask to become this famous. Somehow the zeitgeist and some imbecile activist newspaper reporter decided to make them famous as people who are really bad at modeling anything. God help these people if they attempt to model something real, like chemical reaction dynamics, or, say, the earth’s atmosphere.

Returning to the mendacious loon, Ahmed, who brought this paper to world fame and attention. He asserts that the paper actually compares historical civilizations using this model. It does nothing of the sort. The paper mentions historical civilizations, but they don’t even make legalistic arguments that, say, the ancient Egyptians, whose civilization lasted for thousands of years, somehow follow these equations.  All they say is, ancient cultures were cyclical; they rise and fall; something everyone has known from the time of Heraclitus. Cyclical behavior does not imply this complex pastiche of differential equations; there are cyclical behaviors in nature which can’t be modeled by any differential equations. Finally, Ahmed asserts that the model predicts things. It doesn’t; nor does it claim to. It claims to model things. Modeling things and predicting things are very different.

The model itself was bad enough. What the activist-reporter said about it is inexcusable. The fact that everyone credulously picked up on this nonsense without questioning how Nafeez Ahmed made his living is even worse. Science by activist press release. Yeah, thanks a lot, “science journalists.” Nobody even noticed the clown who broke this story is a goddamned 911 truther.

A more reliable narrator than the Ahmed bozo who broke this story

I find all this intensely sad. I’m sad for the boobs who wasted their lives cranking out a model this useless. I’m sad for our civilization that it is possible to make a living publishing rubbish, and that talented people can’t make a living doing interesting and correct research which will benefit humanity. I’m also sad that journalists aren’t fired over their credulity regarding this fraud. I’m sad that ideological hogwash is published in all the papers as some kind of scientific truth, while nobody notices simple things, like the fact that the world fisheries are presently undergoing collapse, or the fact that there are no more rhinos because Chinese people haven’t discovered viagra yet.

I’m also sad that people are so obsessed with the end of the world. Maybe some day we’ll experience some kind of ecological apocalypse, or the imbeciles in the White House will nuke the slightly less stupid cavemen in the Kremlin. Chances are pretty good though, that before these things happen, we will all be dead. Wiser men than me have pointed out that anxiety about the end of the world is a sort of transference for anxiety about their own impending demise. As Spengler put it, “perhaps it is not the end of the world, but just the end of you.”


text:
# Taylor expansion of $f$ in stability analysis of 2-step Adams-Bashforth method

Given the two-step Adams-Bashforth method $$u_{n+1} = u_n + \tfrac{h}{2}(3f_n - f_{n-1})$$ find its order.

Some notation: $t_n = t_0 + nh$ is the $n$-th node and $y_n = y(t_n)$; $f_n$ stands for $f(t_n,y_n)$ and $u_n$ is an approximation of $y_n$. Being $u^*_{n+1} = y_n + \tfrac{h}{2}(3f_n - f_{n-1})$, what one can say about the local truncament error is that

$$\tau_{n+1} = \frac{y_{n+1} - u^*_{n+1}}{h}$$

A first step in getting the LTE is expanding $y_{n+1}$ in $y_n + hy'_n + \tfrac{h^2}{2}y''_n + \tfrac{h^3}{6}y'''_n(\xi)$, however I can't properly explain to myself why

$$u^*_{n+1} = y_n + \tfrac{3}{2}hy'_n - \tfrac{h}{2}\left(y'_n - hy''_n + \tfrac{h^2}{2}y'''_n(\chi)\right)$$

How does one get there? What I'm asking is basically an explanation about how should I do the Taylor expansion of $3f_n - f_{n-1}$.

The order of the method is 2. The solution I'm trying to understand is the one proposed by my teacher.

I assume you are exploring the standard first order equation $\frac{dy}{dt}=f(t,y)$. Then

$$\frac{dy}{dt}\Big|_{t=t_k}=f(t_k,y_k)$$

for each $k$. Hence

$$f_n=y'_n$$

and

$$f_{n-1}=y'_{n-1}=y'_n-hy''_n+\frac{h^2}{2}y'''(\chi)$$

for some $\chi$ between $t_{n-1}$ and $t_n$. The expression for $f_{n-1}$ is determined by finding the Taylor series for $y'(t_n-h)$ centered at $t_n$.


text:
# Finding an Argument Pattern for Function Defintion

I'm defining what's called a fractional integral in Mathematica, which acts on a list of functions that depend on $x$:

integral[α_, g_[x_][[i_]], x_] := Integrate[(x-t)^(α-1) g[t][[i]], {t, 0, x}]

with some assumptions that say the $x$ in the bounds is nonzero.

What it does is it takes a function $f(x)$, kept in a list, changes the variable to $t$, and integrates it along with a power law, evaluating the bounds at $0$ and $x$. The problem is that sometimes I have to input a different form of a function, for example,

integral[α, (g[x][[i]])^3, x].

Mathematica doesn't recognize it as a viable function and just returns it back without doing anything.

I need to find a robust pattern that would take any function of $x$ and change it to a function of $t$ inside the integral. Changing, in the definition,

g_[x_][[i_]] -> g_[x_]

doesn't help.

I appreciate any help!

• When you say the functions are kept in a list, what do you mean exactly? Can you provide an example list (suitably short and simple) that shows what form the functions are in? Depending on the answer to this question, I would suggest something much simpler than specifying a pattern for the function. In addition, why put the Part specification in the Pattern when you can just Map integral over the list of functions? – march Aug 8 '16 at 22:38

Here's one possibility that does away with having to do any complicated pattern-matching. Suppose you have a list of expressions to be integrated, given by

lst = {x^2, (x + 1)^2, x};

Define a function

Clear@integral
integral[a_, func_, var_] := Integrate[(var - t)^(a - 1) Evaluate[func /. var -> t], {t, 0, var}]

In this case, the symbol that goes into var must match the independent variable in your list of expressions. Then, if you want to integrate the functions in lst, just Map integral over the list:

integral[2, #, x] & /@ lst
(* {x^4/12, x^2/2 + x^3/3 + x^4/12, x^3/6} *)

The key is to use the replacement in

Evaluate[func /. var -> t]

to change variables inside the Integrate call.

Alternatively, if you need to specify different variables, then we can define an alternative version:

Clear@integral
integral[a_, func_, inVar_, x_] := Integrate[(x - t)^(a - 1) Evaluate[func /. inVar -> t], {t, 0, x}]
integral[a_, func_, var_] := integral[a, func, var, var]

Now suppose the list was

lst = {x^2, (y + 1)^2, z};

Then, we can do either

MapThread[integral[2, #1, #2] &, {lst, {x, y, z}}]
(* {x^4/12, y^2/2 + y^3/3 + y^4/12, z^3/6} *)

or, if you want the outputs to have all the same output variable,

MapThread[integral[2, #1, #2, x] &, {lst, {x, y, z}}]
(* {x^4/12, x^2/2 + x^3/3 + x^4/12, x^3/6} *)


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# Which of the following inequalities is true?

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Which of the following inequalities is true?  [#permalink]

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27 Jun 2018, 21:37
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Which of the following inequalities is true?

A. $$\frac{1}{11}< 0.08 < \frac{1}{9}$$

B. $$\frac{1}{10}< 0.11 < \frac{1}{8}$$

C. $$\frac{1}{7}< 0.17 < \frac{1}{6}$$

D. $$\frac{1}{5}< 0.26 < \frac{1}{4}$$

E. $$\frac{1}{3}< 0.08 < \frac{1}{2}$$

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Re: Which of the following inequalities is true?  [#permalink]

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27 Jun 2018, 23:33

Solution

To find:
• From the given inequalities in the option choices, which one is true

Approach and Working:
We can convert the fractions into corresponding approximate decimal values to compare them as follows:
• $$\frac{1}{11} < 0.08 < \frac{1}{9}$$
o 0.09 < 0.08 < 0.11 Not true as 0.09 is not less than 0.08

• $$\frac{1}{10} < 0.11 < \frac{1}{8}$$
o 0.10 < 0.11 < 0.125 True

• $$\frac{1}{7} < 0.17 < \frac{1}{6}$$
o 0.142 < 0.17 < 0.167 Not true as 0.167 not greater than 0.17

• $$\frac{1}{5} < 0.26 < \frac{1}{4}$$
o 0.20 < 0.26 < 0.25 Not true as 0.25 not greater than 0.26

• $$\frac{1}{3} < 0.08 < \frac{1}{2}$$
o 0.33 < 0.08 < 0.5 Not true as 0.08 not greater than 0.33

Hence, the correct answer is option B.

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Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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Re: Which of the following inequalities is true? &nbs [#permalink] 27 Jun 2018, 23:33
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# Which of the following inequalities is true?

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