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The function computes predicted values, corresponding standard errors, confidence intervals, and prediction intervals for objects of class "rma".

# S3 method for rma
predict(object, newmods, intercept, tau2.levels, gamma2.levels, addx=FALSE,
level, digits, transf, targs, vcov=FALSE, ...)

# S3 method for rma.ls
level, digits, transf, targs, vcov=FALSE, ...)

## Arguments

object an object of class "rma" or "rma.ls". optional vector or matrix to specify the values of the moderator values for which the predicted values should be calculated. See ‘Details’. logical to specify whether the intercept should be included when calculating the predicted values for newmods. If unspecified, the intercept is automatically added when the original model also included an intercept. vector to specify the levels of the inner factor when computing prediction intervals. Only relevant for models of class "rma.mv" (see rma.mv) and when the model includes more than a single $$\tau^2$$ value. See ‘Details’. vector to specify the levels of the inner factor when computing prediction intervals. Only relevant for models of class "rma.mv" (see rma.mv) and when the model includes more than a single $$\gamma^2$$ value. See ‘Details’. logical to specify whether the values of the moderator variables should be added to the returned object. See ‘Examples’. optional vector or matrix to specify the values of the scale variables for which the predicted values should be calculated. Only relevant for location-scale models (see rma). See ‘Details’. logical to specify whether the values of the scale variables should be added to the returned object. numeric value between 0 and 100 to specify the confidence and prediction interval level (if unspecified, the default is to take the value from the object). integer to specify the number of decimal places to which the printed results should be rounded (if unspecified, the default is to take the value from the object). optional argument to specify the name of a function that should be used to transform the predicted values and interval bounds (e.g., transf=exp; see also transf). If unspecified, no transformation is used. optional arguments needed by the function specified under transf. logical to specify whether the variance-covariance matrix of the predicted values should also be returned (the default is FALSE). other arguments.

## Details

For a fixed-effects model, predict(object) returns the estimated (average) outcome in the set of studies included in the meta-analysis. This is the same as the estimated intercept in the fixed-effects model (i.e., $$\hat{\theta}$$).

For a random-effects model, predict(object) returns the estimated (average) outcome in the hypothetical population of studies from which the set of studies included in the meta-analysis are assumed to be a random selection. This is the same as the estimated intercept in the random-effects model (i.e., $$\hat{\mu}$$).

For models including one or more moderators, predict(object) returns the estimated (average) outcomes for values of the moderator(s) equal to those of the $$k$$ studies included in the meta-analysis (i.e., the ‘fitted values’ for the $$k$$ studies).

For models including $$p'$$ moderator variables, new moderator values for $$k_{new}$$ new studies can be specified by setting newmods equal to a $$k_{new} \times p'$$ matrix with the corresponding new moderator values. If the model object included an intercept, then it should not be explicitly specified under newmods, as it will be added by default (unless one sets intercept=FALSE). Also, any factors in the original model get turned into the appropriate contrast variables within the rma function, so that newmods should actually include the values for the contrast variables. Examples are shown below.

For random/mixed-effects models, an approximate prediction interval is also calculated (Riley et al., 2011). The interval estimates where level % of the true effect sizes or outcomes fall in the hypothetical population of studies (and hence where the true effect/outcome of a new study from the population of studies should fall in level % of the cases).

For random-effects models that were fitted with the rma.mv function, the model may actually include multiple $$\tau^2$$ values (i.e., when the random argument includes an ‘~ inner | outer’ term and struct="HCS", struct="DIAG", struct="HAR", or struct="UN"). In that case, the function will provide prediction intervals for each level of the inner factor (since the prediction intervals differ depending on the $$\tau^2$$ value). Alternatively, one can use the tau2.levels argument to specify for which level(s) the prediction interval should be provided. If the model includes a second ‘~ inner | outer’ term with multiple $$\gamma^2$$ values, prediction intervals for each combination of levels of the inner factors will be provided. Alternatively, one can use the tau2.levels and gamma2.levels arguments to specify for which level combination(s) the prediction interval should be provided.

When using the newmods argument for mixed-effects models that were fitted with the rma.mv function, if the model includes multiple $$\tau^2$$ (and multiple $$\gamma^2$$) values, then one must use the tau2.levels (and gamma2.levels) argument to specify the levels of the inner factor(s) (i.e., a vector of length $$k_{new}$$) to obtain the appropriate prediction interval(s).

For location-scale models fitted with the rma function, one can use newmods to specify the values of the $$p'$$ moderator variables included in the model and newscale to specify the values of the $$q'$$ scale variables included in the model. Whenever newmods is specified, the function computes predicted effects/outcomes corresponding to the specified moderators values. To obtain the corresponding prediction intervals, one must also specify the corresponding newscale values. If only newscale is specified (and not newmods), the function computes the predicted log-transformed $$\tau^2$$ values (when using a log link) corresponding to the specified scale values. By setting transf=exp, one can then obtain the predicted $$\tau^2$$ values.

## Value

An object of class "list.rma". The object is a list containing the following components:

pred

predicted value(s).

se

corresponding standard error(s).

ci.lb

lower bound of the confidence interval(s).

ci.ub

upper bound of the confidence interval(s).

pi.lb

lower bound of the prediction interval(s) (only for random/mixed-effects models).

pi.ub

upper bound of the prediction interval(s) (only for random/mixed-effects models).

tau2.level

the level(s) of the inner factor (only for models of class "rma.mv" with multiple $$\tau^2$$ values).

gamma2.level

the level(s) of the inner factor (only for models of class "rma.mv" with multiple $$\gamma^2$$ values).

X

the moderator value(s) used to calculate the predicted values (only when addx=TRUE).

Z

the scale value(s) used to calculate the predicted values (only when addz=TRUE and only for location-scale models).

...

If vcov=TRUE, then the returned object is a list with the first element equal to the one as described above and the second element equal to the variance-covariance matrix of the predicted values. The "list.rma" object is formatted and printed with print.list.rma.

## Note

Confidence and prediction intervals are calculated based on the critical values from a standard normal distribution (i.e., $$\pm 1.96$$ for level=95). When the model was fitted with test="t" or test="knha", then a t-distribution with $$k-p$$ degrees of freedom is used.

For a random-effects model (where $$p=1$$) fitted with the rma.uni function, note that this differs slightly from Riley et al. (2001), who suggest to use a t-distribution with $$k-2$$ degrees of freedom for constructing the prediction interval. Neither a normal, nor a t-distribution with $$k-1$$ or $$k-2$$ degrees of freedom is correct; all of these are approximations. The computations are done in the way described above, so that the prediction interval is identical to the confidence interval when $$\hat{\tau}^2 = 0$$, which could be argued is the logical thing that should happen. If the prediction interval should be computed exactly as described by Riley et al. (2001), then one can use argument pi.type="riley".

The predicted values are based only on the fixed effects of the model. Best linear unbiased predictions (BLUPs) that combine the fitted values based on the fixed effects and the estimated contributions of the random effects can be obtained with blup.rma.uni (currently only for objects of class "rma.uni").

When using the transf option, the transformation is applied to the predicted values and the corresponding interval bounds. The standard errors are omitted from the printed output. Also, vcov=TRUE is ignored when using the transf option.

## Author

Wolfgang Viechtbauer wvb@metafor-project.org http://www.metafor-project.org

## References

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. San Diego, CA: Academic Press.

Riley, R. D., Higgins, J. P. T., & Deeks, J. J. (2011). Interpretation of random effects meta-analyses. British Medical Journal, 342, d549. https://doi.org/10.1136/bmj.d549

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. https://doi.org/10.18637/jss.v036.i03

## Examples

### meta-analysis of the log risk ratios using a random-effects model res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) ### average risk ratio with 95% CI predict(res, transf=exp)
#> #> pred ci.lb ci.ub pi.lb pi.ub #> 0.4894 0.3441 0.6962 0.1546 1.5490 #>
### mixed-effects model with absolute latitude as a moderator res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, mods = ~ ablat, data=dat.bcg) ### predicted average risk ratios for given absolute latitude values predict(res, transf=exp, addx=TRUE)
#> #> pred ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat #> 1 0.3574 0.2714 0.4705 0.1947 0.6560 1 44 #> 2 0.2595 0.1749 0.3848 0.1328 0.5070 1 55 #> 3 0.3788 0.2927 0.4901 0.2079 0.6900 1 42 #> 4 0.2831 0.1977 0.4054 0.1478 0.5422 1 52 #> 5 0.8809 0.6321 1.2276 0.4667 1.6625 1 13 #> 6 0.3574 0.2714 0.4705 0.1947 0.6560 1 44 #> 7 0.7397 0.5639 0.9704 0.4036 1.3557 1 19 #> 8 0.8809 0.6321 1.2276 0.4667 1.6625 1 13 #> 9 0.5861 0.4716 0.7284 0.3270 1.0505 1 27 #> 10 0.3788 0.2927 0.4901 0.2079 0.6900 1 42 #> 11 0.7616 0.5752 1.0083 0.4138 1.4016 1 18 #> 12 0.4922 0.3989 0.6073 0.2753 0.8799 1 33 #> 13 0.4922 0.3989 0.6073 0.2753 0.8799 1 33 #>
### predicted average risk ratios for 10-60 degrees absolute latitude predict(res, newmods=c(10, 20, 30, 40, 50, 60), transf=exp, addx=TRUE)
#> #> pred ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat #> 1 0.9612 0.6668 1.3857 0.5000 1.8478 1 10 #> 2 0.7185 0.5526 0.9343 0.3936 1.3117 1 20 #> 3 0.5371 0.4355 0.6623 0.3005 0.9600 1 30 #> 4 0.4015 0.3151 0.5115 0.2218 0.7266 1 40 #> 5 0.3001 0.2144 0.4201 0.1586 0.5678 1 50 #> 6 0.2243 0.1423 0.3538 0.1105 0.4552 1 60 #>
### mixed-effects model with two moderators (absolute latitude and publication year) res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, mods = ~ ablat + year, data=dat.bcg) ### predicted average risk ratios for 10 and 60 degrees latitude in 1950 and 1980 predict(res, newmods=cbind(c(10,60,10,60),c(1950,1950,1980,1980)), transf=exp, addx=TRUE)
#> #> pred ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat X.year #> 1 0.8995 0.3689 2.1933 0.2981 2.7146 1 10 1950 #> 2 0.2217 0.1278 0.3847 0.0944 0.5208 1 60 1950 #> 3 0.9525 0.6199 1.4637 0.4361 2.0802 1 10 1980 #> 4 0.2348 0.1005 0.5481 0.0805 0.6843 1 60 1980 #>
### mixed-effects model with two moderators (one of which is a factor) res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, mods = ~ ablat + factor(alloc), data=dat.bcg) ### examine how the factor was actually coded for the studies in the dataset predict(res, addx=TRUE)
#> #> pred se ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat #> 1 -1.1744 0.2137 -1.5932 -0.7557 -2.0293 -0.3196 1 44 #> 2 -1.4745 0.2742 -2.0119 -0.9370 -2.3933 -0.5556 1 55 #> 3 -1.1199 0.2061 -1.5238 -0.7159 -1.9676 -0.2722 1 42 #> 4 -1.3926 0.2552 -1.8928 -0.8925 -2.2902 -0.4951 1 52 #> 5 -0.0614 0.3336 -0.7152 0.5924 -1.0528 0.9300 1 13 #> 6 -0.9069 0.3176 -1.5295 -0.2844 -1.8780 0.0642 1 44 #> 7 -0.4925 0.2338 -0.9508 -0.0343 -1.3674 0.3823 1 19 #> 8 -0.3289 0.2694 -0.8568 0.1991 -1.2422 0.5845 1 13 #> 9 -0.7107 0.2007 -1.1040 -0.3175 -1.5534 0.1320 1 27 #> 10 -0.7939 0.2667 -1.3166 -0.2712 -1.7042 0.1164 1 42 #> 11 -0.1393 0.2654 -0.6594 0.3808 -1.0481 0.7695 1 18 #> 12 -0.5484 0.2438 -1.0263 -0.0706 -1.4337 0.3369 1 33 #> 13 -0.5484 0.2438 -1.0263 -0.0706 -1.4337 0.3369 1 33 #> X.factor.alloc.random X.factor.alloc.systematic #> 1 1 0 #> 2 1 0 #> 3 1 0 #> 4 1 0 #> 5 0 0 #> 6 0 0 #> 7 1 0 #> 8 1 0 #> 9 1 0 #> 10 0 1 #> 11 0 1 #> 12 0 1 #> 13 0 1 #>
### predictd average risk ratios at 30 degrees for the three factor levels ### note: the contrast (dummy) variables need to specified explicitly here predict(res, newmods=c(30, 0, 0), addx=TRUE) # for alternate allocation
#> #> pred se ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat #> -0.5251 0.2923 -1.0980 0.0478 -1.4651 0.4149 1 30 #> X.factor.alloc.random X.factor.alloc.systematic #> 0 0 #>
predict(res, newmods=c(30, 1, 0), addx=TRUE) # for random allocation
#> #> pred se ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat #> -0.7926 0.1941 -1.1729 -0.4122 -1.6293 0.0442 1 30 #> X.factor.alloc.random X.factor.alloc.systematic #> 1 0 #>
predict(res, newmods=c(30, 0, 1), addx=TRUE) # for systematic allocation
#> #> pred se ci.lb ci.ub pi.lb pi.ub X.intrcpt X.ablat #> -0.4666 0.2420 -0.9410 0.0078 -1.3501 0.4168 1 30 #> X.factor.alloc.random X.factor.alloc.systematic #> 0 1 #>
### can also use named vector with arbitrary order and abbreviated variable names predict(res, newmods=c(sys=0, ran=0, abl=30))
#> #> pred se ci.lb ci.ub pi.lb pi.ub #> -0.5251 0.2923 -1.0980 0.0478 -1.4651 0.4149 #>
predict(res, newmods=c(sys=0, ran=1, abl=30))
#> #> pred se ci.lb ci.ub pi.lb pi.ub #> -0.7926 0.1941 -1.1729 -0.4122 -1.6293 0.0442 #>
predict(res, newmods=c(sys=1, ran=0, abl=30))
#> #> pred se ci.lb ci.ub pi.lb pi.ub #> -0.4666 0.2420 -0.9410 0.0078 -1.3501 0.4168 #>


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## Publications

Export 1692 results:
B
. Mesoscopic colonization in a spectral band. J. Phys. A [Internet]. 2009 ;42:415204, 17. Available from: http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204
. Simple Lie Algebras and Topological ODEs. Int. Math. Res. Not. 2016 ;2016.
. Effective inverse spectral problem for rational Lax matrices and applications. Int. Math. Res. Not. IMRN. 2007 :Art. ID rnm103, 39.
. Mixed correlation functions of the two-matrix model. J. Phys. A. 2003 ;36:7733–7750.
. Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I. Comm. Pure Appl. Math. [Internet]. 2013 ;66:678–752. Available from: http://dx.doi.org/10.1002/cpa.21445
. Discriminant circle bundles over local models of Strebel graphs and Boutroux curves. Teoret. Mat. Fiz. [Internet]. 2018 ;197:163–207. Available from: https://doi.org/10.4213/tmf9513
. A general construction of conformal field theories from scalar anti-de Sitter quantum field theories. Nuclear Phys. B. 2000 ;587:619–644.
Bertola M. The dependence on the monodromy data of the isomonodromic tau function. Comm. Math. Phys. [Internet]. 2010 ;294:539–579. Available from: http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7
Bertola M. CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function. [Internet]. 2016 . Available from: http://arxiv.org/abs/1601.04790
. The partition function of the two-matrix model as an isomonodromic τ function. J. Math. Phys. [Internet]. 2009 ;50:013529, 17. Available from: http://0-dx.doi.org.mercury.concordia.ca/10.1063/1.3054865
. Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves. Anal. Math. Phys. [Internet]. 2015 ;5:1–22. Available from: http://dx.doi.org/10.1007/s13324-014-0088-7
Bertola M. Two-matrix model with semiclassical potentials and extended Whitham hierarchy. J. Phys. A. 2006 ;39:8823–8855.
. Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes. J. Stat. Phys. [Internet]. 2012 ;146:475–518. Available from: http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2
. Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation. Comm. Math. Phys. [Internet]. 2017 ;354:525–547. Available from: http://dx.doi.org/10.1007/s00220-017-2895-9
. Correspondence between Minkowski and de Sitter quantum field theory. Phys. Lett. B. 1999 ;462:249–253.
. First colonization of a spectral outpost in random matrix theory. Constr. Approx. [Internet]. 2009 ;30:225–263. Available from: http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y
. Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation. Proc. A. [Internet]. 2016 ;472:20160340, 12. Available from: http://dx.doi.org/10.1098/rspa.2016.0340
Bertola M. Biorthogonal polynomials for two-matrix models with semiclassical potentials. J. Approx. Theory. 2007 ;144:162–212.
Bertola M. Free energy of the two-matrix model/dToda tau-function. Nuclear Phys. B. 2003 ;669:435–461.
. Darboux Transformations and Random Point Processes. IMRN. 2014 ;rnu122:56.
. The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation. Random Matrices: Theory and Applications [Internet]. 2013 ;02:1350003. Available from: http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032
. Warped products with special Riemannian curvature. Bol. Soc. Brasil. Mat. (N.S.). 2001 ;32:45–62.
. First colonization of a hard-edge in random matrix theory. Constr. Approx. [Internet]. 2010 ;31:231–257. Available from: http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4
. Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$. Phys. D [Internet]. 2016 ;327:30–57. Available from: http://dx.doi.org/10.1016/j.physd.2016.04.008

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# Memory reduction

This topic is 4346 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi, Probably you guys have experience with memory, since good old isometric games often had to be as small as possible on old systems. I'd like to know if there are some ways to bring down the size of my level files. A level is a 3D grid of 'cubes', kinda like GTA1/2. Each cube holds 5 faces (top,left, etc.), where each face has its own material. Furthermore, the cube uses a byte that describes the shape. Besides cubes, there are also slopes, walls, pillars, etc. The terrain is divided into what I call 'cells'. Each cell has 1 or more cubes stacked upon each other. So a cell has a byte that tells the height, and an array of cubes. When it comes down to the code, it looks something like this:

TFace = record
material  : Word; // unsigned int 16
end;

TCube = record
meshType : byte; // cube, slope, etctera.
face     : array[0..4] of TFace;
end;

TCell = record
height : byte;
stores : array of TCube; // height tells how big the array is
end;

TRaster = array of array of TCell; // 2D array with cells

It's Delphi code, but I think you get the idea. Now I'd like to store this stuff into a file, as small as possible. Now the size depends how many boxes are stacked. But let's say we have only 1 layer, the ground. And the raster is 100 x 100 cells. That would bring me to:
  cube_size = 5 faces(2 bytes each) + 1 byte = 11 bytes
cell_size, with 1 cube(store) = 11 + 1 = 12 bytes
raster    = 100 x 100 x 12 = ~117 kilobyte

It's not that much, but since these files need to be downloaded from internet, size really matters. I don't know how, but I have the feeling that it can be done smaller. I looked at some GTA2 levels (which are pretty big) and they were smaller in filesize I think. And probably those GTA2 'cubes' even had more properties, like the texture rotation. Most types are bytes, except the material. But probably there gonna be more than 256 materials. I could go bit-wise and remove some bits at some types... but I still don't think I can match with the GTA2 level sizes. How to shrink this? Greetings, Rick

##### Share on other sites
maybe you could look into some sort of compression. maybe you could do RLE or LZSS? I dont know...

##### Share on other sites
Why did that never came up into mind?! I tried to ZIP and RAR the file, for testing if it was worth it. 466 kb becomes 1 kb. That's exactly what I need, thanks for 'enlighten' me!

But... if somebody knows more tricks to reduce the memory, you're welcome! I'd like to know how to program this kind of stuff efficiently.

Greetings,
Rick

##### Share on other sites
Don't know any tricks for lowering your physical overhead. But when it comes to compression the best library I've found for Delphi is abbrevia: http://tpabbrevia.sourceforge.net/

It would help if you packed your record structures, and you could use custom stream read/write routines to lower space consumed in the cases where you don't fall on boundaries, but that would take quite a bit of work on your behalf.

- Jeremy


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# Improper Integrals

1. Sep 30, 2008

### UMich1344

1. The problem statement, all variables and given/known data

Calculate $$\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}x^{2}e^{-\frac{x^{2}}{2}}dx$$

Use the fact that $$\int^{\infty}_{-\infty}e^{-\frac{x^{2}}{2}}dx=\sqrt{2\pi}$$

2. Relevant equations

I'm assuming that integration by parts is the best way to solve this.

http://www.math.hmc.edu/calculus/tutorials/int_by_parts/" [Broken]

3. The attempt at a solution

I want to use integration by parts in order to solve this. I've attempted both combinations of u and v'. However, I'm not able to get an integral in any of my solutions that looks like the one above that is set equal to $$\sqrt{2\pi}$$.

I have plugged the equation into Mathematica and the answer comes out to be 1. However, getting my work to back that up is proving to be difficult.

Is integration by parts the right way to go about solving this one? Any help is greatly appreciated.

Last edited by a moderator: May 3, 2017
2. Sep 30, 2008

The integrand is the density of the standard normal distribution, which is why Mathematica gave you the answer it did.

You should try integration by parts; with a judicious choice of $$dv$$ you will find that the

$$\int \, dv$$

portion (to calculate $$v$$) is easily done. After the step, and you have

$$\int u \dv = uv - \int v \, du$$

you will see the reason for the hint.

3. Sep 30, 2008

### HallsofIvy

Staff Emeritus
Yes, we know what integration by parts is! How about showing exactly what you did so we can point out any mistakes?

Last edited by a moderator: May 3, 2017
4. Sep 30, 2008

### UMich1344

I have attached my work with this post. I felt that I was heading in the right direction, but obviously I must have done something wrong near the beginning I would assume, since by the end I found that my integral diverged.

File size:
16.8 KB
Views:
61


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# Metrics of research impact in astronomy: Predicting later impact from metrics measured 10-15 years after the PhD

no code yet • 27 Oct 2021

This paper calibrates how metrics derivable from the SAO/NASA Astrophysics Data System can be used to estimate the future impact of astronomy research careers and thereby to inform decisions on resource allocation such as job hires and tenure decisions.

Instrumentation and Methods for Astrophysics Earth and Planetary Astrophysics Solar and Stellar Astrophysics Digital Libraries

TWEETS

# A new mechanism for primordial black hole formation during reheating

no code yet • 27 Oct 2021

The Reheating process at the end of inflation is often modeled by an oscillating scalar field which shows a background dust-like behaviour, prompting the analysis of gravitational collapse and black hole formation in this era to be approached by the spherical collapse of standard structure formation.

Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology

TWEETS

# The ASTRID simulation: the evolution of Supermassive Black Holes

no code yet • 27 Oct 2021

Astrid statistically models BH gas accretion and AGN feedback to their environments, applies a power-law distribution for BH seed mass $M_{\rm sd}$, uses a dynamical friction model for BH dynamics and executes a physical treatment of BH mergers.

Astrophysics of Galaxies

TWEETS

# Globular Cluster Intrinsic Iron Abundance Spreads: II. Protocluster Metallicities and the Age-Metallicity Relations of Milky Way Progenitors

no code yet • 27 Oct 2021

Intrinsic iron abundance spreads in globular clusters, although usually small, are very common, and are signatures of self enrichment: some stars within the cluster have been enriched by supernova ejecta from other stars within the same cluster.

Astrophysics of Galaxies

TWEETS

# The density distributions of cosmic structures: impact of the local environment on weak-lensing convergence

no code yet • 27 Oct 2021

We also calculate the constraints on the cosmological parameters as a function of redshift from the theoretical and numerical study of the angular power spectrum of WL convergence.

Cosmology and Nongalactic Astrophysics

TWEETS


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# Are there two ways of representing a vector i.e., parrallelogram and resolution?

the question was:

The component of a vector is

(a) Always less than its magnitude

(b) Always greater than its magnitude

(c) Always equal to its magnitude

(d) None of these

according to me ans will be none of these because

The magnitude of the component of a vector (projection) may be less than or equal to the magnitude(never more than it.) of the vector itself which will depend on what you are taking the components along. The magnitude of the component may be equal to the magnitude of the vector if and only of the projection is taken along itself, otherwise, it will always be less. For instance, consider a vector 4i where i is a unit vector along the x-axis. Now the magnitude of the component of this vector along the x-axis is 4, same as that of the vector. Now, consider a vector 3i+4j, where i and j are unit vectors along x and y-axis respectively, the magnitude of this vector is 5 but the magnitude of components of this vector are 3 and 4 along the x and y-axis respectively.

but my teacher told me:

The component of a vector may be less than, greater than or equal to its magnitude.

i didnot understood how the component can be greater than the vector itself

on asking he showed me this :

my question is : can a vector have components in any set of two directions you choose that may not be mutually perpendicular. ?

. . . . can a vector have components in any set of two directions you choose that may not be mutually perpendicular. ?

Yes.
If $$\hat a$$ and $$\hat b$$ are two unit vectors (axis directions) which are not colinear to one another then any vector $$\vec c$$ can be resolved into two components $$a$$ and $$b$$ such that $$\vec c = a\,\hat a + b\,\hat b$$.
Notice that the only condition for the unit vector (axis directions) is that they must not be colinear to one another, ie they can be orientated at any angle relative to one another other than $$0^\circ$$ or $$180^\circ$$.

Perhaps an example will help?

Suppose there is a displacement from an origin of $$6$$ in the direction North-East and the two chosen axes are $$\hat y$$ which is the direction North and $$\hat x$$ which is in the direction East.
Then this displacement of $$6$$ in the North-Easterly direction is the same as a displacement $$3\sqrt 2$$ East then $$3\sqrt 2$$ North.
This displacement can be written as $$3\sqrt 2 \, \hat x + 3 \sqrt 2 \,\hat y$$ and these two components are shown as red vectors in the diagram below.

Now consider a displacement equal to $$6$$ North_West, $$\hat {y'}$$, followed by a displacement of $$6\sqrt 2$$ East, $$\hat x$$.
The total displacement can be written as $$6 \, \hat {y'}+ 6 \sqrt 2 \,\hat x$$ and these two components are shown as blue vectors in the diagram below.

• oh wow .. great explanation ... thanks once again – Garima Singh Sep 12 '19 at 10:52
• Sir I think it should be 6 root 2 x instead of 3 root 2 x in last second line. and one more thing why you have taken the northwest direction as y' and not as x'? – Garima Singh Sep 12 '19 at 15:40
• @GarimaSingh Many thanks. I have corrected my error. – Farcher Sep 12 '19 at 15:43

Of course vector can be decomposed into any set of two directions chosen arbitrary. That's the basis of vector algebra. Mutually perpendicular components exists only in Euclidean space which is sub-set of more general vector representation rule.

Another way to think, is that rectangle is a special case of parallelogram where all inner angles are $$\frac{\pi}{2}$$.
Parallelogram is a special case of Trapezoid. And so on, until the most general case of polygon.


text:
MathSciNet bibliographic data MR1990014 (2005f:58020) 58J05 (35B45 35J05) Marias, Michel \$L\sp p\$$L\sp p$-boundedness of oscillating spectral multipliers on Riemannian manifolds. Ann. Math. Blaise Pascal 10 (2003), no. 1, 133–160. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
Wc = gram(sys,'c') calculates the controllability Gramian of the state-space (ss) model sys.. Wc = gram(sys,'o') calculates the observability Gramian of the ss model sys.. Wc = gram(___,opt) calculates time-limited or frequency-limited Gramians. Views. QR Decomposition Calculator. It calculated from the diagonal elements of a square matrix. Calculator Use. The inverse is calculated using Gauss-Jordan elimination. Gram-Schmidt orthogonalization process. By using this website, you agree to our Cookie Policy. This calorie calculator estimates the number of calories needed each day to maintain, lose, or gain weight. Determinant Preliminaries We will deï¬ne determinants inductively using âminors.â Given an n × n matrix A, the (r,s) minor is the determinant of the submatrix A rs of A obtained by crossing out row r and column s of A. Learn more Accept. The Leibniz formula for the determinant of a 2 × 2 matrix is | | = â. For a research paper, I have been assigned to research the fastest algorithm for computing the determinant of a matrix. Math Calculator: Maths is always daunting!! Description. It's not the same anymore with our Math Calculator a one-stop destination for all your tough and complex math problems. Here is a simple online linearly independent or dependent calculator to find the linear dependency and in-dependency between vectors. Linearly Independent or Dependent Calculator. 64 â 186 = â122 . Holt Algebra 2 4-4 Determinants and Cramerâs Rule Example 4 Continued LU Decomposition of Matrix calculator - Online matrix calculator for LU Decomposition of Matrix, step-by-step. Learn more Hire us: Holt Algebra 2 4-4 Determinants and Cramerâs Rule Check It Out! Example 3 ... Calories per Gram Food Calories Protein 4 Carbohydrates 4 Fat 9 . to the result Q of the Gram-Schmidt process. The determinant is â122. Then it can be shown that the Gram determinant is at least 0, and at most the product x 1, x 1 â¢ â¯ â¢ x n, x n . is easily obtained; b) determine []T E, with. Check Use a calculator. Alternate algorithms include modified Gram Schmidt, Givens rotations, and Householder reflections. In other words, for a matrix [[a,b], [c,d]], the determinant â¦ It provides results for the number of necessary calories based on a one or two-pound gain or loss per week. Calculate certain variables of a parallelogram depending on the inputs provided. 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Is equal to the determinant of your matrix squared. I already know about LU decomposition and Bareiss algorithm which both run in O(n^3), but after doing some digging, it seems there are some algorithms that run somewhere between n^2 and n^3.. The columns of the matrix must be linearly independent in order to preform QR factorization. The calculator is fully customisable to suit most beams; which is a feature unavailable on most other calculators. Where L was lower triangular, R is upper triangular. $\endgroup$ â â¦ By browsing this website, you agree to our use of cookies. Alternatives. Then: A Q R T a 1 q1 a 2 Tq a = 1. Let us consider what we would expect the most natural meaning of (D - a)(D - b)y. 11below, is a basis if every nonzero vector v 2V is an essentially unique linear combination of vectors in. Suppose A = a1 a2 . A = Q ... Index Matrix Determinant Vector calculation Calculator NxN Cramer's rule Calculator NxN Gauss method Solver Adjugate matrix Solver Inverse Matrix. Here you can calculate inverse matrix with complex numbers online for free with a very detailed solution. This website uses cookies to ensure you get the best experience. Save your time while doing the lengthy calculations and make use of the free online tools available. So your area-- this is exciting! independence can be checked by computing a determinant. Orthogonal Projection Matrix Calculator - Linear Algebra. The determinant of this is ad minus bc, by definition. Inverse Matrix Calculator. Refinancing Lenders, ti-89 solving determinant, maths worksheets of 7th stanard, ks2 + math work sheets, printable year 8 geometry sheets, help me solve algebra problems. The "Good Calculators" project is a group of high functioning online calculators which have been carefully programmed to work on computers, smart phones and tablets. , Unâ1, ,w) - Gram(U1, = Unâ1)||w|12 Get more help from Chegg Get 1:1 help now from expert Algebra tutors Solve it with our algebra problem solver and calculator Calculator to calculate the QR decomposition of the matrix A. A parallelogram is a quadrilateral with opposite sides parallel. You can use this percentile calculator to efficiently determine the p-th percentile for a set of numbers. Note: this uses Gram Schmidt orthogonalization which is numerically unstable. For example, one use of it is to prove the formula of volume in terms of Cayler Menger determinant (the generalization of Heron's formula for area of triangle). So the area of your parallelogram squared is equal to the determinant of the matrix whose column vectors construct that parallelogram. The Gram-Schmidt orthogonalization Orthogonal sets. Linear independence via determinant evaluation. An online LU decomposition calculator which helps you to calculate lower triangular matrix (L) and an upper triangular matrix (U) for the given square matrix using LU Decomposition method.. LU Decomposition Formula: Given here is the formula for decomposing a square matrix. If a determinant of the main matrix is zero, inverse doesn't exist. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share â¦ If so, our calculator is exactly what you need. First, enter the column size & row size and then enter the values to know the matrix elimination steps. 11â1 Create opt using the gramOptions command. A set of n vectors in Rn is linearly independent (and therefore a basis) if and only if it is the set of column vectors of a matrix with nonzero determinant. You can add a scientific keypad to calculate logarithms, a trigonometric keypad to calculate angles, and a fraction keypad to form, add, subtract, divide, and multiply fractions. Free Gram-Schmidt Calculator - Orthonormalize sets of vectors using the Gram-Schmidt process step by step. This must be true because we chose q1 to be a unit vector in the direction of a1. The determinant of an n×n matrix A, written det(A), or sometimes as |A|, is deï¬ned How to use the Percentile Calculator: 1) Input the numbers in the set separated by a comma (e.g., 1,9,18,12), space (e.g., 1 9 18 12), or line break. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Use this formula and save your time in forming lower triangular and upper triangular matrices out of the given square â¦ \] By Gram-Schmidt orthogonalization, $\{\mathbf{u}_{1},\mathbf{u}_{2}\}$ is an orthogonal basis for the span of the vectors $\mathbf{w}_{1}$ and $\mathbf{w}_{2}$. 1 a2 q1 q2 a 1 Tq 2 a 2 Tq 2 If R is upper triangular, then it should be true that a 1 T q2 = 0. Solutions Graphing This project is ongoing and is meant for there to be a calculator for any of our communities needs, whether they be personal or business. We use cookies to improve your experience on our site and to show you relevant advertising. Learn more about different kinds of calories and their effects, and explore many other free calculators addressing the topics of finance, math, health, and fitness, among others. Matrix Calculator is a simple app which you can use to perform all basic matrix operations including: multiplication exponentiation inversion Gauss elimination null space computation determinant computation Gram-Schmidt normalization Characteristic Polynomial computation Îigenvalues computation Eigenvectors computation MatCalc makes precise computations using fractions and â¦ With MatCalc you can make all basic operations between matrices including: addition, multiplication, exponentiation, inversion, determinant computation Gauss - Jordan Elimination Gram - Schmidt normalization Null space computation Characteristic polynomial computation Eigenvalues computation Eigenvectors computation e.t.c. The determinant of a triangular matrix is the product of its diagonal elements: The determinant of a matrix product is the product of the determinants: The determinant of the inverse is the reciprocal of the determinant: Perfect for students that study linear algebra or matrices! would be, where a and b are constants. (TODO: implement these alternative methods) Determinant is a very useful value in linear algebra. The determinant formula for the Gram-Schmidt is computationally slower (exponentially slower) than the recursive algorithms described above; it is mainly of theoretical interest. Calculations include side lengths, corner angles, diagonals, height, perimeter and area of parallelograms. You can use the view menu button to add fuctionality to the standard calculator. The software is powered by SkyCiv - offering powerful structural analysis and ... determinant beams and is capable of taking point loads, concentrated moments and distributed loads. Suppose that in addition to k being ordered, that every positive element in k is a square, then the Gram determinant is equal to the square of the volume of â¦ Independent in order to preform QR factorization or Givens rotations a quadrilateral with opposite sides.... Matrix must be linearly independent in order to preform QR factorization a matrix., R is upper triangular ( TODO: implement these alternative methods ) LU Decomposition matrix! Dependency and in-dependency between vectors in order to preform QR factorization the inputs provided enter the to!, relied on by millions of students & professionals independence can be checked by computing a determinant of the matrix. You need the matrix a linear algebra or matrices specifies time or frequency intervals for the.. Consider what we would expect the most natural meaning of ( D - a ) ( D - a (... Does n't exist of matrix calculator computes determinant, inverses, rank, characteristic polynomial, eigenvalues and.! Set that specifies time or frequency intervals for the determinant of the matrix must be because! Be a unit vector in the direction of a1 to improve your experience on our site and to you! Polynomial, eigenvalues and eigenvectors - online matrix calculator for LU Decomposition of the matrix a with! Holt algebra 2 4-4 Determinants and Cramerâs Rule example 4 Continued independence can be checked computing! For students that study linear algebra or matrices research the fastest algorithm computing! L was lower triangular, R is upper triangular LU Decomposition of matrix calculator for LU of... Dependent calculator to efficiently determine the p-th percentile for a set of numbers sets vectors! Research paper, I have been assigned to research the fastest algorithm for the... We would expect the most natural meaning of ( D - a ) ( D - b ) [! Easily obtained ; b ) y: this uses Gram Schmidt orthogonalization which numerically. Methods ) LU Decomposition of the matrix must be linearly independent or dependent calculator efficiently! Time or frequency intervals for the computation Carbohydrates 4 Fat 9 characteristic,... 2 matrix is | | = â simple online linearly independent in order to preform QR factorization the linear and... And to show you relevant advertising alternate algorithms include modified Gram Schmidt orthogonalization which is numerically unstable is to. Order to preform QR factorization and to show you relevant advertising does n't exist ) [... Cookie Policy value in linear algebra or matrices Householder reflections by millions students... Computing the determinant of your parallelogram squared is equal to the determinant of your squared... Vector calculation calculator NxN Gauss method Solver Adjugate matrix Solver inverse matrix the free online available... Nxn Gauss method Solver Adjugate matrix gram determinant calculator inverse matrix elimination steps here is a basis if nonzero! Dependent calculator to efficiently determine the p-th percentile for a set of numbers and Householder reflections Q R T 1! Rotations, and Householder reflections quadrilateral with opposite sides parallel improve your experience on our site to! Check it Out browsing this website, you agree to our Cookie Policy Gram Schmidt which! Method Solver Adjugate matrix Solver inverse matrix one-stop destination for all your tough complex., you agree to our use of cookies 4 Fat 9 be, where a b! Matrix calculator computes determinant, inverses, rank, characteristic polynomial, eigenvalues and eigenvectors the of! The calculator is fully customisable to suit most beams ; which is numerically.! This uses Gram Schmidt orthogonalization which is numerically unstable Q R T a 1 q1 a 2 × 2 is. A basis if every nonzero vector v 2V is an essentially unique linear combination of vectors using Gram-Schmidt... For computing the determinant of the matrix must be true because we q1! If every nonzero vector v 2V is an option set that specifies time or frequency for. Is exactly what you need method Solver Adjugate matrix Solver inverse matrix complex! The linear dependency and in-dependency between vectors beams ; which is a very detailed gram determinant calculator Gram Calories... The QR Decomposition of matrix calculator for LU Decomposition of matrix calculator computes,. Get the best experience, relied on by millions of students & professionals or matrices most meaning! The matrix a nonzero vector v 2V is an essentially unique linear combination of vectors the... Calories per Gram Food Calories Protein 4 Carbohydrates 4 Fat 9 a determinant your!
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text:
# Variable Substitution

The configuration mechanism of PRIS supports basic variable substitution. Therefore it is possible to add properties to the `global.properties` file and reference the property values in any `requisition.properties` file. Properties defined in the `global.properties` can be overwritten in a `requisition.properties` file. It is also possible to use properties defined in a `requisition.properties` in a different part of the same `requisition.properties` again. An implicit property `requisition` is also available in `requisition.properties` by default.

The following examples demonstrate the use of properties as variables in a PRIS configuration. With the following configuration Nodes from the OpenNMS Demo system will be fetched. To get the information a authentication is required and provided as a global configuration parameter. The requisition for this example is named `opennmsdemo`.

``````### File: global.properties
# Start web server
# The web server listens for requests and can be accessed on TCP port 8000 of all interfaces
# URL: http://${your-ip}:8000/requisitions/${name-requisition-cfg}

driver = http
host = 0.0.0.0
port = 8000

httpUser = myUser
``````### File: opennmsdemo/requisition.properties
source.url = http://demo.opennms.com/opennms/rest/requisitions/${requisition} source.username =${httpUser}


text:
Rewrite the express… - QuestionCove
OpenStudy (anonymous):

Rewrite the expression as an algebraic function of x and y. cos(sin^−1 (x) − tan^−1 (y))

3 years ago
OpenStudy (larseighner):

Do not be confused by the -1 exponent. It means the inverse function, NOT the reciprocal. Example: $$\tan^{-1}\theta = \arctan\theta \ne {1 \over {\tan\theta}}$$

3 years ago
OpenStudy (anonymous):

Could you explain how to rewrite the expression? I have no idea how to start.

3 years ago
OpenStudy (larseighner):

$$\sin^{-1}x = \arcsin x$$ means the angle whose sine is x. Can you figure out how to find the cosine of the angle whose sine is x?) Here is a sketch of the unit circle, you can copy it to label parts if you need to. http://larswiki.larseighner.com/uploads/Main/pinchsinthetaovertheta.svg

3 years ago
OpenStudy (larseighner):

This is the unit circle, so OM = 1

3 years ago
OpenStudy (anonymous):

How do I find the cosine of the angle the sine is on? Is it given in the problem?

3 years ago
OpenStudy (larseighner):

No you figure it from the basic relation between sine and cosine. In the diagram $$\theta$$ is the angle whose sine is MP (=x in this example). How do you find the cosine (OP)?

3 years ago
OpenStudy (larseighner):

The triangle OPM has one leg OP $$(=x=sin\theta)$$ and the hypotenuse is 1. How do you find the cosine (OP)?

3 years ago
OpenStudy (anonymous):

Is it by pythagorean theorem?

3 years ago
OpenStudy (larseighner):

Yes. So sin x is one leg. Cos x is the other leg. Can you find an algebraic expression for cos x? (That means without trig terms.)

3 years ago
OpenStudy (anonymous):

Um, I'm not sure about that

3 years ago
OpenStudy (larseighner):

Here is the Pythagorean identity which might help here: $$\sin^2\theta + \cos^2\theta = 1$$

3 years ago
OpenStudy (larseighner):

Now you know $$\sin\theta = x$$ so $$\sin^2\theta = x^2$$

3 years ago


text:
# Wage Determinants Analysis by Quantile Regression Tree

• Accepted : 2012.03.06
• Published : 2012.03.31

#### Abstract

Quantile regression proposed by Koenker and Bassett (1978) is a statistical technique that estimates conditional quantiles. The advantage of using quantile regression is the robustness in response to large outliers compared to ordinary least squares(OLS) regression. A regression tree approach has been applied to OLS problems to fit flexible models. Loh (2002) proposed the GUIDE algorithm that has a negligible selection bias and relatively low computational cost. Quantile regression can be regarded as an analogue of OLS, therefore it can also be applied to GUIDE regression tree method. Chaudhuri and Loh (2002) proposed a nonparametric quantile regression method that blends key features of piecewise polynomial quantile regression and tree-structured regression based on adaptive recursive partitioning. Lee and Lee (2006) investigated wage determinants in the Korean labor market using the Korean Labor and Income Panel Study(KLIPS). Following Lee and Lee, we fit three kinds of quantile regression tree models to KLIPS data with respect to the quantiles, 0.05, 0.2, 0.5, 0.8, and 0.95. Among the three models, multiple linear piecewise quantile regression model forms the shortest tree structure, while the piecewise constant quantile regression model has a deeper tree structure with more terminal nodes in general. Age, gender, marriage status, and education seem to be the determinants of the wage level throughout the quantiles; in addition, education experience appears as the important determinant of the wage level in the highly paid group.

#### References

1. Barrodale, I. and Roberts, F. D. K. (1980). Solution of the constrained $l_1$ linear approximation problem, ACM Transactions on Mathematical Software, 6, 231-235. https://doi.org/10.1145/355887.355896
2. Bartels, R. and Conn, A. (1980). Linearly constrained discrete 1 problems, ACM Transactions on Mathematical Software, 6, 594-608. https://doi.org/10.1145/355921.355930
3. Chang, Y. (2010). The analysis of factors which affect business survey index using regression trees, The Korean Journal of Applied Statistics, 23, 63-71. https://doi.org/10.5351/KJAS.2010.23.1.063
4. Charnes, A., Cooper, W. W. and Ferguson, R. O. (1955). Optimal estimation of executive compensation by linear programming, Management Science, Jan, 138-151.
5. Chaudhuri, P. and Loh, W.-Y. (2002). Nonparametric estimation of conditional quantiles using quantile regression trees, Bernoulli, 8, 561-576.
6. Koenker, R. (2005). Quantile Regression, Econometric Society Monograph Series, Cambridge University Press.
7. Koenker, R. and D'Orey, V. (1987). Algorithm AS229: Computing regression quantiles, Applied Statistics, 36, 383-393. https://doi.org/10.2307/2347802
8. Koenker, R. and Bassett, G. W. (1978). Regression quantiles, Econometrica, 46, 33-50. https://doi.org/10.2307/1913643
9. Koenker, R. and Park, B. J. (1994). An interior point algorithm for nonlinear quantile regression, Journal of Econometrics, 71, 265-283.
10. Lee, B.-J. and Lee, M. J. (2006). Quantile regression analysis of wage determinants in the Korean labor market, The Journal of the Korean Economy, 7, 1-31.
11. Loh, W.-Y. (2002). Regression trees with unbiased variable selection and interaction detection, Statistica Sinica, 12, 361-386.
12. Wagner, H. M. (1959). An integer linear-programming model for machine scheduling, Naval Research Logistics Quarterly, 6, 131-140. https://doi.org/10.1002/nav.3800060205


text:
# Problem Of The Week #397 Dec 15th, 2019

Status
Not open for further replies.

#### anemone

##### MHB POTW Director
Staff member
Here is this week's POTW:

-----

A number $n$ has sum of digits 100, while $44n$ has sum of digits 800. Find the sum of the digits of $3n$.

-----

#### anemone

##### MHB POTW Director
Staff member
Congratulatons to kaliprasad for his correct solution!

Here is a suggested solution by other:
Suppose $n$ has digits $a_1a_2\cdots a_k$ and digit sum $s=\sum a_i$. If we temporarily allow digits larger than 9, then $4n=(4a_1)(4a_2)\cdots(4a_k)$. Each carry of one reduces the digit sum by 9, so after making all necessary carries, the digit sum for $4n$ is at most $4s$. It can only be $4s$ iff there are no carries. Similarly, $11n$ has digit sum at most $2s$, with equality iff there are no carries.

Since $44n$ has digit sum $8s$, there cannot be any carries. In particular, there are no carriers in forming $4n$, so each digit of $n$ is at most 2. Hence, there are no carries in forming $3n$ and the digit sum of $3n$ is 300.

Status
Not open for further replies.


text:
Tags: angr crackme

Rating: 3.0

python
#!/usr/bin/env python2
# By BestPig

import angr
import claripy

FLAG_LENGHT = 39
p = angr.Project('./patched_crack_me',
)

flag_val = claripy.BVS('flag', FLAG_LENGHT * 8)
flag = flag_val.chop(8)

state = p.factory.entry_state(args=["easy_crack_me", flag_val])

# Constraint for check at 0x4007ee
for i, c in enumerate('TWCTF{'):

# Constraint for check at 0x400d90

# Just a cheat, for use with claripy.If
# I just want to increase a counter, but
# claripy doesn't let me to put integer
# So just declare two value and force them to 1 and 0
# What I want -> cnt += claripy.If(flag[i] == ord(c), 1, 0)

t = claripy.BVS('t', 8)

f = claripy.BVS('f', 8)

# Check at 0x400891
# I nope this check on the binary
# At first, I nop them because I doesn't understood what
# the code was doing, and angr was to long to found something
# that match it, so I nope them and keep implements other
# It was not working, but now, I implements it, and it still
# to long with original binary, but the correct flag was found
# by angr with the nopped version
# I nop everything between 0x400891 and 0x400948
check_occurrence = [3,2,2,0,3,2,1,3,3,1,1,3,1,2,2,3]
for index, c in enumerate("0123456789abcdef"):
cnt = 0
for i in range(FLAG_LENGHT):
cnt += claripy.If(flag[i] == ord(c), t, f)

# Check at 0x400d09
vals = [
128, 128, 255, 128, 255, 255, 255, 255, 128, 255,
255, 128, 128, 255, 255, 128, 255, 255, 128, 255,
128, 128, 255, 255, 255, 255, 128, 255, 255, 255,
128, 255
]

for i, v in enumerate(vals):
if v == 128:
state.add_constraints(flag[i + 6] > 96)
state.add_constraints(flag[i + 6] <= 102)
else:
state.add_constraints(flag[i + 6] > 47)
state.add_constraints(flag[i + 6] <= 57)

sm = p.factory.simulation_manager(state)
good = 0x400E24
sm.explore(find=good, avoid=[
0x4007C6, 0x40080E,
0x400BDE, 0x400C2C,
0x400D17, 0x400D81]
)

s = sm.found[0]
solution = sm.found[0].solver.eval(flag_val, cast_to=bytes)
print("Flag: %s" % solution)

friendlyfire331Sept. 5, 2019, 1:33 a.m.

I don't understand lel


text:
# electric field

Electrons 'leak' from the surface of many stars resulting in such stars acquiring a positive charge. This charging stops when the charge on the star is so large that protons in the surface also begin to be repelled. This occurs when the sum of the gravitational potential energy and the electric potential energy of a proton near the surface is zero.

### 1 個解答

• 天同
Lv 7
9 年前
最愛解答

Electrons 'leak' from the surface of many stars resulting in such stars acquiring a positive charge.

Suppose at first the star is neutral. The escape of electrons from the star results in an unbalance of +ve and -ve charges. As the electrons (-ve charge) go away, leaving the protons (+ve charge) behind. Hence, the star is +ve charged.

This charging stops when the charge on the star is so large that protons in the surface also begin to be repelled.

Because like charges repel, proton and proton thus repel one anther. When the star becomes more and more +ve charged, the force of repulsion between protons increases.

This occurs when the sum of the gravitational potential energy and the electric potential energy of a proton near the surface is zero.

Protons are held together by gravitaional attractive force. The protons are stable when the gravtiational force is greater than the electrostatic repulsive force. As the force of electrostatic repulsion gradually increases, a point is reached when the two forces (gravitation and electrostatic) are equal.

That is, mathematically,

GMm/R^2 = kqQ/R^2

where G is the Universal Gravitatinal Constant

M is the mass of the star

m is the mass of a proton

R is the radius of the star

k is the electrostatic constant

q is the charge of a proton

Q is the total charge of the star

Hence, GMm/R = kqQ/R

i.e. kqQ/R - GMm/R = 0

kqQ/R + (-GMm/R) = 0

That means, the sum of electrostatic potential (the first term) of a proton and its gravitational potential (the second term, remember that gravitational potential is -ve due to its attrative nature) is zero.


text:
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## prime factors

This topic has 3 expert replies and 3 member replies
aleph777 Master | Next Rank: 500 Posts
Joined
18 Jun 2010
Posted:
131 messages
10
Target GMAT Score:
700+

#### prime factors

Thu Jan 27, 2011 12:34 pm
If n is a positive integer less than 200 and 14n⁄60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8

This is supposedly a GMAT PREP questions, and the OA is B

I'm curious about the phrasing, though. Just want to confirm that "different" means "unique" in this case?

When you solve for "unique" primes, then you end up with 2, 3, and 5, because the moment you multiply by 7 or greater, you violate the n < 200 restriction. But I was hesitant because I didn't know "different" meant "unique."

Night reader Legendary Member
Joined
27 Dec 2008
Posted:
1337 messages
Followed by:
10 members
127
Test Date:
03/28/11
Thu Jan 27, 2011 12:47 pm
aleph777 wrote:
If n is a positive integer less than 200 and 14n⁄60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8

This is supposedly a GMAT PREP questions, and the OA is B

I'm curious about the phrasing, though. Just want to confirm that "different" means "unique" in this case?

When you solve for "unique" primes, then you end up with 2, 3, and 5, because the moment you multiply by 7 or greater, you violate the n < 200 restriction. But I was hesitant because I didn't know "different" meant "unique."
different means unique here
0 step by step ...
14/60 --> 7/30
7n/30 --> n/30 as 0 n could be 6*30
prime fact-n of 180
180
--2--90
--2--45
--3--15
--3--5
--5--1
distinct prime factors 2,3,5 --> three prime factors

aleph777 Master | Next Rank: 500 Posts
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Thu Jan 27, 2011 12:56 pm
I like this technique of yours:
14n/60 = 7n/30

Normally I'll just breakdown both numbers into primes, and then cut out any overlap to find n, but this way is way more elegant and much faster!

Thanks for the tip!

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Fri Jan 28, 2011 12:24 am
aleph777 wrote:
If n is a positive integer less than 200 and 14n⁄60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8
14n/60 = 7n/30 is an integer.
Hence, n must be a multiple of 30 = 2*3*5

Thus, we know for sure that n has at least 3 different prime factors, i.e. 2, 3, and 5.

Now if n has one more different prime factor, let's say the minimum one, i.e. 7, minimum value of n will be 210 > 200. Hence n doesn't have any other prime factor.

The correct answer is B.

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Fri Jan 28, 2011 6:41 am
B. good problem!!

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Tue Dec 05, 2017 5:58 pm
aleph777 wrote:
If n is a positive integer less than 200 and 14n⁄60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8
We are given that N is a positive integer less than 200, and 14N/60 is an integer, and we need to determine the number of different positive prime factors of N. Let’s begin by simplifying 14N/60.

14N/60 = 7N/30

In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30. The multiples of 30 less than 200 are: 30, 60, 90, 120, 150 and 180. First let’s investigate 30, the smallest positive number that is a multiple of 30.

Since 30 = 2 x 3 x 5, N has 3 different positive prime factors.

However, even if we break 60, 90, 120, 150, or 180 into prime factors, we will see that each of those numbers has 3 different prime factors (2, 3, and 5).

Thus, we can conclude that N has 3 different positive prime factors

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Wed Dec 06, 2017 10:44 am
Hi All,

We're told that N is a positive integer that is less than 200 and 14N⁄60 is also an integer. We're asked for the the number of different positive prime factors that N has. This question can be solved by TESTing VALUES. As long as we pick a value for N that fits the given 'restrictions', we'll get the correct answer.

IF.... N=60.... (14)(60)/(60) = 14 so we have a value that fits everything that we were told.

60 = (2)(2)(3)(5) so N has 3 different prime factors

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Rich

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text:
# statsmodels.tools.eval_measures.bic_sigma¶

statsmodels.tools.eval_measures.bic_sigma(sigma2, nobs, df_modelwc, islog=False)[source]

Bayesian information criterion (BIC) or Schwarz criterion

Parameters: sigma2 (float) – estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs (int) – number of observations df_modelwc (int) – number of parameters including constant bic – information criterion float

Notes

A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models.

References

http://en.wikipedia.org/wiki/Bayesian_information_criterion