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# Rocket with variable mass, how do you solve for ratio of weight of fuel and weight of rocket?

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1. Sep 28, 2016

### Sudo

1. The problem statement, all variables and given/known data
Rockets are propelled by the momentum of the exhaust gases expelled from the tail. Since these gases arise from the reaction of the fuels carried in the rocket, the mass of the rocket is not constant, but decreases as the fuel is expended. Show that for a Rocket starting initially from rest, and taking the velocity of the exhaust gases relative to the rocket, $v'$ = 2.1 m/s and a rate of mass loss per second L = 1/60 of the initial mass, to reach the escape velocity of the Earth ($v_e$ = 11.2 km/s), the ratio of the weight of the fuel to the weight of the rocket must be almost 300!

2. Relevant equations
I know that $F=m(\frac {dp} {dt})=ma=m\frac {dv} {dt}$

3. The attempt at a solution
First, I work in the frame of the rocket; so we have two forces, the weight $W=mg$ and the force of the exhaust exiting the rocket $\frac {dm} {dt}v'$. Both forces are pointing downward, thus I set up the following equation: $$ma=m\frac {dv} {dt}=-v'(\frac {dm} {dt})-mg$$ Now I rewrite $m\frac {dv} {dt}$ as $m\frac {dv} {dm}\frac {dm} {dt}$; now I have this expression:$$m\frac {dv} {dm}\frac {dm} {dt}=-v'(\frac {dm} {dt})-mg$$As $\frac {dm} {dt}=L=-\frac {m_0} {60}$ and dividing both sides by $m$ we have:$$\frac {dv} {dm}(-\frac {m_0} {60})=-\frac {v'} {m}(-\frac {m_0} {60})-g$$Dividing both sides by $L$ yields:$$\frac {dv} {dm}=-\frac {v'} {m}+\frac {60g} {m_0}$$Now we're ready to write our differential equation as follows:$$dv=-\frac {v'} {m}~dm+\frac {60g} {m_0}~dm$$We can now integrate, this knowing that we start from $v_0=0$ and from a certain initial mass given by $m_0=m_{rocket}+m_{fuel}$ and a final mass $m_f=m_{rocket}$$$\int_0^v dv=-v'\int_{m_0}^{m_f} \frac {1} {m} \ dm+\frac {60g} {m_0}\int_{m_0}^{m_f} dm$$After integrating and evaluating I get the following expression:$$v=-v'ln(\frac {m_f} {m_0})+\frac {60g} {m_0}(m_f-m_0)$$This can be rewritten as:$$v=-v'ln(\frac {m_{rocket}} {m_{rocket}+m_{fuel}})-\frac {60g} {m_{rocket}+m_{fuel}}(m_{fuel})$$Then, if $m_{fuel}>>m_{rocket}$ we can ignore the term $m_{rocket}$ in $\frac {1} {m_{rocket}+m_{fuel}}$, and the expression can be rewritten as:$$v=-v'ln(\frac {m_{rocket}} {m_{fuel}})-60g=v'ln(\frac {m_{fuel}} {m_{rocket}})-60g$$Solving for the desired ratio I get:$$\frac {m_{fuel}} {m_{rocket}}=e^{\frac {v+60g} {v'}}$$However when plugging in the equation the values $v'=2.1 m/s$, $v=11.2 km/s$, and $g$ the value is much, much bigger than 300.

What did I did wrong? Did I chooses the incorrect frame? To my understanding my equation $ma=m\frac {dv} {dt}=-v'(\frac {dm} {dt})-mg$ should be true for this frame, thus $v'$ indeed is 2.1 m/s

Thank you for your time! As always I appreciate detailed answers, thanks again!

2. Sep 28, 2016

### TSny

The value given for $v'$ looks too small. Could it actually be 2.1 km/s?

You stated that both the thrust force and the gravitational force act downward. But the rocket goes upward.
However, I think your equations are correct.

Last edited: Sep 28, 2016
3. Sep 29, 2016

### Sudo

I'm not completely sure, the problem states m/s.

Do you think that, even when considering that $v'$ is relative to the rocket (i.e., measured by someone in the rocket, not an observer on ground), 2.1 m/s would still, anyway, be too small?

4. Sep 29, 2016

### jbriggs444

Too small by exactly a factor of 1000. An exhaust velocity so laughably low and a coincidence so striking that it is quite obviously an error in the problem statement.

An arthritic cripple could throw bowling balls out the back end of a rocket faster than 2.1 m/s. 300 such throws would achieve a velocity around 25 miles per hour (*) -- somewhat less than escape velocity.

(*) Assuming that the arthritic cripple starts with a pile of 300 bowling balls on his lap and has the same mass as one of the balls.

Last edited: Sep 29, 2016


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# Physics307L F09:People/Dougherty/Notebook/071022

## Balmer Series

p27-30

According to the manual i calibrated the apparatus with the mercury spectrum. i first found the right measurement for the red line that shows up in the spectrum. by fixing the screw drive to that measurement i could then fix the prism so the actual red line of the spectrum fell on the cross hairs in the viewing lens. this way the red line of the spectrum fell exactly on the right wavelength of the screw drive. and then moving the screw drive to the second wavelength, i could see the blue/green line fell on the same measurement as in the manual.

also in the manual, they specifically expressed turning the screw drive in only one direction. this is because there could be dead spots if turned the opposite way. dead spots meaning if you reverse the direction, you might turn the screw drive a fraction of an inch or so before the spectrum itself actually starts moving. for this reason i decided to take 2 measurements. one turning the screw drive completely counter-clockwise and moving it along the spectrum, and then turning it completely clockwise and moving it the other way along the spectrum. this way i could minimize any error in the movement of the screw drive.

SJK 03:18, 29 November 2007 (CST)
03:18, 29 November 2007 (CST)
Nice primary notebook!

As for deadspots, the key is to calibrate in the same direction that you ultimately take data in. I.e., calibrate moving counter-clockwise and then take data this way too (or vice versa).

## Data

 Hydrogen

turned screw drive all the way counter-clockwise

RED 653 nm 484.7 nm 433.5 nm 409.6 nm

turned screw drive all the way clockwise

RED 655 nm 485.9 nm 433.8 nm 409.8 nm
 Deuterium

turned screw drive all the way counter-clockwise

RED 651.6 nm 484.3 nm 432.8 nm 409.9 nm

turned screw drive all the way clockwise

RED 654.8 nm 484.8 nm 433.9 nm 409.4 nm

## Data Analysis

$\frac{1}{\lambda} = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right), n=3,4,5,...$

For Balmer series the red line's atomic number, n, starts as 3 and moves up as the spectrum moves left. (blue/green = 4, violet = 5, and violet (faint) = 6.)

 Hydrogen

counter-clockwise

R (m^-1) 1.1026*10^7 1.10034*10^7 1.0985*10^7 1.0986*10^7

clockwise

R (m^-1) 1.0992*10^7 1.0976*10^7 1.0977*10^7 1.0981*10^7
 Deuterium

counter-clockwise

R (m^-1) 1.10497*10^7 1.10125*10^7 1.100255*10^7 1.09783*10^7

clockwise

R (m^-1) 1.09957*10^7 1.10011*10^7 1.09747*10^7 1.09917*10^7

## R average

counter-clockwise

 Hydrogen - R = 1.10001*10^7 m^-1

 Deuterium - R = 1.10107*10^7 m^-1

clockwise

 Hydrogen - R = 1.09815*10^7 m^-1

 Deuterium - R = 1.09908*10^7 m^-1

## Hydrogen

 R = 1.099*10^7 m^-1

## Deuterium

 R = 1.100*10^7 m^-1

## standard error of the mean

$s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2}$
 Hydrogen = 16696.87738

 Deuterium = 23383.54027

$SE = \frac{s}{\sqrt{N}}$
 Hydrogen SE = 5903.23761

 Deuterium SE = 8267.329947

## Final value of R

 Hydrogen = 1.099*10^7 m^-1 +/- 5.903*10^3

 Deuterium = 1.100*10^7 m^-1 +/- 8.267*10^3

## error

$%error= \frac{|Actual-Experimental|}{|Actual|}x100$

actual value = 1.0967758*10^7 m^-1

 Hydrogen e= 0.20%

 Deuterium e= 0.29%

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# Is it possible to know if a planet is located in the Habitable Zone knowing it's properties?

Is there an equation that can give me the possibile distance of the planet from his star knowing planet's temperature (or other datas)?

I found this method for calculating the Habitable Zone but it's based only on star's properties.

• The planet temperature depends on it's atmosphere and the properties of the star and the distance to the star. – ProfRob Mar 19 '16 at 12:56
• Venus is hotter than Mercury, so, atmosphere obviously matters. Jupiter emits more heat than it receives from the sun, so, heat of formation matters, especially for larger planets. There's a variety of factors, the planet's color being another important factor. How much water, CO2/CH4 vs O2 ratios. There's quite a few moving parts to planetary temperature, so I don't think you'll find a straight forward formula anywhere. That said, I think the method for calculating habitable ZONE that you posted isn't bad. The zone is fairly large, our solar system's zone probably extends past mars. – userLTK Mar 19 '16 at 21:44

The habitable zone is, roughly, defined as the region around a star in which a planet could have liquid surface water. So if the surface temperature of the planet is between 0 and 100*C then the planet is in the habitable zone. The converse, however, is not true.

The reason for this definition is that the sort of chemical reactions that are needed for life work best when there are complex molecules dissolved in some kind of solvent, and the best polar solvent is H2O.

If you know the distance a planet is from its star, the temperature can be estimated from the properties of the star and the atmosphere of the planet. Not every planet in the habitable zone actually has liquid water. Venus, Earth and Mars are all in the Habitable zone of the sun, since they could all have liquid water if they had the right atmosphere. But of course only Earth actually does have liquid water in any substantial amounts.

So just being in the habitable zone, doesn't make a planet certainly suitable for life, and even if water does exist on the surface, it does not mean that humans could inhabit the planet.

• Of course! rephrased to make this obvious. – James K Mar 19 '16 at 21:59
• So is there an equation that can give me the habitable zone based on the properties you wrote? – astronomy-domine Mar 20 '16 at 15:31
• $0<T<100$ Habitable zone really just mean it is possible that there might be liquid water. – James K Mar 20 '16 at 15:41
• I guess what I mean is that if you know the planet's properties, like its surface temperature, you don't need to know if it is in the habitable zone or not. The purpose of finding if the planet is in the habitable zone is to get some idea of what the surface temperatures of the planet might be. Analogy if you have a meat thermometer, you don't need to time your roast. But if you don't then knowing how long your joint has been in the oven allows you to estimate if it has been cooked properly. – James K Mar 20 '16 at 16:08
• Oh I see. In fact i need this to build a little exoplanet data simulator so if i can decide the temperature i won't need to know if it's in the habitable zone or not. – astronomy-domine Mar 20 '16 at 17:43


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## Hankel and Toeplitz-Schur multipliers.(English)Zbl 1030.47019

The Schur product of matrices $$A=\{a_{jk}\}_{j,k\geq 0}$$ and $$B=\{b_{jk}\}_{j,k\geq 0}$$ is the matrix $$A\star B=\{a_{jk}b_{jk}\}_{j,k\geq 0}$$. Given a class $$\mathcal{X}$$ of bounded linear operators on the space $$l^2$$, a matrix $$A$$ is called a Schur multiplier of $$\mathcal{X}$$ if $$A\star B\in\mathcal{X}$$ for every $$B\in\mathcal{X}$$. For $$0<p<\infty$$, let $$\mathfrak{M}_p$$ be the space of Schur multipliers of the Schatten-von Neumann class $${\mathbf S}_p$$ and let $\|A\|_{\mathfrak{M}_p}=\sup\left\{\|A\star B\|_{{\mathbf S}_p}:\|B\|_{{\mathbf S}_p}\leq 1\right\}.$ For $$p\geq 1$$, $$\|\cdot\|_{\mathfrak{M}_p}$$ is a norm on $$\mathfrak{M}_p$$ and $\|A_1+A_2\|^p_{\mathfrak{M}_p}\leq\|A_1\|^p_{\mathfrak{M}_p}+ \|A_2\|^p_{\mathfrak{M}_p}\quad\text{ if}\quad 0<p\leq 1.$
The present paper is devoted to studying the Hankel-Schur multipliers of $${\mathbf S}_p$$, i.e., matrices of the form $$\{\gamma_{j+k}\}_{j,k\geq 0}$$ in $$\mathfrak{M}_p$$, and the Toeplitz-Schur multipliers of $${\mathbf S}_p$$, i.e., matrices of the form $$\{t_{j-k}\}_{j,k\geq 0}$$ in $$\mathfrak{M}_p$$, for $$0<p<1$$. Some general results concerning Schur multipliers of $${\mathbf S}_p$$ are established. Several sharp necessary conditions and sufficient conditions for Hankel matrices to be Schur multipliers of $${\mathbf S}_p$$ are found. A characterization of the Hankel-Schur multipliers of $${\mathbf S}_p$$ whose symbols have lacunary power series is obtained. Applying the results on Hankel-Schur multipliers of $${\mathbf S}_p$$, the authors give the following characterization of the Toeplitz-Schur multipliers of $${\mathbf S}_p$$. A Toeplitz matrix $$\{t_{j-k}\}_{j,k\geq 0}$$ is a Schur multiplier of $${\mathbf S}_p$$ in the case $$0<p<1$$ if and only if there exists a discrete measure $$\mu$$ on $$\mathbb{T}$$ of the form $\mu=\sum_{j\in\mathbb{Z}}\alpha_j\delta_{\tau_j},\quad \alpha_j\in\mathbb{C},\quad \tau_j\in\mathbb{T},$ with $\|\mu\|_{\mathcal{M}_p}:=\biggl(\sum_j |\alpha_j|^p\biggr)^{1/p}<\infty,$ such that $$t_j=\widehat{\mu}(j)$$, $$j\in\mathbb{Z}$$. Moreover, in that case $\big\|\{t_{j-k}\}_{j,k\geq 0}\}\big\|_{\mathfrak{M}_p}= \|\mu\|_{\mathcal{M}_p}.$ Finally, the Hankel-Schur multipliers of $${\mathbf S}_p$$ whose symbols are complex measures on $$\mathbb{T}$$ are studied.

### MSC:

 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B10 Linear operators belonging to operator ideals (nuclear, $$p$$-summing, in the Schatten-von Neumann classes, etc.)
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## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### On the distribution of rank two $\tau$-congruent numbers

#### Abstract

A positive integer $n$ is the area of a Heron triangle if and only if there is a non-zero rational number $\tau$ such that the elliptic curve \begin{equation*} E_{τ}^{(n)}: Y^{2} = X(X-nτ)(X+nτ^{-1}) \end{equation*} has a rational point of order different than two. Such integers $n$ are called $\tau$-congruent numbers. In this paper, we show that for a given positive integer $p$, and a given non-zero rational number $\tau$, there exist infinitely many $\tau$-congruent numbers in every residue class modulo $p$ whose corresponding elliptic curves have rank at least two.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 93, Number 5 (2017), 37-40.

Dates
First available in Project Euclid: 29 April 2017

https://projecteuclid.org/euclid.pja/1493431381

Digital Object Identifier
doi:10.3792/pjaa.93.37

Mathematical Reviews number (MathSciNet)
MR3645658

Zentralblatt MATH identifier
1374.14028

#### Citation

Davis, Chad Tyler. On the distribution of rank two $\tau$-congruent numbers. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 5, 37--40. doi:10.3792/pjaa.93.37. https://projecteuclid.org/euclid.pja/1493431381

#### References

• M. A. Bennett, Lucas' square pyramid problem revisited, Acta Arith. 105 (2002), no. 4, 341–347.
• J. S. Chahal, On an identity of Desboves, Proc. Japan Acad. Ser. A Math. Sci. 60 (1984), no. 3, 105–108.
• J. S. Chahal, Congruent numbers and elliptic curves, Amer. Math. Monthly 113 (2006), no. 4, 308–317.
• H. Cohen, Number theory. Vol. I. Tools and Diophantine equations, Graduate Texts in Mathematics, 239, Springer, New York, 2007.
• C. T. Davis and B. K. Spearman, On the distribution of $\tau$-congruent numbers, Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 7, 101–103.
• E. H. Goins and D. Maddox, Heron triangles via elliptic curves, Rocky Mountain J. Math. 36 (2006), no. 5, 1511–1526.
• C. L. Siegel, Über einige Anwendungen diophantischer Approximationen [reprint of Abhandlungen der Preußischen Akademie der Wissenschaften. Physikalisch-mathematische Klasse 1929, Nr. 1, 1–41], in On some applications of Diophantine approximations, Quad./Monogr., 2, Ed. Norm., Pisa, 2014, pp. 81–138.
• J. H. Silverman and J. Tate, Rational points on elliptic curves, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1992.


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# ON A CLASS OF UNIVALENT FUNCTIONS

• NOOR, KHALIDA INAYAT (Mathematics Department, College of Science, King Saud University) ;
• RAMADAN, FATMA H. (Mathematics Department, College of Science, King Saud University)
• Received : 1992.05.21
• Published : 1993.07.01
• 22 2

#### Abstract

For A and B, $-1{\leq}B<A{\leq}1$, let P[A, B] be the class of functions p analytic in the unit disk E with P(0) = 1 and subordinate to $\frac{1+Az}{1+Bz}$. We introduce the class $T_{\alpha}[A,B]$ of functions $f:f(z)=z+\sum\limits_{n=2}^{{\infty}}a_nz^n$ which are analytic in E and for $z{\in}E$, ${\alpha}{\geq}0$, $[(1-{\alpha}){\frac{f(z)}{z}}+{\alpha}f^{\prime}(z)]{\in}P[A,B]$. It is shown that, for ${\alpha}{\geq}1$, $T_{\alpha}[A,B]$ consists entirely of univalent functions and the radius of univalence for $f{\in}T_{\alpha}[A,B]$, $0<{\alpha}<1$ is obtained. Coefficient bounds and some other properties of this class are studied. Some radii problems are also solved.

#### Keywords

Univalent;convolution;prestarlike;radius


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# Nuclear Spectroscopy

 2019-06-2415:26 [GSI-2019-00763] Journal Article et al In-beam study of $^{254}$No 2019-06-1117:28 [GSI-2019-00724] Journal Article et al Study of isomeric states in $^{198,200,202,206}$Pb and $^{20}$Hg populated in fragmentation reactions 2019-06-1117:18 [GSI-2019-00723] Journal Article Gerl, J. The AGATA Campaigns at GSI and GANIL Nuclear physics news 28(3), 16 - 19 (2018) [10.1080/10619127.2018.1495478] 2019-06-1117:16 [GSI-2019-00722] Journal Article Wollersheim, H. J. Towards detailed knowledge of atomic nuclei—the past, present and future of nuclear structure investigations at GSI Physica scripta 91(10), 103001 (2016) [10.1088/0031-8949/91/10/103001] 2019-03-2212:09 [GSI-2019-00567] Journal Article et al Neutron skin and signature of the N = 14 shell gap found from measured proton radii of $^{17−22}$N Physics letters / B B 790, 251 - 256 (2019) [10.1016/j.physletb.2019.01.024] OpenAccess: PDF; 2019-02-2416:05 [GSI-2019-00488] Journal Article et al Simulated characteristics of the DEGAS γ -detector array 2019-02-2415:55 [GSI-2019-00487] Journal Article et al β decays of the heaviest N = Z − 1 nuclei and proton instability of $^{97}$In Physical review / C covering nuclear physics 97(5), 051301 (2018) [10.1103/PhysRevC.97.051301] 2019-02-2415:46 2019-02-2415:31 [GSI-2019-00475] Journal Article et al Shape coexistence and isospin symmetry in A = 70 nuclei: Spectroscopy of the T = −1 nucleus 70Kr Physics letters / B B 785, 441 - 446 (2018) [10.1016/j.physletb.2018.07.067] Restricted: PDF; 2019-02-2410:12 [GSI-2019-00456] Dissertation / PhD Thesis Pietralla, N. γ-ray spectroscopy of $^{92,94}$Se isomeric decay 154 pp. (2018) = Dissertation, Technische Universitaet Darmstadt, 2018 The isomeric decay of 92,94Se has been studied by means of gamma-ray decay spectroscopy, in order to explore the nuclear structure of these very neutron-rich exotic nuclei far way from the ‘stability line’. The experiment was conducted in March 2015 at the Radioactive Ion Beam Factory of the RIKEN Nishina Center (RIBF-RIKEN) located in Japan. [...]


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Let’s have a look at a simple example to better understand the package: import numpy as np import statsmodels.api as sm import statsmodels.formula.api as smf # Load data dat = sm.datasets.get_rdataset("Guerry", "HistData").data # Fit regression model (using the natural log of one of the regressors) results = smf.ols('Lottery ~ … A scientific reason for why a greedy immortal character realises enough time and resources is enough? ordinal_gee(formula, groups, data[, subset, …]), nominal_gee(formula, groups, data[, subset, …]), gee(formula, groups, data[, subset, time, …]), glmgam(formula, data[, subset, drop_cols]). The following are 30 code examples for showing how to use statsmodels.api.add_constant().These examples are extracted from open source projects. Generate lagmatrix for 2d array, columns arranged by variables. Canonically imported This is essentially an incompatibility in statsmodels with the version of scipy that it uses: statsmodels 0.9 is not compatible with scipy 1.3.0. ols (formula = 'Sales ~ TV + Radio', data = df_adv). hessian (params) The Hessian matrix of the model: information (params) Fisher information matrix of model: initialize loglike (params) The likelihood function for the clasical OLS model. if the independent variables x are numeric data, then you can write in the formula directly. See the documentation for the parent model for details. Create a proportional hazards regression model from a formula and dataframe. add_trend(x[, trend, prepend, has_constant]). statsmodels.formula.api: A convenience interface for specifying models ... No constant is added by the model unless you are using formulas. Find the farthest point in hypercube to an exterior point. using import statsmodels.api as sm. Why can't I run this ARMA? Bayesian statistics in Python: This chapter does not cover tools for Bayesian statistics.Of particular interest for Bayesian modelling is PyMC, which implements a probabilistic programming language in Python. Making statements based on opinion; back them up with references or personal experience. An intercept is not included by default and should be added by the user. The API focuses on models and the most frequently used statistical test, and tools. How to import statsmodels module to use OLS class? AttributeError: module 'statsmodels.formula.api' has no attribute 'OLS' 京东618-京享红包限时领取 由 青春壹個敷衍的年華 提交于 2020-02-14 05:45:48 Re: [pystatsmodels] ImportError: No module named statsmodels.api: jseabold: 8/4/12 4:04 PM: That helped us to determine that the model we tried was no good. We can list their members with the dir() command i.e. Christiano Fitzgerald asymmetric, random walk filter. Are there some weird dependencies I should be worried about? Perform automatic seasonal ARIMA order identification using x12/x13 ARIMA. Current function value: 802.354181 Iterations: 3 Function evaluations: 5 Gradient evaluations: 5 >>> res=c.fit([0.4],method="bfgs") Optimization terminated successfully. statsmodels.formula.api.ols. Multiple Imputation with Chained Equations. Python 3 version of the code can be obtained by running 2to3.py over the entire statsmodels source. Marginal Regression Model using Generalized Estimating Equations. We do this by taking differences of the variable over time. GEE(endog, exog, groups[, time, family, …]). Calculate the crosscovariance between two series. # AVOIDING THE DUMMY VARIABLE TRAP X = X[:, 1:] NOTE : if you have n dummy variables remove one dummy variable to avoid the dummy variable trap. Detrend an array with a trend of given order along axis 0 or 1. lagmat(x, maxlag[, trim, original, use_pandas]), lagmat2ds(x, maxlag0[, maxlagex, dropex, …]). AttributeError: module 'statsmodels.formula.api' has no attribute 'OLS' 以上のようなエラーが出ました。 ドキュメント通りに進めたつもりでしたが、どこか不備があるのでしょうか。 We can perform regression using the sm.OLS class, where sm is alias for Statsmodels. Adjusted R-squared. statsmodels ols does not include all categorical values, I don't understand RidgeCV's fit_intercept, and how to use it for my data. qqplot_2samples(data1, data2[, xlabel, …]), Description(data, pandas.core.series.Series, …), add_constant(data[, prepend, has_constant]), List the versions of statsmodels and any installed dependencies, Opens a browser and displays online documentation, acf(x[, adjusted, nlags, qstat, fft, alpha, …]), acovf(x[, adjusted, demean, fft, missing, nlag]), adfuller(x[, maxlag, regression, autolag, …]), BDS Test Statistic for Independence of a Time Series. What are the best practices for data formatting? See the detailed topic pages in the User Guide for a complete You need to understand which one you want. Может ли эта ошибка быть из версии, которую я использую? The only problem is that I'm not sure where the intercept is. Canonically imported using import statsmodels.formula.api as smf The API focuses on models and the most frequently used statistical test, and tools. Calling fit() throws AttributeError: 'module' object has no attribute 'ols'. # import formula api as alias smf import statsmodels.formula.api as smf # formula: response ~ predictor + predictor est = smf. Using strategic sampling noise to increase sampling resolution. AutoReg(endog, lags[, trend, seasonal, …]), ARIMA(endog[, exog, order, seasonal_order, …]), Autoregressive Integrated Moving Average (ARIMA) model, and extensions, Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors model, arma_order_select_ic(y[, max_ar, max_ma, …]). We have to add one column with all the same values as 1 to represent b0X0. A nobs x k array where nobs is the number of observations and k is the number of regressors. Import Paths and Structure explains the design of the two API modules and how importing from the API differs from directly importing from the module where the model is defined. # Using statsmodels.api.OLS(Y, X).fit(). But there is no harm in removing it by ourselves. R-squared of the model. Calculate partial autocorrelations via OLS. See https://stackoverflow.com/a/56284155/9524424, You need to have a matching scipy version (1.2 instead of 1.3). Catatan penting : Jika Anda benar-benar awam tentang apa itu Python, silakan klik artikel saya ini. missing str sklearn.linear_model.LinearRegression¶ class sklearn.linear_model.LinearRegression (*, fit_intercept=True, normalize=False, copy_X=True, n_jobs=None) [source] ¶. glsar(formula, data[, subset, drop_cols]), mnlogit(formula, data[, subset, drop_cols]), logit(formula, data[, subset, drop_cols]), probit(formula, data[, subset, drop_cols]), poisson(formula, data[, subset, drop_cols]), negativebinomial(formula, data[, subset, …]), quantreg(formula, data[, subset, drop_cols]). Wrap a data set to allow missing data handling with MICE. Ecclesiastical Latin pronunciation of "excelsis": /e/ or /ɛ/? What is the physical effect of sifting dry ingredients for a cake? Were there often intra-USSR wars? $\begingroup$ It is the exact opposite actually - statsmodels does not include the intercept by default. OLS is only going to work really well with a stationary time series. statsmodels.tsa.api: Time-series models and methods. However the linear regression model that is built in R and Python takes care of this. properties and methods. Regression is a popular technique used to model and analyze relationships among variables. Compute information criteria for many ARMA models. GLS(endog, exog[, sigma, missing, hasconst]), GLSAR(endog[, exog, rho, missing, hasconst]), Generalized Least Squares with AR covariance structure, WLS(endog, exog[, weights, missing, hasconst]), RollingOLS(endog, exog[, window, min_nobs, …]), RollingWLS(endog, exog[, window, weights, …]), BayesGaussMI(data[, mean_prior, cov_prior, …]). It has been reported already. Currently the only way we can get this information is through the formulas. I’ll use a simple example about the stock market to demonstrate this concept. Each univariate distribution is an instance of a subclass of rv_continuous (rv_discrete for discrete distributions): ... Test whether a dataset has normal kurtosis. 7. There are dozens of models, but I wanted to summarize the six types I learned this past weekend. We can list their members with the dir() command i.e. The numerical core of statsmodels worked almost without changes, however there can be problems with data input and plotting. For a user having some familiarity with OLS regression and once the data is in a pandas DataFrame, powerful regression models can be constructed in just a few lines of code. Here are the topics to be covered: Background about linear regression The DynamicVAR class relies on Pandas' rolling OLS, which was removed in version 0.20. Thank you. Partial autocorrelation estimated with non-recursive yule_walker. Using StatsModels. df = pd.read_csv(...) # file name goes here exog array_like. ols = statsmodels.formula.api.ols(model, data) anova = statsmodels.api.stats.anova_lm(ols, typ=2) I noticed that depending on the order in which factors are listed in model, variance (and consequently the F-score) is distributed differently along the factors. Why does the FAA require special authorization to act as PIC in the North American T-28 Trojan? Once you are done with the installation, you can use StatsModels easily in your … Kwiatkowski-Phillips-Schmidt-Shin test for stationarity. Bayesian Imputation using a Gaussian model. AttributeError: module 'statsmodels.api' has no attribute '_MultivariateOLS' If I run an OLS (i.e. We used this model to make our forecasts. It only takes a minute to sign up. Did China's Chang'e 5 land before November 30th 2020? Dynamic factor model with EM algorithm; option for monthly/quarterly data. This behavior occurs with statsmodels 0.6.1. Class representing a Vector Error Correction Model (VECM). An intercept is not included by default and should be added by the user. import statsmodels.api as sm File "C:\Python27\lib\site-packages\statsmodels\tools\tools.py", line 14, in from pandas import DataFrame ImportError: No module named pandas...which confuses me a great deal, seeing as how that particular produced no errors before, i.e. import statsmodels.api as sm File "C:\Python27\lib\site-packages\statsmodels\tools\tools.py", line 14, in from pandas import DataFrame ImportError: No module named pandas...which confuses me a great deal, seeing as how that particular produced no errors before, i.e. Nominal Response Marginal Regression Model using GEE. Import Paths and Structure explains the design of the two API modules and how I get . The AR term, the I term, and the MA term. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. Statsmodels also provides a formulaic interface that will be familiar to users of R. Note that this requires the use of a different api to statsmodels, and the class is now called ols rather than OLS. How do I orient myself to the literature concerning a research topic and not be overwhelmed? 前提・実現したいこと重回帰分析を行いたいです。ここに質問の内容を詳しく書いてください。 発生している問題・エラーメッセージ下記のエラーが解消できず、困っています。AttributeError: module 'statsmodels.formula.api' has no attribute 'O using import statsmodels.tsa.api as tsa. We then estimated a competing model, which performed much better. ... from_formula (formula, data[, subset]) Create a Model from a formula and dataframe. Formulas are also available for specifying linear hypothesis tests using the t_test and f_test methods after model fitting. list of available models, statistics, and tools. ProbPlot(data[, dist, fit, distargs, a, …]), qqplot(data[, dist, distargs, a, loc, …]). Now one thing to note that OLS class does not provide the intercept by default and it has to be created by the user himself. Ordinary least squares Linear Regression. # Plot a linear regression line through the points in the scatter plot, above. Q-Q plot of the quantiles of x versus the quantiles/ppf of a distribution. my time of original posting. I think you need to use a dataframe or a dictionary with the correct name of the explanatory variable(s). To learn more, see our tips on writing great answers. If you upgrade to the latest development version of statsmodels, the problem will disappear: For me, this fixed the problem. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. Jika Anda awam tentang R, silakan klik artikel ini. The idea is… Statsmodels also provides a formulaic interface that will be familiar to users of R. Note that this requires the use of a different api to statsmodels, and the class is now called ols rather than OLS. See statsmodels.tools.add_constant. Django advanced beginner here. We can either use statsmodel.formula.api or statsmodel.api to build a linear regression model. When I pass a new data frame to the function to get predicted values for an out-of-sample dataset result.predict(newdf) returns the following error: 'DataFrame' object has no attribute 'design_info'. model is defined. NominalGEE(endog, exog, groups[, time, …]). hessian (params) The Hessian matrix of the model: information (params) Ordinary Least Squares. In a regression there is always an intercept that is usually listed before the exogenous variables, i.e. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. rsquared_adj. How to explain the LCM algorithm to an 11 year old? Use MathJax to format equations. MICE(model_formula, model_class, data[, …]). It has been reported already. $\endgroup$ – desertnaut May 26 … Is it considered offensive to address one's seniors by name in the US? Does your organization need a developer evangelist? In statsmodels it supports the basic regression models like linear regression and logistic regression.. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. import statsmodels Simple Example with StatsModels. Copy link Member ChadFulton commented May 20, 2017. This is defined here as 1 - ssr/centered_tss if the constant is included in the model and 1 - ssr/uncentered_tss if the constant is omitted. $\begingroup$ It is the exact opposite actually - statsmodels does not include the intercept by default. This exploration has demonstrated both the ease and capability of the Statsmodels GLM module. What does the phrase, a person with “a pair of khaki pants inside a Manila envelope” mean? 1.2.10. statsmodels.api.OLS ... Has an attribute weights = array(1.0) due to inheritance from WLS. - sample code: values = data_frame['attribute_name'] - import statsmodel.api as sm - initialise the OLS model by passing target(Y) and attribute(X).Assign the model to variable 'statsModel' - fit the model and assign it to variable 'fittedModel, make sure you add constant term to input X' - sample code for initialization: sm.OLS(target, attribute) The Statsmodels package provides different classes for linear regression, including OLS. import statsmodels.formula.api as smf Alternatively, each model in the usual statsmodels.api namespace has a from_formula classmethod that will create a model using a formula. The Statsmodels package provides different classes for linear regression, including OLS. Perform x13-arima analysis for monthly or quarterly data. hessian (params) The Hessian matrix of the model: information (params) Fisher information matrix of model: Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. This is essentially an incompatibility in statsmodels with the version of scipy that it uses: statsmodels 0.9 is not compatible with scipy 1.3.0. MarkovAutoregression(endog, k_regimes, order), MarkovRegression(endog, k_regimes[, trend, …]), First-order k-regime Markov switching regression model, STLForecast(endog, model, *[, model_kwargs, …]), Model-based forecasting using STL to remove seasonality, ThetaModel(endog, *, period, deseasonalize, …), The Theta forecasting model of Assimakopoulos and Nikolopoulos (2000). An alternative would be to downgrade scipy to version 1.2. #regression with formula import statsmodels.formula.api as smf #instantiation reg = smf.ols('conso ~ cylindree + puissance + poids', data = cars) #members of reg object print(dir(reg)) reg is an instance of the class ols. coint(y0, y1[, trend, method, maxlag, …]). MI performs multiple imputation using a provided imputer object. Estimation and inference for a survival function. This API directly exposes the from_formula Fit VAR(p) process and do lag order selection, Vector Autoregressive Moving Average with eXogenous regressors model, SVAR(endog, svar_type[, dates, freq, A, B, …]). ImportError: No module named statsmodels.api I looked and it is in the folder is in the directory. add_constant (data[, prepend, has_constant]): This appends a column of ones to an array if prepend==False. Statsmodels version: 0.8.0 Pandas version: 0.20.2. Khary-- StriperCoast SurfCasters Club. from_formula (formula, data[, subset]) Create a Model from a formula and dataframe. This module contains a large number of probability distributions as well as a growing library of statistical functions. import statsmodels.formula.api as smf. BinomialBayesMixedGLM(endog, exog, exog_vc, …), Generalized Linear Mixed Model with Bayesian estimation, Factor([endog, n_factor, corr, method, smc, …]). State space models were introduced in version 0.8, so you'll have to update your statsmodels to use them. Seasonal decomposition using moving averages. Since it is built explicitly for statistics; therefore, it provides a rich output of statistical information. It might be possible to add a non-formula API to specify which columns belong together. The source of the problem is below. Filter a time series using the Baxter-King bandpass filter. Traceback (most recent call last): File "", line 1, in File "statsmodels/api.py", line 7, in from .regression.recursive_ls import RecursiveLS Residuals, normalized to have unit variance. A generalized estimating equations API should give you a different result than R's GLM model estimation. DynamicFactor(endog, k_factors, factor_order), DynamicFactorMQ(endog[, k_endog_monthly, …]). Statsmodels is an extraordinarily helpful package in python for statistical modeling. Is there a way to notate the repeat of a larger section that itself has repeats in it? 4.4.1.1.10. statsmodels.formula.api.OLS¶ class statsmodels.formula.api.OLS (endog, exog=None, missing='none', hasconst=None, **kwargs) [source] ¶. The following are 30 code examples for showing how to use statsmodels.api.OLS().These examples are extracted from open source projects. https://stackoverflow.com/a/56284155/9524424. Parameters endog array_like. I would call that a bug. Thanks for contributing an answer to Data Science Stack Exchange! fit([method, cov_type, cov_kwds, use_t]) Future posts will cover related topics such as exploratory analysis, regression diagnostics, and advanced regression modeling, but I wanted to jump right in so readers could get their hands dirty with data. I have the following ouput from a Pandas pooled OLS regression. properties and methods. MICEData(data[, perturbation_method, k_pmm, …]). We can perform regression using the sm.OLS class, where sm is alias for Statsmodels. Canonically imported The argument formula allows you to specify the response and the predictors using the column names of the input data frame data. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Parameters: formula (str or generic Formula object) – The formula specifying the model; data (array-like) – The data for the model.See Notes. I'm banging my head against the wall trying to figure this one out. fit () Handling Categorical Variables Y = a + ßx1 + ßx2 + error_term I do not see it in my regression. e predict() function of the statsmodels.formula.api OLS implementation. 前提・実現したいこと重回帰分析を行いたいです。ここに質問の内容を詳しく書いてください。 発生している問題・エラーメッセージ下記のエラーが解消できず、困っています。AttributeError: module 'statsmodels.formula.api' has no attribute 'O See the SO threads Coefficients for Logistic Regression scikit-learn vs statsmodels and scikit-learn & statsmodels - which R-squared is correct?, as well as the answer … I'm trying to run an ARMA model using statsmodels.tsa.ARIMA.ARMA, but I get AttributeError: module 'pandas' has no attribute 'WidePanel'. The main statsmodels API is split into models: statsmodels.api: Cross-sectional models and methods. ... from_formula (formula, data[, subset]) Create a Model from a formula and dataframe. OLS method. How to get an intuitive value for regression module evaluation? However the linear regression model that is built in R and Python takes care of this. statsmodels.regression.linear_model.OLS¶ class statsmodels.regression.linear_model.OLS (endog, exog=None, missing='none', hasconst=None, **kwargs) [source] ¶. An extensive list of descriptive statistics, statistical tests, plotting functions, and result statistics are available for different types of data and each estimator. Let’s say you have a friend who says that a feature is absolutely of no use. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. my time of original posting. The following are 14 code examples for showing how to use statsmodels.api.Logit().These examples are extracted from open source projects. Oppose a potential hire that management asked for an opinion on based on prior work?... Hasconst=None, * * kwargs ) [ source ] ¶ very simple interpretative... Cast at 4th level have 40 HP, or 55 HP TV + Radio ',,! For linear regression is a popular technique used to estimate an OLS ( i.e imputer object ~ TV + '. Way I try to ensure that statsmodels is fully loaded - git clone, importing the API! Statsmodels.Api.Logit ( ).These examples are extracted from open source projects any case like that yet Inc. Of the methods exposed in the scatter plot, above formula and module 'statsmodels formula api has no attribute 'ols available to in. Get similar estimates in statsmodels it supports the basic regression models like regression... Showing how to professionally oppose a potential hire that management asked for an opinion on based on work! Code module 'statsmodels formula api has no attribute 'ols for showing how to use statsmodels.api.add_constant ( ) function of the methods exposed in the formula API applying. ' if I run an OLS ( ordinary least squares ( OLS ) regression model ) (... Points in the formula API are generic to estimate an OLS ( formula data. Col, dictnames, drop ] ) ' Appreciate the help data Science Stack Inc. To estimate an OLS ( i.e value error array with 0 features linear. Categorical variables + predictor est = smf excelsis '': /e/ or /ɛ/ that a is. Require special authorization to act as PIC in the formula API are generic categorical ( data [,,. T_Test and f_test methods after model fitting observations and k is the physical of... While theory was a large component of the input data frame data intercept is formula and dataframe calling fit )! And plotting clicking “ post your answer ”, you need to use statsmodels.api.Logit ( ) throws AttributeError module. To data Science Stack Exchange responding to other answers, y1 [, … ] Create..., then you can write in the formula directly e predict ( ) examples... For Python 3.2 almost without changes, however there can be problems with data input and plotting to an... Method, maxlag, … ] ): Returns a dummy matrix given an with! Explicitly for statistics ; therefore, it provides a rich output of statistical information extracted open! Package in Python using statsmodels ( VECM ) может ли эта ошибка быть версии. Friend who says that a feature is absolutely of no use LCM algorithm to an 11 year old proportional regression... And dataframe statsmodels.regression.linear_model.OLS ( endog, exog=None, missing='none ', data = df_adv ) y a... However which way I try to ensure that statsmodels is an extraordinarily helpful package in Python using statsmodels if exog! Use OLS class ; therefore, it provides a rich output of statistical information of... Science Stack Exchange Inc ; user contributions licensed under cc by-sa OLS class,,. The physical effect of sifting dry ingredients for a module 'statsmodels formula api has no attribute 'ols notate the repeat of a larger that. Data frame data on models and methods ( *, fit_intercept=True, normalize=False,,., value error array with lags included given an array if prepend==False that asked. Problem will disappear: for me, this fixed the problem will disappear: for me, this fixed problem! A proportional hazards regression model from a formula and dataframe attribute 'ols ', all works.... Open source projects API to specify the response and the most frequently statistical. Twython_Django_Oauth tied into contrib.auth to register and login users going to work really well with a stationary time.! To downgrade scipy to version 1.2 that is built in R and Python takes of! Offensive to address one 's seniors by name in the formula API dry for..., normalize=False, copy_X=True, n_jobs=None ) [ source ] ¶ May 20, 2017 monthly/quarterly data 2to3.py. Are also available for specifying models using formula strings and DataFrames class for implementing Backward.. See our tips on writing great answers most frequently used statistical test, and tools function similar to formula. Show you how to use them numerical core of statsmodels worked almost without changes, however there can obtained. Pandas as pd statsmodels source exogenous variables, i.e you through building linear regression line through the formulas columns together! Directly exposes the from_formula class method of models, but I wanted to the. Statsmodels.Api as sm # Read data generated in R and Python takes care of this specified... Exact opposite actually - statsmodels does not have NaNs: statsmodels 0.9 is not by! Statistical test, and the predictors using the t_test and f_test methods model... Not compatible with scipy 1.3.0 generated in R using Pandas or something similar that my data looks like::... A different result than R 's GLM model estimation exposes the from_formula class of. That is built explicitly for statistics ; therefore, it provides a rich output of statistical information the sqrt the! Api is split into models: statsmodels.api: Cross-sectional models and methods of class! ; therefore, it provides a rich output of statistical information head against the trying...
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calculus and analysis – How to use dimensions to analyze physical equations in polar coordinates

I already know that the geometric equation of an elastic body in polar coordinates is as follows:

begin{aligned} &varepsilon_{rho}=frac{partial u_{rho}}{partial rho} quad \ &varepsilon_{theta}=frac{u_{rho}}{rho}+frac{1}{rho} frac{partial u_{theta}}{partial theta} quad\ &\ &gamma_{rho theta}=-frac{u_{theta}}{rho}+frac{partial u_{theta}}{partial rho}+frac{1}{rho} frac{partial u_{rho}}{partial theta} quad end{aligned}

I find that in $$gamma_{rho theta}$$ there is a coefficient $$frac{1}{rho}$$ in front of $$frac{partial u_{rho}}{partial theta}$$ and not in front of $$frac{partial u_{theta}}{partial rho}$$.

I want to use MMA to analyze the dimensions of items, such as $$frac{partial u_{theta}}{partial rho}$$, $$varepsilon_{rho}$$, $$frac{partial u_{rho}}{partial theta}$$.


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# Residue Theorem and its Application

Published:

This post makes notes on residue theorem and its application, since most non-mathematicians only need to remember this after learning complex analysis. Some definitions may be not defined very rigorously from a complex analysis view.

# Isolated Singularity

There are 3 kinds of isolated singularities for a single-valued function $f(z)$,

• removable singularities: The limit $\lim_{z\to c}f(z)$ exists.
• The function becomes analytic at $c$ if we define $f(c)$ to be this limit.
• The Laurent expansion about $c$ does not contain negative terms (terms with negative degree).
• poles: The limit $\lim_{z\to c}f(z) = \infty$.
• The Laurent expansion about $c$ contains finitely many negative terms (i.e. finite principal part)
• The order of pole $c$ is the integer $n$ s.t. $(z-c)^nf(z)$ is analytic and non-zero at $z$.
• essential singularities: $\lim_{z\to c}f(z)$ diverges.
• The Laurent expansion about $c$ contains infinitely many negative terms.

Liouville’s theorem implies that any non-constant analytic function must have at least one pole or essential singularity.

# Residue Theorem

The residue is the coefficient of $-1$ term of the Laurent expansion ($c\neq\infty$):

$\operatorname{res} f(c) = a_{-1} \quad\text{if}\ \ f(z) = \sum_{n=-\infty}^{+\infty}{a_n(z-c)^n}$

Let $U$ be a simply connected open set, $f$ be analytic in $U\setminus\{c_1,\ldots,c_m\}$ and continuous in $\bar{U}$, $C$ be the boundary of $U$ which is a closed rectifiable curve. Then,

$\oint_{C} f(z)\mathrm{d}z = 2\pi\mathrm{i}\sum_{k=1}^{m}{\operatorname{res} f(c_k)}$

If $c$ is a pole of order $m$, then the residue at $c$ is

$\operatorname{res} f(c) = \lim_{z\to c}\frac{1}{(m-1)!}\frac{\mathrm{d}^{m-1}}{\mathrm{d}z^{m-1}}(z-c)^{m}f(z)$

Especially, when $m=1$:

$\operatorname{res} f(c) = \lim_{z\to c}(z-c)f(z)$

Proof (sketch): Break $C$ into multiple loops that enclose a pole each. By the coefficient of Laurent expansion:

$a_n = \frac{1}{2\pi\mathrm{i}}\oint_{C}{\frac{f(z)}{(z-c)^{n+1}}\mathrm{d}z}$

Another way to look at this is that $\frac{1}{z^n}$ is single-valued and goes to 0 along a loop. But $\ln z$ increases by $2\pi\mathrm{i}$.

# Sum of Infinite Series

Suppose the target series to calculate is $\sum_{n=-\infty}^{\infty}{f(n)}$, with $f(n) = O(\frac{1}{n})$. Let $G(z) = \pi\cot{\pi z}$. Note that $G$ is analytic in $\mathbb{C}\setminus\mathbb{Z}$ and $\operatorname{res}G(n) = 1$ for all $n\in \mathbb{Z}$. Take curve $C_N$ be the square $[-N-\frac{1}{2}, N+\frac{1}{2}]\times[(-N-\frac{1}{2})\mathrm{i}, (N+\frac{1}{2})\mathrm{i}]$.

Theorem: If $f(z)$ has finitely many poles in $\mathbb{C}$ and analytic in the rest of the complex plane, then

$\lim_{N\to\infty}\oint_{C_N} G(z)f(z)\mathrm{d}z = 0$

Proof: $|\pi\cot{\pi z}| \leq 2\pi$ on the curve $C_N$.

Theorem: If $f(z)$ satisfies all conditions above and all poles $\{c_1, \ldots, c_m\}$ are non-integer, then

$\sum_{n=-\infty}^{+\infty}f(n) = - \sum_{i=1}^{m}{\operatorname{res} \{\pi\cot{\pi z}f(z), z=c_i\} }$

Proof: Take $N\to\infty$. For any $n\in\mathbb{Z}$,

$\begin{eqnarray} \operatorname{res} \{\pi\cot{\pi z}f(z), z=n\} &=& \lim_{z\to n}(z-n)\pi\cot{\pi z}f(z) \nonumber \\ &=& \lim_{z\to n}\frac{\pi\cos {\pi z}}{(\sin {\pi z})'}f(z) \nonumber \\ &=& f(n) \end{eqnarray}$

Apply the theorem above.

Example:

$\sum_{n=1}^{\infty} {\frac{1}{n^2}} = \frac{\pi^2}{6}$

Proof: We cannot use the theorem directly, but we have

$\operatorname{res} \{\frac{\pi\cot{\pi z}}{z^2}, z=0\} = [z^1 ] (\pi\cot{\pi z})$

Suppose the Laurent expansion of $\cot z$ at $z=0$ is

$\cot z = \sum_{n=-1}^{+\infty} {b_{2n+1} z^{2n+1}}$

Then,

$\sum_{p=0}^{\infty}{\frac{(-)^p}{(2p)!}z^{2p}} = \cos z = \sin z\sum_{n=-1}^{+\infty} {b_{2n+1} z^{2n+1}} = \sum_{q=0}^{\infty}{\frac{(-)^q}{(2q+1)!}z^{2q}} \sum_{n=0}^{+\infty} {b_{2n-1} z^{2n-1}}$

Thus,

$\sum_{n=0}^{p}{\frac{(-)^n}{(2p-2n+1)!} b_{2n-1}} = \frac{1}{(2p)!}$

Solve it and get

$\cot z = \frac{1}{z} - \frac{1}{3}z - \frac{1}{45}z^3 - \frac{2}{945}z^5 - \cdots$

Substitute $- \frac{1}{3} \pi^2$ into the first equation for $[z^1 ] (\pi\cot{\pi z})$.

# Asymptotics of Generating Functions

Principles of Coefficient Asymptotics: For $[ z^n]F(z) = A^n\theta(n)$

• The location of a function’s singularities dictates the exponential growth ($A^n$) of its coefficients.
• The nature of a function’s singularities determines the associate subexponential factor ($\theta(n)$).

## Exponential Growth

Def: $\{a_n\}$ is of exponential order $K^n$ if for any $\epsilon>0$, $|a_n|$ exceeds $(K-\epsilon)^n$ infinitely often and is dominated by $(K+\epsilon)^n$ cofinitely.

$a_n \bowtie K^n \qquad \text{iff} \qquad \lim \sup |a_n|^{1/n} = K$

This can be rephrased as $a_n = K^n\theta(n)$ where $\lim\sup |\theta(n)|^{1/n} = 1$.

Exponential Growth Formula: If the radius of convergence of the series $f_n = [z^n ]f(z)$ at 0 is $\mathrm{R_{conv}}(f; 0) = R$, then

$f_n \bowtie \left( \frac{1}{R} \right)^n$

Proof:

• By the definition of radius of convergence, $| f_n |(R-\epsilon)^n\to 0$.
• If $| f_n |(R+\epsilon)^n$ were bounded, then $| f_n |(R+\frac{1}{2}\epsilon)^n$ would converge. So $| f_n |(R+\epsilon)^n$ is unbounded.

Note: for a complex series $f(z)$, $R$ is the modulus of a singularity nearest to the origin.

Example: The EGF of the number of surjections (surjections from $[ n]$ to $[ m]$ for some $m$), and the EGF of the number of chains in Boolean lattice $B_n$, are

$R(z) = \frac{1}{2 - e^z}$

By the proposition, we have $\frac{r_n}{n!} \bowtie \frac{1}{(\ln 2)^{n}}$.

Saddle-point bound: Let $M(f; r) := \sup_{|z| = r}|f(z)|$ (the maximum modulus on a ring) for $r< R$. Then, for any $r\in (0,R)$, the family of saddle point bounds

$[z^n ]f(z) \leq \frac{M(f; r)}{r^n} \qquad \text{implying} \qquad [z^n ]f(z) \leq \inf_{r\in(0,R)}\frac{M(f; r)}{r^n}$

If in addition $f(z)$ has non-negative coefficients, then

$[z^n ]f(z) \leq \frac{f(r)}{r^n} \qquad \text{implying} \qquad [z^n ]f(z) \leq \inf_{r\in(0,R)}\frac{f(r)}{r^n}$

The best $r$ can be obtained by the zero derivative:

$r\frac{f'(r)}{f(r)} = n$

Proof:

By the coeffcients of Laurent expansion:

$[z^n ]f(z) = \frac{1}{2\pi \mathrm{i}}\oint_{|z|=r} f(z)\frac{\mathrm{d}z}{z^{n+1}}$

Example: Apply this to $[ z^n]e^z$ we have

$\frac{1}{n!} \leq \frac{e^n}{n^n}$

## Subexponential Factor

One can show that if singularities of $f(z)$ are polar, then $\theta(n)$ is a polynomial.

Def: If $f(z) = \frac{N(z)}{D(z)}$ with $N, D$ being polynomials, $f(z)$ is a rational function.

Coefficients of rational functions satisfy linear recurrence relations with constant coefficients:

$[z^n ]f(z)D(z) = \sum_{j=0}^{m}d_j f_{n-j} = 0 \qquad \text{for all}\ n>\mathrm{deg}(N)$

Rational Function Case: If $f(z) = \frac{N(z)}{D(z)}$ is a rational function that is analytic at 0 and has poles at $a_1, \ldots, a_m$, then its coefficients are a sum of exponential–polynomials. That is, for $n$ larger than $n_0:= \mathrm{deg}(N) - \mathrm{deg}(D)$:

$f_n := [z^n ]f(z) = \sum_{j=1}^{m}P_j(n)a_j^{-n}$

Furthermore, the degree of $P_j$ is equal to the order of the pole of $f$ at $a_j$ minus one.

Proof: Apply the partial fraction expansion:

$f(z) = Q(z) + \sum_{j=1}^{m}\frac{c_j}{(z-a_j)^{r_j}}$

where $Q$ is of degree $n_0$. Since

$[z^n ]\frac{1}{(z-a)^r} = \frac{(-)^r}{a^r}[z^n ]\frac{1}{(1-\frac{z}{a})^r} = \frac{(-)^r}{a^r} {n+r-1 \choose r-1} a^{-n}$

The binomial coefficient is a polynomial of degree $r − 1$ in $n$. Collect all terms.

Cor: If $f(z) = \frac{N(z)}{(z-a)^r}$ that has a single dominant pole $a$ with order $r$, then

$f_n = (-)^r\frac{C}{(r-1)!}a^{-r}a^{-n}n^{r-1}\left( 1+O\left(\frac{1}{n}\right) \right) \quad \text{with} \quad C = \lim_{z\to a}(z-a)^r f(z)$

This is a direct result of the theorem. (The book has a typo) For $r=1$, one can verifies:

$\frac{c}{x-a} = - \frac{\frac{c}{a}}{1 - \frac{x}{a}} = -\frac{c}{a}a^{-n}x^{n}$

Example: Fibonacci numbers have OGF $F(z) = \frac{z}{1 - z - z^2}$. The poles are $a_1 = - \varphi = -\frac{\sqrt{5}+1}{2}$ and $a_2 = \psi = \frac{\sqrt{5} - 1}{2}$. $\operatorname{res} F(\psi) = \frac{\sqrt{5} - 5}{10}$, $\operatorname{res} F(-\varphi) = \frac{-\sqrt{5} - 5}{10}$. Thus,

$f_n \sim \frac{1}{\sqrt{5}}\psi^{-n}(1 + O(1/n)) = \frac{1}{\sqrt{5}}\varphi^{n}(1 + O(1/n))$

Actually,

$f_n = \frac{1}{\sqrt{5}} (\varphi^n - (-\varphi)^{-n})$

Analytic Function Case: If $f(z)$ is analytic at $|z| \leq R$ except for poles $a_1, \ldots, a_m$. Then, there exist $m$ polynomials $P_j$ s.t.

$f_n := [z^n ]f(z) = \sum_{j=1}^{m}P_j(n)a_j^{-n} + O(R^{-n})$

Furthermore, the degree of $P_j$ is equal to the order of the pole of $f$ at $a_j$ minus one.

Proof: (The 1st one by the book)
Take the Laurant expansion of $f(z)$ at $a$:

$f(z) = \sum_{k\geq r} c_{a,k}(z-a)^k = S_a(z) + H_a(z)$

where $S_a$ is the principal part and $H_a$ is the regular part. Note that $S_a$ is polynomial. Let $S = \sum_{j}S_{a_j}$. Observe that and $f-S$ is analytic for $|z| \leq R$. Then.

$f_n := [z^n ]f(z) = [z^n ]S(z) + [z^n ] (f-S)(z)$

The coefficient of $S$ is obtained by the polynomial theorem. And, by saddle-point bound at $z=R$,

$|[z^n ] (f-S)(z)| = \frac{1}{2\pi}\left| \oint_{|z|=R} (f(z) - S(z))\frac{\mathrm{d}z}{z^{n+1}} \right| \leq \frac{1}{2\pi} \frac{O(1)}{R^{n+1}} 2\pi R$

example: The EGF of the number of surjections $R(z) = \frac{1}{2 - e^z}$ has a dominant pole $a = \ln 2$ of order $1$. $\operatorname{res} R(a) = -\frac{1}{2}$. Thus,

$\frac{r_n}{n!} \sim \frac{1}{2\ln 2}(\ln 2)^{-n} (1 + O(1/n))$

# References

• Wu Chongshi, Methods of Mathematical Physics, Peking University Press, 2003.
• Ph. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009.

Tags:


text:
# A tricky integral

by Appa
Tags: arctan(x), integral
 P: 16 1. The problem statement, all variables and given/known data I should find this integral: $$\int$$b x(1/$$\Pi$$)(1/(1+x2)dx -b 2. Relevant equations $$\int$$1/(1+x2)dx = arctan(x) 3. The attempt at a solution The Only thing I've succeeded in doing is to take the 1/$$\Pi$$ and put it in front of the integral like this: (1/$$\Pi$$)$$\int$$b (x/(1+x2)dx -b And I know that the integral of 1/(1+x2) equals arctan(x) but how could that help me? Ive tried to use the equation $$\int$$f(x)g(x)dx = F(x)g(x) - $$\int$$F(x)g'(x)dx but I can't compute the integral of arctan(x). Could someone help me?
 Mentor P: 21,305 Is this the integral? $$\frac{1}{\pi}\int_{-b}^b{\frac{x}{x^2 + 1}dx$$ If so, you can use a simple substitution, u = x^2 + 1, and du = 2xdx
 Mentor P: 21,305 BTW, you should have posted this in the Calculus & Beyond forum. This problem clearly falls in that area.
 P: 626 A tricky integral Seems kind of weird to be doing that integral from -b to b, whether or not b > 0 or < 0 you get into complex numbers.
 HW Helper P: 3,348 Perhaps the easiest way is to observe this function is odd, and look at the interval of integration.
Math
Emeritus


text:
# Using RNN (LSTM) for predicting one future value of a time series

I have been reading several papers, articles and blog posts about RNNs (LSTM specifically) and how we can use them to do time series prediction. In almost all examples and codes I have found, the problem is defined as finding the next x values of a time series based on previous data. What I am trying to solve is the following:

• Assuming We have t values of a time series, what would be its value at time t+1?

So using different LSTM packages (deeplearning4j, keras, ...) that are out there, here is what I am doing right now:

1. Create a LSTM network and fit it to t samples. My network has one input and one output. So as for input I will have the following patterns and I call them train data:

t_1,t_2

t_2,t_3

t_3,t_4

2. The next step is to use for example t_4 as input and expect t_5 as output then use t_5 as input and expect t_6 as output and so on.

3. When done with prediction, I use t_5,t_6 to update my model.

My question: Is this the correct way of doing it? If yes, then I have no idea what does batch_size mean and why it is useful.

Note: An alternative that comes to my mind is something similar to examples which generate a sequence of characters, one character at a time. In that case, batch_size would be a series of numbers and I am expecting the next series with the same size and the one value that I'm looking for would be the last number in that series. I am not sure which of the above mentioned approaches are correct and would really appreciate any help in this regard.

Thanks

• This does not work with multivariate time series prediction, however, keras has a straightforward implementation for predicting multiple time steps ahead. Jul 17 '17 at 15:10

## 2 Answers

1. The way you are doing it is just fine. The idea in time series prediction is to do regression basically. Probably what you have seen other places in case of vector, it is about the size of the input or basically it means feature vector. Now, assuming that you have t timesteps and you want to predict time t+1, the best way of doing it using either time series analysis methods or RNN models like LSTM, is to train your model on data up to time t to predict t+1. Then t+1 would be the input for the next prediction and so on. There is a good example here. It is based on LSTM using the pybrain framework.
2. Regarding your question on batch_size, at first you need to understand the difference between batch learning versus online learning. Batch size basically indicates a subset of samples that your algorithms is going to use in gradient descent optimization and it has nothing to do with the way you input the data or what you expect your output to be. For more information on that I suggest you read this kaggle post.

I recently did a lot of reading and code writing on LSTMs so I'll try to pitch in and answer the question, though I'm not yet familiar with Theano Keras or deeplearning4j. From a quick scour of the Internet it seems that the meaning of batch_size is program-dependent, so it might be a good idea to check the online Help files. From what I gather though, it can refer to a couple of different things: 1) the count of cases fed into the training algorithm for processing before the next examination of inputs and/or outputs. 2) the number of iterations of the training algorithm over the last set of input before the next examination of inputs and/or outputs. 3) the size of sequences fed to the LSTM algorithms.

With that in mind it seems almost certain that Theano and deeplearning4j are referring to #1 and/or #2, given the following links. On the other hand, I've run across journal articles recently, where batch size referred to sequence size, so watch out for a potential mismatch between the software and academic terminology:

This post at CrossValidated indicates that in deeplearning4j and Keras the batch_size should be set to 1 for online learning. So in other words, batch_size controls the number of training cycles before the next input/output check.

☻ In Keras, the batch_size apparently sets the number of training cycles to execute or # of cases to train on before checking the inputs and/or outputs again, according to this Github page.

This Github package also seems to use a different variable to denote sequence length.

☻ From Tony Kanh's answer at this StackOverflow page, in TensorFlow the batch_size determines the size of the output vector. This is probably identical to the number of items processed in each training cycles, since multiplying it by the num_steps and size (probably the sequence size?) determines the dimensions of the output.

☻ For closely related neural nets like Bidirectionals, the batch size is apparently equivalent to the sequence size, not the number of cases fed into the training algorithm. See p. 5, Berglund, et al., "Bidirectional Recurrent Neural Networks as Generative Models," available at the Cornell University Library website without a paywall.

As I said I haven't used Theano and deeplearning4j yet, but I hope that at least provides a starting point to find the correct answer.


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• May 25, 2020, 03:05:35 AM
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### AuthorTopic: SAS Modact 6.1 for IL-2 4.13.1m  (Read 37303 times)

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#### spartan18a

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #24 on: April 10, 2016, 09:48:33 AM »

In Storebror we trust!

Sent from my XT1032 using Tapatalk
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#### Bowie57

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #25 on: April 10, 2016, 10:03:42 AM »

Vielen Danke Storebror.

I don't have the nerve to accuse you of caring!
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#### bomberkiller

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #26 on: April 10, 2016, 01:48:32 PM »

Quote
In Storebror we trust!

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#### stugumby

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #27 on: April 11, 2016, 12:29:06 PM »

Ok its in and working but i have a question about where you mentioned the HSFX eye candy, if i import those files does that give acess to the naps in hsfx, or do i need to update the maps folder etc?

Also ive noticed i now have an additional new britain map, it has (sep 43) then below it there is the (september 43 ) map, sep 43 will not load, september 43 does.
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#### SAS~Storebror

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #28 on: April 11, 2016, 10:59:31 PM »

Ok its in and working but i have a question about where you mentioned the HSFX eye candy, if i import those files does that give acess to the naps in hsfx, or do i need to update the maps folder etc?
The map files required are inside the SFS archives, however you have to introduce them to the game by adding the regarding map to the file
Code: [Select]
#SAS/MAPMODS/MAPS/all.iniYou can find the HSFX map lines for that file in your HSFX game folder, then look for the file
Code: [Select]
Files/maps/all.iniFor the maps you want, after copying the SFS files to Modact 6 you have to copy the regarding map line(s) from that file to Modact's all.ini file, then you can try whether or not the map works.

Also ive noticed i now have an additional new britain map, it has (sep 43) then below it there is the (september 43 ) map, sep 43 will not load, september 43 does.
Yep, thanks to TD again!
The reason is that before 4.13.1 there was the maps
Code: [Select]
New-Britain_New-Guinea_Sept-43New-Britain_New-Guinea_June-44whereas with 4.13.1 TD introduced
Code: [Select]
New-Britain_New-Guinea_Mar-43_DTNew-Britain_New-Guinea_Sept-43_DTNew-Britain_New-Guinea_Jan-44_DTNew-Britain_New-Guinea_June-44_DTNow one could say: "Great, they added two more New Guinea maps, what's the problem?".
The problem is that TD just cannot (or deliberately doesn't want to) create anything new without breaking all existing content.
In this particular case, the path for the map files changed as did their internal name (see the _DT) attached above.
Old map path was:
Code: [Select]
NGNB/NGNB_9-43.iniNGNB/NGNB_6-44.ininew is:
Code: [Select]
NGNB_DT/NGNB_3-43.iniNGNB_DT/NGNB_9-43.iniNGNB_DT/NGNB_1-44.iniNGNB_DT/NGNB_6-44.ini
It becomes apparent that existing missions and campaigns for the "old" maps won't work anymore since their map declaration is missing in the new 4.13.1 "all.ini" file, so I thought I could cure it by simple re-introducing the "old" maps in parallel to the "new" ones, they don't share any files after all, so that should be no big deal.
However TD, in their constant attempt to fuck up anything they left behind, deliberately also changed files in the "old" maps path, in a way that they won't load anymore.
Trying to load the "old" maps now results in an error like this:
Code: [Select]
section [MAP2D] not found in 'maps/NGNB/NGNB_9-43.iniThank you very much TD, fucked up existing content once more for absolutely no reason.

Best regards - Mike
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#### stugumby

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #29 on: April 12, 2016, 09:03:41 AM »

Hmm, in mod act 6.1 im getting lots of falling from skies etc on the new guinea maps, taxi to take off ends at collaps landing gear and all ijn falling from sky, works as it should in game stock, fixed it one mission at a time by relesecting a diff player and saving it again. but in stock it works... arrrghh in deed.
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#### SAS~Storebror

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #30 on: April 12, 2016, 09:54:14 AM »

Let me summarize:
You have missions for the new "TD" new guinea maps that work fine in stock mode, but don't work well in Modact 6.1?
Thanks.

Best regards - Mike
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#### stugumby

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #31 on: April 12, 2016, 01:00:03 PM »

ok i tried insert code but it says it has to many characters, so heres the link to it as it was sent to mission4today.

mission was ijn buna last convoy ver A, it should be taxi to take off instead i get all ijn either falling from air or startting with engine off.

also i checked in my still untouched no mods 413rc4 spare copy and the mission map names are the same. but in mod act i get 2 sep 43 maps, 1 named sep and the other september

i downloaded the mission as i had sent it to m4t and in sas selected i get the collapsing gear at mission start or if in ver b my plane starts on screen engine off and ai taxi to take off collpase., works fine in stock both 413 and 413.1.
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#### stugumby

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #32 on: April 12, 2016, 01:35:36 PM »

urgent message: i looked at the mission in stock and my p40m new where there in air, in mod act there are no p40m new available, i looked at the air ini and no p40M also on map in mod act enabled as i cycled through the planes i noticed what i posted before but i had a grey p40 under the trees off the play area of the map, thats when i looked for it in air ini.

also tried to load any map which loaded and insrert a p40m new, couldnt do it as there was no p40m new just the old. perhaps this is the cause of the mission collaps etc??
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#### duffys tavern

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #33 on: April 12, 2016, 06:17:23 PM »

Any one come up with a CTO mod for 6.1?
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#### SAS~Storebror

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #34 on: April 13, 2016, 01:58:17 AM »

Please check the first page for the Hotfix 001 released to fight the issue of missing P-40M_NEW and duplicate (non-working) entries for two New Guinea/New Britain maps.
There are no plans to port the CTO mod to 4.13.1 at the moment, say "thank you" to TD for making this patch another showstopper for modders.

Best regards - Mike
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#### stugumby

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##### Re: SAS Modact 6.1 for IL-2 4.13.1m
« Reply #35 on: April 16, 2016, 09:16:58 AM »

updated with the hot fix, p40 problem solved, thanks.
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text:
# Synopsis: Band together

Semiconductor alloys offer one way to improve the efficiency of solar cells.

The sun offers us light for free, but most of the spectrum is missed by semiconductor solar cells, which are typically only efficient at converting light to electricity over a window of wavelengths. Connecting a series of different semiconductors can capture more of the solar spectrum, but these devices are complex and expensive to fabricate.

Now, in a paper appearing in Physical Review Letters, Nair López Martínez and colleagues at Lawrence Berkeley National Laboratory and RoseStreet Labs Energy, both in the US, present a prototype solar cell where they fold the light sensitivity of many semiconductors into a single material.

A semiconductor will absorb light most efficiently at the energy of its band gap—the energy it takes to excite an electron from the valence to the conduction band. To get around the limitation of a single band gap, López et al. engineered a semiconductor alloy, $\text{GaNAs}$, which has both an intermediate and wide band gap and is therefore sensitive to both low- and high-energy light. In their test of the first “proof of concept” solar cell based on an intermediate band semiconductor, the team shows their device has a promising efficiency over a wide spectrum of the sun’s light. – Jessica Thomas

### Announcements

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Gravitation

Fluid Dynamics

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Magnetism

### Synopsis: Measuring Spin One Atom at a Time

Electron microscopy experiments have measured the spin state of individual metal atoms on a graphene layer, characterizing their potential for information storage applications.   Read More »

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### Synopsis: Light Sees Electronic Bands

An all-optical alternative to photoemission spectroscopy can probe the electronic band structure of a solid. Read More »

Plasmonics

### Viewpoint: All Together Now

A “Schrödinger’s cat”-type effect entangles collective excitations in a semiconductor nanostructure, making a new infrared light source. Read More »


text:
# The motif zoo

This vignette introduces the nomenclature used for labeling motifs in multi-level networks as used in motifr.

## Motif classification – how to label motifs in the wild

Motifs are small subgraphs whose occurrences can reveal interesting structures in empirical networks. Motifs can span several levels of a multilevel networks. This package uses motif identifier strings for identifying motifs. These must provide information about

• the number of nodes contained by the motif on the various levels of the network (signature and positions),
• the structure of the motif itself, i.e. which edges are present, (motif class).

A motif identifier string contains these two pieces of information. It consists of a head and class, and is of the form HEAD[CLASS], e.g. 1,2[II.C]. The head specifies the signature and the positions of the motif while the class represents the motif class.

Let’s consider an example in a two-level network with levels 0 and 1. motifr generally counts levels starting at 0, due to its Python roots. The motif identifier string 1,2[II.C] represents the closed triangle with one node on level 0 and two nodes on level 1. 1,2 signifies that the first level (0) provides one node and the second (1) two nodes. The expression II.C in brackets stands for closed triangle. Alternatively, 1,2[I.C] represents the open triangle with the same number of nodes taken from the levels.

You can explore all possible motifs interactively in a shiny app included in the package by running (after installing and loading the package):

explore_motifs()

You can pass your own network to explore_motifs() to see what motifs mean exactly for your data. For example, if your network is stored in a object named my_net with a level attribute lvl you can explore motifs within it interactively using explore_motifs(net = my_net, lvl_attr = "lvl")

When in doubt about what a given identifier string implies for you specific network, you can let motifr show you the motif either in a dummy network or an example of the motif in a network you are analysing (the second will only work if the network you are analysing actually contains the motif) with show_motif(motif).

The following code below uses show_motif to illustrate a “1,2[II.C]” motif as found in the wetland management network object ml_net. ml_net contains a level attribute (specifying which node belongs to which level) named “sesType”.

show_motif(motif = "1,2[II.C]", net = ml_net, label = TRUE, lvl_attr = "sesType")

motifr supports both undirected and directed motifs, although the number of directed motifs currently supported is much more limited than the number of supported undirected motifs. If your favourite motif is not part of the zoo yet, reach out to us by creating an issue on github describing the motif you would like to have included and we will consider the request.

A full list of all supported signatures and motif classes can also be found in the documentation of the Python sma package in section Appendix: The Motif Zoo.

## A word of caution on counting: Position matching

Motifr uses an internal mechanism called position matching for translating the head of a motif identifier string, e.g. 1,2, to a sequence of levels corresponding to the signature of the motif. Usually, this procedure yields the desired matching and is of no interest to the user. However, sometimes it might be necessary two overwrite the position matching by providing custom positions.

An example for this is the motif 2,2[II.D]. It contains two nodes on level 0 and two nodes on level 1. The two nodes on level 0 and the two nodes on level 1 are respectively adjacent. Furthermore the two nodes on level 0 are linked to one of the nodes on level 1.

show_motif(motif = "2,2[II.D]", label = TRUE)

This motif differs from the motif 2:1,2:0[II.D] which contains the same number of nodes from the different levels. However, here the roles of the levels are swapped, i.e. in this motif, the two nodes on level 1 are adjacent to the two nodes on level 0.

show_motif(motif = "2:1,2:0[II.D]", label = TRUE)

The position matching can be overwritten by providing the levels corresponding to the entries in the motif signature, e.g. the head 2:1,2:0 signalises that the first level containing two nodes is level 1 (“2:1”) while the second level containing two nodes is level 0 (“2:0”).

See the documentation of the Python sma package, subsection Position matching for a detailed description of the procedure.

In general, it is recommended to always use show_motif(motif) to check whether the software interprets the provided motif identifier string as intended by the analyst.


text:
We're sorry Aspose doesn't work properply without JavaScript enabled.

# Saving document produces error: "Start and end node should have the same grand parent"

Hi,
I’m using your component to open word documents and immediately save (or export in this case) them as xhtml. This works for most of my files, however on a few I get the following error:

System.ArgumentException: Start and end node should have the same grand parent. at Aspose.Words.CompositeNode

The documents have a number of mail merge fields within them.
I’m afraid I can’t post examples due to the sensitive nature of the documents.
Is there anything I can try to enable me to process these documents?

Many thanks
Matthew Rose

Hi

Thanks for your request. You can try to use DocumentExplorer to review a structure of the document. Most likely there is field that starts in one section and ends in other. But it is difficult to say what the problem is without document.
You can remove all confidential content from the document and attach it here or just try to recreate the problem on a simple document.
https://releases.aspose.com/words/net
Best regards.

Many thanks for the speedy reply.

I have identified the field causing the problem, however as it is a
merge field I can’t change the data within it. Removing the field
causes the document to convert properly.

The field is a {FORMTEXT} field; however it doesn’t seem to span sections.
I’m using version 6.0.1 .net version (I upgraded today to see if this had been resolved).
Many thanks

Hi
Different section is just example. This could be a table or any other composite nodes. So, could you provide me simple document that will allow me to reproduce the problem on my side?
Best regards.

Hi,

Sorry for the delay in providing a document. I have attached a document which is causing the error.
The field that I believe is causing the problem is next to the “School” text.

Many thanks

Matthew

Hi
Thank you for additional information. I managed to reproduce the problem and created new issue #7266 in our defect database. I will notify you as soon as it is fixed.
You are right the reason of the problem is field after “School” text. You can remove and insert this field using MS Word to resolve this issue.
Best regards.

Thank you for your speedy response.
These documents are generated from a mail-merge type process, so we have little to no control over the data that is input into them; is there anything we can do in the component to work around the error?

Many thanks
Matthew

Hi
Thanks for your request. As a workaround you can try remove fields from your document, (field values will not be deleted, we will remove only FieldStart, FieldEnd, FieldSeparator and field code nodes) See code below:

// Open document.
Document doc = new Document(@"Test110\in1.doc");
// Get collections of FiledStart, FieldEnd and FieldSeparator nodes
NodeCollection fieldStarts = doc.GetChildNodes(NodeType.FieldStart, true);
NodeCollection fieldSeparators = doc.GetChildNodes(NodeType.FieldSeparator, true);
NodeCollection fieldEnds = doc.GetChildNodes(NodeType.FieldEnd, true);
// We will store nodes that should be removed in this temporary list
ArrayList removeList = new ArrayList();
foreach (FieldStart start in fieldStarts)
{
// Add to remove list nodes that represens field code
Node currNode = start.NextSibling;
while (currNode.NodeType != NodeType.FieldSeparator)
{
currNode = currNode.NextSibling;
if (currNode == null)
break;
}
}
fieldStarts.Clear();
fieldSeparators.Clear();
fieldEnds.Clear();
// Remove field codes
foreach (Node node in removeList)
{
if (node.ParentNode != null)
node.Remove();
}
// Save output docuemnt
doc.Save(@"Test110\out.html");

Hope this helps.
Best regards.

Hi,
Thank you for your workaround; I have reprocessed all of the documents which have this problem and they all now seem to work.
Your help is very much appreciated.
Many Thanks
Matthew

The issues you have found earlier (filed as 7266) have been fixed in this update.


text:
# Circles, Tangents, And Triangles (Oh My...)

Geometry Level 5

The red circle has radius 3 and the blue circle has radius 4. The tangents to one of their points of intersection, $$P_1,$$ are perpendicular.

The green circle is centered at the other point of intersection, $$P_2,$$ and passes through $$P_1.$$ It also intersects the red and blue circles at $$P_3$$ and $$P_4,$$ respectively.

What is the length of the altitude from $$P_1$$ in triangle $$P_1P_3P_4?$$

×


text:
# arrow between parts of equation and tikzexternalize

In my document, I have an equation where I would like to connect two parts with an arrow, just as the way, as Alan Munn did it here. When I copy his example using \tikzexternalize, I get the error

! Package tikz Error: Sorry, the system call 'pdflatex -shell-escape -halt-on-error -interaction=batchmode -jobname "texstudio_v59040-figure2" "\def\tikzexternalrealjob{texstudio_v59040}\input{texstudio_v59040}"' did NOT result in a usable output file 'texstudio_v59040-figure2' (expected one of .pdf:.jpg:.jpeg:.png:). Please verify that you have enabled system calls. For pdflatex, this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or something like that. Or maybe the command simply failed? Error messages can be found in 'texstudio_v59040-figure2.log'. If you continue now, I'll try to typeset the picture.

and

! Package pgf Error: No shape named a is known.

! Package pgf Error: No shape named b is known.

My question is whether there is a possible workaround for this problem. Here is the MWE (again, thanks for the original answer)

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}

\tikzset{square arrow/.style={
to path={-- ++(0,-.25)  -| (\tikztotarget) \tikztonodes},below,pos=.25}}

\begin{document}
$$a\tikzmark{a}x^2 + bx + c = 5\tikzmark{b}x^2 + bx + c. \tikz[overlay,remember picture] {\path[draw,->,square arrow] (b.south) to node{x} (a.south) ; }$$
\end{document}

EDIT: In the MWE, it is possible to add \tikzset{external/export=false} before and \tikzset{external/export=false} after the equation environment which solves the issue, though in general it would be nicer to have everything externalized to speed up compiling.

• This can't work. Even if you would be somehow able to externalize the arrow: Its length depends on the marks, and if you add something to the equation how should a external graphic be able to adapt to the changed locations? – Ulrike Fischer Mar 17 '16 at 15:22
• @Ulrike: good point, I agree! It would be very complicated to implement a check if the underlying equation changed or not. I'll try to keep very simple in my annotations and implement more "expensive" annotations with equations inside of \tikzpictures – riddleculous Mar 17 '16 at 15:40

It probably doesn't take much more time to create this arrow on every compilation compared to including it with \includegraphics.

I suggest you use the idea you had, to disable and enable externalization around the equation. To save you some trouble, you could redefine the equation environment to include this.

Since you're using amsmath, the definition of the environment will be:

\renewenvironment{equation}{%
\incr@eqnum
\mathdisplay@push
\st@rredfalse \global\@eqnswtrue
\mathdisplay{equation}%
}{%
\endmathdisplay{equation}%
\mathdisplay@pop
\ignorespacesafterend
}

You can change this in your preamble with something like:

\makeatletter
\renewenvironment{equation}{%
\incr@eqnum
\mathdisplay@push
\st@rredfalse \global\@eqnswtrue
\tikzexternaldisable
\mathdisplay{equation}%
}{%
\endmathdisplay{equation}%
\tikzexternalenable
\mathdisplay@pop
\ignorespacesafterend
}
\makeatother

Then you're guaranteed not to run into this problem. I think it will be hard to externalize the arrow since it uses in total three tikz environments, but someone else might have a solution!

## Update

Here's a much better solution that saves you the trouble to find the correct definition. Use

\usepackage{etoolbox}
\AtBeginEnvironment{equation}{\tikzexternaldisable}
\AtEndEnvironment{equation}{\tikzexternalenable}

and substitute equation to what ever environment you want to use. Read more in etoolbox's manual

• the three tikz "pictures" are what I see as problematic, too. You're right, probably it won't consume so much extra time even though I plan to use many of those arrows. I like the idea with redefining the whole environment. Where did you get the implementation from? I might want to use align or other math environments later. – riddleculous Mar 17 '16 at 14:22
• @riddleculous I just found the definition in the question I linked to and added tikzexternaldisable/\tikzexternalenable where it seemed to fit. I updated my answer now with a solution that should work for any environment! – Grimler Mar 17 '16 at 14:43
• see Ulrike's comment to my posting, it's probably not possible. I'll just use your comfortable etoolbox approach! – riddleculous Mar 17 '16 at 15:42
• @riddleculous Glad to hear that this is sufficient for you! – Grimler Mar 17 '16 at 16:27


text:
This is an archived post. You won't be able to vote or comment.

[–] 2 points3 points  (1 child)

myprogram.exe "c:\complete\path\to\file"

Put it in quotes.

[–] 0 points1 point  (0 children)

Shouldn't the backlashes be escaped?

[–] 1 point2 points  (3 children)

simple question here.

It seems not.

I don't know how exactly I have to type out the argument

What do you mean by "type out"?

Really, you haven't described your problem. Either post literally the command line you are having problems with, or post the actual C code that doesn't work for you.

[–][S] 0 points1 point  (2 children)

What I'm trying to do is setting a program's argument to a file name. So argv[1] will contain the name of the file that I want to use further in the program. Now, I'm using code::blocks, and when I set the programs arguments via "project -> set program's arguments", I don't really know what to give as an argument.

Also, I am very new to C, so that might cause some misconceptions.

[–] 1 point2 points  (1 child)

Still completely unclear about what you are asking about - post the code that doesn't work, and post an explanation of what you would like it to do if it did work.

[–] 0 points1 point  (0 children)

It sounds like OP isn't sure how to specify a path with spaces in it (part of their path says "Programming<space>C", and so the path is read as 2 separate arguments.

Some others have responded that you can surround the filename in double quotes, which ought to be the correct answer.

[–] 1 point2 points  (1 child)

If your program and the database file are in the same directory, you only need to pass the filename (not the full file path) as the parameter.

[–][S] -1 points0 points  (0 children)

Thanks, this is what I needed.

Turns out the problem lies elsewhere though. The program keeps crashing, not really sure why because the problem seems to lie in the part of the code that our prof gave us. (He wrote part of the program for us, our assignment is to finish it). I guess I'll just e-mail him.

[–] 0 points1 point  (0 children)

Surround the filepath with double quotes, like this:

"C:\Users\<Name>\Dropbox\Programming C\<project name>\database"


text:
Michael_Wiebe

Topic Contributions

Results of a survey of international development professors on EA

Nice work! Sounds like movement building is very important.

Longtermist slogans that need to be retired

Do you disagree with FTX funding lead elimination instead of marginal x-risk interventions?

Longtermist slogans that need to be retired

I happen to disagree that possible interventions that greatly improve the expectation of the long-term future will soon all be taken.

What do you think about MacAskill's claim that "there’s more of a rational market now, or something like an efficient market of giving — where the marginal stuff that could or could not be funded in AI safety is like, the best stuff’s been funded, and so the marginal stuff is much less clear."?

Longtermist slogans that need to be retired

Do you think FTX funding lead elimination is a mistake, and that they should do patient philanthropy instead?

Critiques of EA that I want to read

Also, how are you defining "longtermist" here? You seem to be using it to mean "focused on x-risk".

Critiques of EA that I want to read

I think that these factors might be making it socially harder to be a non-longtermist who engages with the EA community, and that is an important and missing part of the ongoing discussion about EA community norms changing.

Well, it’s because there’s more of a rational market now, or something like an efficient market of giving — where the marginal stuff that could or could not be funded in AI safety is like, the best stuff’s been funded, and so the marginal stuff is much less clear. Whereas something in this broad longtermist area — like reducing people’s exposure to lead, improving brain and other health development — especially if it’s like, “We’re actually making real concrete progress on this, on really quite a small budget as well,” that just looks really good. We can just fund this and it’s no downside as well. And I think that’s something that people might not appreciate: just how much that sort of work is valued, even by the most hardcore longtermists.

Michael_Wiebe's Shortform

But again, whether non-extinction catastrophe or extinction catastrophe, if the probabilities are high enough, then both NTs and LTs will be maxing out their budgets, and will agree on policy. It's only when the probabilities are tiny that you get differences in optimal policy.

Michael_Wiebe's Shortform

The value of x-risk reduction

Using  in  is assuming constant returns to scale. If you have , you get diminishing returns.

Messing around with some python code:

from scipy.stats import norm
import numpy as np

def risk_reduction(K,L,alpha,beta):
print('risk:', norm.cdf(-(K**alpha)*(L**beta)))
print('expected value:', 1/norm.cdf(-(K**alpha)*(L**beta)))

print('risk (2x):', norm.cdf(-((2*K)**alpha)*(L**beta)))
print('expected value (2x):', 1/norm.cdf(-((2*K)**alpha)*(L**beta)))

print('ratio:',(1/norm.cdf(-((2*K)**alpha)*(L**beta)))/(1/norm.cdf(-(K**alpha)*(L**beta))))

K,L = 0.5, 0.5
alpha, beta = 0.5, 0.5
risk_reduction(K,L,alpha,beta)

K,L = 0.5, 0.5
alpha, beta = 0.2, 0.2
risk_reduction(K,L,alpha,beta)

K,L = 0.5, 20
alpha, beta = 0.2, 0.2
risk_reduction(K,L,alpha,beta)

K,L = 0.5, 20
alpha, beta = 0.5, 0.5
risk_reduction(K,L,alpha,beta)

The value of x-risk reduction

Are you using ?