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# How does Knuth's algorithm for calculating logarithm work?

I had a look at Knuth's The Art of Computer Programming, book 1. In chapter 1, section 1.2.2, exercise 25, he presents the following algorithm for calculating logarithm:

given $x\in[1,2)$, do the following:

L1: [Initialize] Set $y\leftarrow0$, $z\leftarrow x/2$, $k\leftarrow1$.

L2: [Test for end] If $x=1$, stop.

L3: [Compare] If $x-z<1$, go to L5.

L4: [Reduce values] Set $x\leftarrow x-z$, $z\leftarrow x/2^k$, $y\leftarrow y+\log_b(2^k/(2^k-1))$, and go to L2.

L5: [Shift] Set $z\leftarrow z/2$, $k\leftarrow k+1$, and go to L2.

(The algorithm needs an auxiliary table which stores $\log_b2$, $\log_b(4/3)$, and so on, to as many values as the precision of the computer.

Then Knuth concludes: this exercise is to explain why the above algorithm will terminate and why it computes an approximation of $y=\log_b x$.

Well, I see that it works, but I am not able to explain why...

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Just to be clear, the result that you return is supposed to be the final value of $y$? –  Aaron Sep 3 '11 at 17:39
Yes, $y$ is the result. I'll make it clear. –  zar Sep 3 '11 at 19:06

The idea is that if we can express $x$ as a product $x=\prod a_i$, where the $1<a_{i+1}\leq a_{i}$, then $\log x = \sum \log a_i$, and if the $a_i$ decrease fast enough, then we can get a good approximation by taking partial sums, assuming that we have precomputed $\log a_i$.

Obviously, with such an algorithm, we very often will NOT terminate, and so we will have to stop when we are good enough. This is because if the $a_i$ are chosen from some countable set $B=\{b_i\}$, then only countably many numbers will have expressions as products of only finitely many $b_i$ (using repetitions). So step $L2$ needs to be modified to a condition like$|x-1|<\epsilon$, for some $\epsilon$ determining the accuracy.

So what does the algorithm do? At each stage, it starts with $x$, and finds the smallest $k$ such that $x-z=x(1-2^{-k})>1$, which is equivalent to $x>(1-2^{-k})^{-1}=\frac{2^k}{2^k-1}=a_i$. We then replace $x$ with $x/a_i$ and continue recursively, knowing that $\log x = \log a_i + \log x/a_i$.

In the end, we know that we will be off my a (multiplicative) factor of no more than $\log(1+\epsilon)\approx \epsilon$ (if $\epsilon$ is small, and we can use Taylor series to put explicit bounds on $\epsilon$ to make the error in this approximation as small as desired), and because of our assumption that $1\leq x <2$, this translates to an absolute error of at most $\log 2 \log (1+\epsilon) < 2\epsilon$.

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There is a note, in Knuth's explanation, that says: "The algorithm involves an intentional computational error in step L5, as $z$ is shifted to the right one place, so that eventually $x$ will be reduced to 1 and the algorithm will terminate". So it seems that the algorithm is correct, and it will terminate without corrections. Am I missing something? –  zar Sep 3 '11 at 22:23
@zar As far as I can see, the only way the algorithm will terminate as stated is if you assume that you are working with fixed precision. In this case, the difference between $x$ and $1$ will eventually be less than the level of precision. Even if you assume floating (where you only keep a certain number of significant digits), then because $x\approx 1$, you will still terminate (modulo problems with equality of floating numbers). However, if you assume arbitrary precision, the algorithm will usually not terminate as written. What assumptions does Knuth make about the mode of computation? –  Aaron Sep 3 '11 at 22:34
Knuth just says "suppose we have a binary computer". But he notes that $z$ is shifted to the right one place, thene $x$ will eventually reduced to 1. So I think he uses fixed precision (working at low level, with bit shifting). –  zar Sep 4 '11 at 8:49
@Aaron Sorry, Aaron, but I don't get the absolute value in $|x-1| < \epsilon$. Notice, in fact, that since $1 \leq x < 2$, $x-1$ will always be > 0. Moreover, where did you derive from that the multipicative factor left off in the computation is $\log(1+\epsilon)$, when you only know that $\log|x-1| < \log \epsilon$? –  Riccardo Del Monte May 31 '14 at 17:20
@Aaron Also, I think you should review your upper bound for the error made by the algorithm: you say that it is $\log2\log(1+\epsilon)$, but first I don't see how you came up with this simply starting from the fact that $1 \leq x < 2$, and, most importantly, I don't think I would disagree with my computer which tells me, with tons of tests, that the relation $\log x-\log'x < \log(1+\epsilon)$ is valid, while yours is not. By the way, keep in mind that I'm not still completely sure that $\log(1+\epsilon)$ is the actual upper bound of the error; I only see that the error is less than such value –  Riccardo Del Monte Jun 14 '14 at 19:29

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Next: 4.7 The Onion Model Up: 4. Mobility Modeling Previous: 4.5 Inversion Layer Mobility

Subsections

# 4.6 High-Field Mobility

Figure 4.8: Velocity saturation in Si.

With an increase in the applied lateral field, carriers gain energies above the ambient thermal energy and are able to transfer energy to the lattice by optical phonon emission. This effect leads to a saturation of the carrier velocity as shown in Fig. 4.8. To account for this velocity saturation, the mobility has to be reduced accordingly. Popular models including this basic feature are the Caughey and Thomas expression [Caughey67],

 (4.104)

and its modification [IuE04],

 (4.105)

Here denotes the low field mobility and the saturation velocity. The parameter influences the transition from low to high fields. Although (4.104) and (4.105) are applicable for a uniform field, they can be used for device simulations where the fields are non-uniform by making an appropriate choice of the lateral field. Different alternatives are available such as (a) the magnitude of the gradient of the quasi-fermi potential, (b) the component of electric field in the direction of current flow, and (c) the component of electric field parallel to the interface. Any of the definitions can be considered for device simulation purposes.

## 4.6.1 Analytical High Field Velocity Model

In general, the high field mobility is modeled differently for the drift-diffusion and the hydrodynamic transport model. In the former case mobility is modeled as a function of the driving force, whereas in the latter case a dependence on the carrier temperature is usually assumed. To describe nonlocal transport effects occurring in aggressively scaled devices a mobility model for the hydrodynamic framework would be desirable. Such a model could include a three-valley band structure and deal with arbitrary strain conditions. It would capture the essential physics of multi-valley transport under a spatially rapidly varying electric field profile. However, one problem is complexity. A nonlinear system of nine unknowns, namely the valley populations, valley velocities and valley temperatures, has to be solved numerically. The strain and carrier temperature dependence for each valley would require careful modeling in order to obtain realistic carrier temperatures and, consequently, realistic valley population. In the past, multi-valley transport models have also been devised for compound semiconductors [Hänsch91]. As a matter of fact, it seems that such multi-valley transport models with separate carrier gases for each valley have never found application in commercial or academic device simulators.

To find a trade-off between physical rigor and an acceptable level of model complexity we abstained from the multi-valley approach and pursued a more empirical approach, where analytical expressions for the velocity-field characteristics are directly fitted to bulk Monte Carlo data. The model is restricted to such strain conditions where only one pair of X-valleys is shifted and four valleys remain degenerate. These conditions include biaxial stress and uniaxial stress applied along the 100 axes of Si. Another condition resulting in a separation of the and valleys is uniaxial stress in the [110] direction. Equation (3.42) shows that the valley splitting depends only on the diagonal elements of the strain tensor. The proposed mobility model is thus applicable, if two diagonal elements are equal, .

To develop a clear understanding of the model, we have to consider three different coordinate systems.

1. The principal coordinate system has to be oriented such that the unit vectors , , and correspond to the [100], [010], and [001] crystallographic directions, respectively. In this system the -valleys are aligned along the [100] and [010] directions, whereas the - valleys are aligned along the [001] direction.

2. The unit vectors , , and constitute the device coordinate system. In this system the device geometry is defined. For performing device simulations it is essential to transform all transport parameters into this coordinate system.

3. A polar coordinate system is employed, comprising a unit vector along the field direction, , and two orthogonal vectors and . The polar axis is aligned with the [001] direction. In terms of the polar angle and the in-plane (azimuth) angle , the unit vectors are defined as follows.

 (4.106)

## 4.6.2 Parallel Velocity Model

Although (4.105) can describe the high field behavior in unstrained Si, it cannot produce the peculiarities of the velocity field relation in the strained case. Here the following expression has been suggested which can handle all types of velocity-field characteristics resulting from the Monte Carlo simulations performed [Dhar05a,Dhar06].

 (4.107)

Here denotes the low-field mobility in the field direction, obtained by projection of the low-field mobility tensor as . The last term incorporated in (4.107) models the velocity kink shown in Fig. 5.12. The relevance of the parameter is twofold: It accounts for the velocity plateau occurring approximately at and also signifies the small negative differential mobility occurring in strained Si for higher strain levels. The parameters and are fitting parameters.

All parameters depend on the strain-induced valley splitting, . The following empirical expressions were assumed.

 (4.108) (4.109) (4.110) (4.111) (4.112)

For all parameters except , a linear dependence was found to be sufficient. The parameter was modeled by the rational expression in (4.112). The parameters , , , , where , are constants for a particular field direction. We have chosen the three high symmetry directions [100], [110], and [001] and two additional directions [101] and [11]. These five sample directions form a spherical triangle on a unit sphere as shown in Fig. 4.9.

Figure 4.9: Spherical triangle with the five field directions chosen.

## 4.6.3 Perpendicular Velocity Model

For the cases where the field is not oriented along a high symmetry direction, it is observed that an electron velocity component perpendicular to the field direction develops. The component , although small for low stress levels, has a significant magnitude for intermediate field regimes and results in a total velocity different from the parallel velocity. For symmetry reasons, the velocity component in the direction vanishes for all five sample directions.

The perpendicular velocity component vanishes for fields along the [100], [110] and [001] directions. For the field directions [101] and [11], the normal velocity can be expressed in terms of and .

 (4.113)

After fitting , the component is fitted using an expression similar to (4.107)

 (4.114)

To ensure the correct low-field behavior, , the magnitude of the electric field in the first term in (4.107) has to be replaced by to obtain (4.114). The correct high-field limit is introduced by replacing in (4.107) by .

The total electron velocity vector for a fixed field direction is obtained by addition of the two components.

 (4.115)

where and are the unit vectors parallel and perpendicular to the field direction.

## 4.6.4 Total Velocity for Arbitrary Field Direction

The velocity-field characteristics can be extended to other field directions using a spherical harmonics interpolation.

 (4.116)

Here, is the function to be interpolated, denote the expansion coefficients and are the associated Legendre polynomials. From the symmetry properties and it follows that must be even and . Truncating (4.116) after the 4 order yields

 (4.117)

where . Evaluating (4.117) for the field directions [100], [110], [001], [101] and [11] gives

 (4.118) (4.119) (4.120) (4.121) (4.122)

To determine the four coefficients from the overdetermined system (4.118) to (4.122), we solve (4.118) to (4.120) exactly and minimize the error in (4.121) and (4.122), as shown in Appendix B.

 (4.123) (4.124) (4.125) (4.126)

## 4.6.5 Simplification to Two-Dimensional Simulation Domains

For two-dimensional simulation domains a simpler interpolation method can be used. In the following we consider the case that lies in the simulation domain, such that is fixed and only the variation of has to be considered. An alternative case would be a uniaxial stress orthogonal to the simulation domain, for example, in the width direction of a MOSFET. Then and varies.

In the first case the quantity can be interpolated using the following polynomial.

 (4.127)

Considering the special case of transport in the () plane (), we can write the equation system

 (4.128) (4.129) (4.130)

which gives the coefficients

 (4.131) (4.132)

Similarly, for transport in a ( ) plane ( ), we have

 (4.133) (4.134) (4.135)

giving

 (4.136) (4.137)

## 4.6.6 Implementation Issues

The present model has been derived for a uniform electric field . To apply it in a drift diffusion based device simulator, the electric field in the model has to be replaced by an appropriately defined driving force . Typical definitions of the driving force employed in practical devices simulators are the electric field component along the current density vector or the gradient of the quasi Fermi level.

For the two-dimensional cases described in Section 4.6.5, only one angle has to be determined. With the constant, two-dimensional vector denoting the [001] direction, one obtains for the polar angle

 (4.138)

The involved vectors are two-dimensional and specified in the device coordinate system.

The task of finding a tensor that relates two given vectors and by has no unique solution. In two dimensions, this vector equation denotes two scalar equations, whereas the 2 by 2 matrix has four unknown elements. The straightforward assumption of a diagonal matrix with diagonal elements and cannot be made, because this definition becomes singular whenever the driving force vector is parallel to the or axis.

To solve this problem one can probe the velocity vector for a second driving force vector. Using Cartesian coordinates, a vector orthogonal to can be easily found as . The four matrix elements can now be uniquely determined from the following two vector equations.

 (4.139) (4.140)

Implementation of a full tensorial mobility model in two dimensions would require the following quantities. We consider some edge of an unstructured mesh, connecting the nodes and . The unit vector along this edge is given by . A vector orthogonal to can be defined as . The box integration method requires the projection of the current density onto the edge, . For a mobility tensor with non-zero off-diagonal elements this current component becomes

 (4.141)

where denotes the carrier concentration at the mid point edge . This equation states that the current component along the edge is driven not only by the driving force component along the edge, , but also by the perpendicular component . The Scharfetter-Gummel scheme [Scharfetter69] gives a discrete representation of the component as a function of the variables at nodes and . The perpendicular component , however, cannot be determined from the variables at the two nodes. It can only be estimated by some kind of interpolation of the parallel components at neighboring edges. One possible extension of the Scharfetter-Gummel discretization has been proposed in [Egley93].

## 4.6.7 Discussion

The high-field velocity model presented has been derived for bulk Si. The model can consistently be used with the drift-diffusion transport model whenever the spatial variations of the potential are sufficiently smooth. However, even nowadays where gate lengths are in the deca-nanometer regime, drift-diffusion based simulations are still widely used to estimate transistor performance, despite the fact that this model cannot capture the strong non-local transport effects. The latter are usually accommodated by changing parameters, in particular by considerably increasing the saturation velocity. Also the high-field velocity model presented cannot include non-local effects, as it is based on populations of the band minima being functions of the local electric field. One should be aware that extending the local drift-diffusion equation with a local high-field velocity model cannot extend the limitation with respect to strongly non-local transport occurring in relevant technologies. Up-scaling the velocity by some technology-dependent parameter may still add some physics to the model, as a rough estimate of the direction-dependence of high-field transport.

Next: 4.7 The Onion Model Up: 4. Mobility Modeling Previous: 4.5 Inversion Layer Mobility

S. Dhar: Analytical Mobility Modeling for Strained Silicon-Based Devices


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# How does the cell membrane change over time?

Mar 27, 2017

The ratio of lipids and proteins in a cell membrane can change over time.

#### Explanation:

$\textcolor{red}{\text{The cellular membrane}}$
The main components of the cellular membrane are:
- phospholipids
- cholesterol
- proteins.

The currently accepted model of the cellular membrane is the fluid-mosaic model. This model states that membranes are very dynamic structures with different components. The lipids that make up the double layer of the membrane and the proteins they harbor can flow freely in the plane of the membrane.

$\textcolor{red}{\text{Changes over time}}$
The fluidity of the membrane also means that there is room for changes. The cellular membrane is crucial for the cell and has to be able to adapt to the circumstances

Some of the possibe changes:

• amount of cholesterol : cholesterol helps to maintain the fluidity of the membrane.
$\textcolor{red}{\text{Example}}$: when the temperature decreases, the concentration cholesterol increases

• the number of proteins : proteins in the cell membrane perform various functions, the need for these proteins can change.
$\textcolor{red}{\text{Example}}$: some proteins help to anchor the cells to their surroundings, when the cell needs to move/migrate there will be less of these proteins compared to when the cell needs to stay anchored.

• the type of protein: the cell membrane receives and transmits signals, different signals require different proteins. This can also change over time.
$\textcolor{red}{\text{Example}}$: immune cells need to be able to 'present' different antigens on the surface to initiate an immune response.

During the lifetime of a cell the proteins and lipids will be damaged by certain molecules in the body (reactive oxygen species, ROS). Due to this aging the membrane will lose some of its integrity.


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# A classical mechanics problem by Anik Mandal

Classical Mechanics Level 3

A point moves with uniform acceleration and $$v_1 , v_2$$ and $$v_3$$ denote the average velocities in three successive intervals of time $$t_1 , t_2$$ and $$t_3$$.Which of the following options is correct?

×


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# All file permissions changed to 755 -- not by me

#6

Check you .htaccess file and see if there is anything in it that forwards users to a domain unknown to you if the referrer is google et al…

#7

[quote=“LakeRat, post:6, topic:57034”]
Check you .htaccess file and see if there is anything in it that forwards users to a domain unknown to you if the referrer is google et al… [/quote]

Nope, it’s fine. Byte-for-byte identical to tarballed backup (which I’d already checked with a script that diff’ed everything, and found only differences I made myself and expected to find). But thanks for trying. Why can’t it be a dreamhost foul-up?

#8

It could be. On the surface the permissions changed to 755 sounds like one of the things that’s been happening lately in the rash of hacked sites. Also as a regular in this forum, I can’t recall a case where file permissions were changed magically by a dreamhost mistake.

The doorway in those cases is usually found to be some insecure theme or plugin someone installed because they think it’s perfect for their needs, but came from an untrusted source.

Support is usually pretty good about the answers they give, but they like anyone can make a mistake.

Also the last time shared server mothman showed up on dreamhoststatus was Sept 2nd, 2011 http://www.dreamhoststatus.com/2011/09/02/shared-server-mothman-being-transferred-to-new-hardware/

#9

All the mod times are the same? Or are they all original mod times? If someone chmoded everything, then all the mod times should be similar/same.

Assuming they are, find out who was logged in at that time with the last command. Failing that, check for that time in the logs to be sure nothing malicious was happening at that time.

Failing that, then it likely is a DH issue and should be addressed. In light of the lapses over the past few months / year, it would help if DH became a bit hyper-vigilant for a while re: security.

#10

Thanks, “bobocat” (sorry for calling you bobcat earlier:), that’s a good idea. I’ve already chmod’ed lots of stuff back, but enough remains so that ls -alct|less makes it clear everything happened 2012-02-15 23:00 (late this past Wednesday, way past lakerat’s 9/2/11), at which time it looks like only “omalonzo” and I were logged on. Kind of suggests I did it myself, but what easy-to-make typo would do that? I can understand an easy typo affecting one directory, e.g., you want rm abc.* but accidentally put a space between the dot and asterisk. But I can’t quite see an unnoticed typo sufficient to affect every directory and subdirectory above the pwd. Too many extra chars required to go unnoticed. But I’d actually feel much better if I stupidly did it myself, rather than a dreamhost mistake or external hack, either of which would represent ongoing and hard-to-calculate risks. So I’ll tentatively accept the “shot myself in the foot” theory unless some additional info suggests otherwise. Thanks, guys.

#11

Any clues from .bash_history?

#12

if you were logged in at that time, try this: history | grep chmod
see if there’s anything in there like chmod -R 755 * or something

#13

No luck guys – I’ve been doing a lot of typing since then, chmod’ing stuff back the way it’s supposed to be, and Wednesday’s history is long gone. Should have thought to look then, or at least saved a copy, but it hadn’t occurred to me I might be to blame.

And an interesting side note that just maybe I’m not to blame… I have two public cgi’s that let people put math expressions in html using img tags, e.g., to see one of them, click http://www.forkosh.com/mathtex.cgi?\frac1{\sqrt{a^2+b^2}} New images are cached, and those two cache directories have 100,000 and 300,000 images, respectively, in them. All cached images created prior to 2012-02-15 23:00 were chmod’ed 755 at that time, and all created afterwards are 644 like they’re supposed to be. But trying to chmod them all back to 644, just gives “Argument list too long” when bash tries to expand the asterisk. So, arguably, I couldn’t have done it myself from the shell. And I’d definitely have noticed if anything I typed tried to do it. So it’s still somewhat of a mystery (at least to me).

#14

interesting. not definitive, but interesting. they could all be chmoded with the find command, or xargs, without giving an error. you’d have to really mess up to do that by accident though. i have a hard time doing it on purpose on the first go!

I think the new/old files might be a red herring though. i’m a not completely sure, but I don’t think chmod changes the umask, so while all files may have had their perms changed, that doesn’t mean new ones won’t have those some perms if the umask is set. I think that’s how it works…

Anyway, one peculiar thing is the time. The odds of mistyping and chmoding everything exactly on the hour is slim. Seems like something a cronjob would do… You don’t have a cronjob set that only runs once a year on Feb 15 @ 2300 do you? Or some long enough time that you would have forgotten the last time it ran?

#15

Yes – somebody else’s (with root privileges) runaway cron job; that’s my new best (and only) guess. Very astute of you to interpret the time that way (I’d noticed it but hadn’t made anything of it). I have no cron jobs of my own, and occasionally do use find to actually find files, but never to -exec anything. So, like you said, I’d have had to “really mess up” to accidentally do anything with the observed effect, which is why I didn’t feel your earlier chmod -R conjecture was very likely. Does dreamhost have any reason to go around chmod’ing bunches of files, like maybe under logs/, and maybe messed up somehow? Do they routinely run any kind of jobs at 11:00pm PST?

#16

You were logged in at that time, though, right? So we can’t rule that out, especially if the IP address at that time belongs to you.

I don’t think DH’s cronjobs work on the user’s dir because all the logs are actually links to files in another dir. I guess they could do something like that in an emergency if an attack left a bunch of files as 777, but I would hope that they would do that conditionally, not touching files that had not been attacked. Again, though, it’s just speculation.

Going with Occam’s razor, if you were logged in at the time of the change, I think the likelihood is that somehow it’s connected to something you or one of your apps did. Given the time, it could have been an automated process. For example, I know wordpress sets up its own cronjobs. If you have something like that running in the same user, a rouge plugin could have chmoded everything for that user.

Any plugins or the like which could have done it?

#17

Yes, I was logged in at that time, so have to agree (especially since nobody else has replied to report a similar experience) the circumstantial evidence best suggests me. I want my lawyer. And it almost certainly looks like me logged on – I have verizon dsl and, from last, whois 98.109.229.53 is verizon’s (and my modem’s currently assigned 98.109.234.92).

But, no, don’t have wordpress or any third-party plugins or any automated processes. I do have various of my own cgi’s that are documented online and intentionally publicly accessible, but they know nothing about chmod-like stuff. And umask, from your earlier reply, doesn’t seem to be any kind of issue, either, as far as I can tell. And assuming no typo within reason would have that effect, I just see no conceivable way it happened. Hence the quandary: must be me, can’t be me. I’m stumped.[hr]

Most suspicious thing I could find was a core file from one of my cgi’s (but timestamped 2012-02-16 14:28, apparently after the incident). From it I gathered REMOTE_ADDR=94.142.134.155, apparently someplace in Latvia. So I added a deny from 94.142.134. but have no idea what, if any, good that might do.

#18

It’s an interesting puzzle though. Obviously you are the type of person who knows what he’s doing, so the odds of this sort of massive mistake are slim. The odds of DH making a mistake… well, let’s not think about that too much but in general I’d say the odds are low.

I assume you’ve checked the logs for that time period? Was there any unusual activity? One possible solution may be that one of your scripts has a heretofore unknown bug which has somehow been exploited? Your diff shows there are no new files or changes, so perhaps the exploit is only minimally useful? Of course, chmoding to 777 would have been more useful if it was due to an exploit…

hmmm…

#19

I checked the logs as best I could, within reason. Those math rendering cgi’s get lots of hits. Within last seven days, including problem period, Successful requests: 4,030,448 (1,653,242), Distinct files requested: 209,669 (47,995), Distinct hosts served: 128,787 (7,825), etc. Needle in ha(ysta)ck.

#20

a little awk magic might help. it should be around the chmod time, and I would guess it’s going to be a crafted set of parameters in the url if it happened that way. You could get i list of unique request for the hour before and after:

gunzip -c ~/logs/WWW.DOMAIN.COM/http/access.log.2012-02-15 | awk '$4~/15\/Feb\/2012:2[23]/{a[$7]++}END{for (i in a) {print i}}'

#21

gunzip -c ~/logs/WWW.DOMAIN.COM/http/access.log.2012-02-15
| awk ‘$4~/15/Feb/2012:2[23]/{a[$7]++}END{for (i in a) {print i}}’

That proved much more useful than my messing around. Actually, I was surprised to find .2012-02-15 since I only keep default 3 days, but it was there so I copied it for safekeeping. Your awk emitted 11,338 lines for that time range. I grep -v’ed it for mathtex and mimetex (the two math cgi’s), which boiled it down to … 54 lines.

What really stands out is that I had a long-forgotten phpBB2 bulletin board for people with questions about those math cgi’s, but disabled it (rm’d the posting and registration scripts) several years ago, after spammers starting relentlessly registering and posting garbage (somehow they got past the gif image with mangled letters they have to enter before registering). But I left the bb there for reading so I could point people sending me email questions to already-written answers.

And included among those remaining 54 lines are
/phpBB2/posting.php?mode=newtopic&f=2&sid=959d73b7b03903c6030f7cdaa13450e8
/viewforum.php?f=2&sid=959d73b7b03903c6030f7cdaa13450e8
/posting.php?mode=newtopic&f=2&sid=959d73b7b03903c6030f7cdaa13450e8
/phpBB2/viewforum.php?f=2

posting shouldn’t even be there. Anyway, I tarballed the entire directory tree and rm r-'ed it.
I also grepped the original log for that sid=, finding six strings of the form

1.161.141.231 - - [15/Feb/2012:22:36:13 -0800] “GET /posting.php?mode=newtopic&f=2&sid=959d73b7b03903c6030f7cdaa13450e8 HTTP/1.0” 404 420 “http://www.forkosh.com/posting.php?mode=newtopic&f=2&sid=959d73b7b03903c6030f7cdaa13450e8” “Mozilla/4.0 (compatible; MSIE 5.5; Windows NT 5.0; .NET CLR 1.1.4322)”

That 404 suggests to me he got nowhere, but I don’t know enough to be completely sure about much of anything regarding this kind of stuff. I added 1.161.141. (apparently some asia-pacific company, Chunghwa Telecom) to .htaccess for good measure. Can’t think of anything else to do about it, assuming it was even anything malicious in the first place.

#22

Well, there’s suspicious activity in a php-based app that may be outdated (you didn’t mention that). Given that the time is close, I would suspect maybe there was an exploit around that time. I would look very carefully at the logs around 23:00 and see what you can dig up. And at minimum, update that app and lock it down!

It’s been an interesting search… good to hone the skills a bit

ps: 4m hits per week? 300k+ inodes. On a shared server!? Your site would never work on most other shared hosts I’ve looked at. DH’s generous resource limits, especially for highly efficient sites as yours appears to be, is what keeps me here.

pps: all your images are giving errors now… red boxes with error message #10 or something

#23

Yeah, I’ve rm -r’ed the entire app. I’d forgotten all about it, despite that its home directory must have scrolled past my eyes many times. And some other guy (some russian ip)…
95.182.40.147 - - [15/Feb/2012:23:00:07 -0800] “POST /phpBB3/includes/index.php HTTP/1.1” 200 4040 “http://forkosh.com/phpBB2/includes/index.php” “Opera/9.80 (Windows NT 6.1; U; ru) Presto/2.10.229 Version/11.61”
…was messing with it at exactly 23:00. The 200 for index.php was expected and presumably benign. But, in any case, the app’s gone for good, now. And so’s 95.182.

DH’s limits are indeed generous. I moved the site from my new york city isp, panix.com, whose limits are way insufficient. (I still forward email there, though, since their shell email and procmail filtering provide much better control.) By the way, for the record, note that my cgi’s are totally free, and the source is all gpl’ed – I don’t make any money off anything I have on the web (except, hopefully, my resume:).

Thanks for the heads-up about those errors. Fixed now. Somehow the cache directory itself had been chmod’ed 644. I wonder if that was a side effect of when I tried chmod 644 * from >>inside<< the directory, and bash complained that it couldn’t expand the *. Maybe there’s some weird bug with that side effect when it fails like that.

#24

[quote=“forkosh, post:23, topic:57034”]And some other guy (some russian ip)…
95.182.40.147 - - [15/Feb/2012:23:00:07 -0800] “POST /phpBB3/includes/index.php HTTP/1.1” 200 4040 “http://forkosh.com/phpBB2/includes/index.php” “Opera/9.80 (Windows NT 6.1; U; ru) Presto/2.10.229 Version/11.61”
…was messing with it at exactly 23:00. The 200 for index.php was expected and presumably benign. [/quote]

I was curious why a file named index.php would be requested from a directory named “includes” as the convention is that files that are included would not be requested by a web browser. In the latest version of phpBB there is no index.php in that directory - a blank index.htm is found instead.

If I were you I would check the /phpBB3/includes/index.php file for backdoor code that might have been added to it. The fact that the status code is 200 simply means the web server had no problems with the request; it says nothing about whether or not such request was malicious in nature and it should not be presumed to be benign without considering why this file would be requested and what code would be executed. Any files being requested that should not be are a red flag.

#25

[quote=“Atropos7, post:24, topic:57034”]I was curious why a file named index.php …[/quote] The entire phpBB directory, and all subdirectories, have been rm -r’ed, and I even deleted the associated mysql databases from the “panel”. I think that particular problem’s probably all gone. I hadn’t been using that application in years, anyway.

I forgot to separately thank you for all the help tracking down this … whatever it is/was/will-be. Assuming, of course, it has been tracked down; who knows?. And assuming it was a hack by that 95.182.40.147 guy, is there a list anywhere of ip addresses that dreamhost users have already found annoying? I added deny from 95.182. to .htaccess after the fact, but would have preemptively done that had I had a n earlier clue.


text:
College Algebra (6th Edition)

$\{a,c,d,e,f,h\}$
Combine the two sets into one set without repeating any terms in it. $\{a,c,d,e\}$ union $\{c,d,f,h\}$ $\{a,c,d,e,f,h\}$


text:
# circumcenter

Circumcenter of triangle or tetrahedron

## Syntax

``C = circumcenter(TR)``
``C = circumcenter(TR,ID)``
``[C,r] = circumcenter(___)``

## Description

example

````C = circumcenter(TR)` returns the coordinates of the circumcenters for each triangle or tetrahedron in the triangulation `TR`.```

example

````C = circumcenter(TR,ID)` returns the coordinates of the circumcenters for the triangles or tetrahedra indexed by `ID`. The identification numbers of the triangles or tetrahedra in `TR` are the corresponding row numbers of the property `TR.ConnectivityList`.```

example

````[C,r] = circumcenter(___)` also returns the radii of the circumscribed circles or spheres in `TR` for either of the previous syntaxes.```

## Examples

collapse all

Load 2-D triangulation data and create a triangulation representation.

```load trimesh2d TR = triangulation(tri,x,y);```

Compute the circumcenters of each triangle in `TR`.

`C = circumcenter(TR);`

Plot the triangulation along with the circumcenters in red. The $x$-coordinates of the circumcenters are contained in the first column of `C` and the corresponding $y$-coordinates are contained in the second column.

```triplot(TR) axis([-100 400 -50 350]) hold on plot(C(:,1),C(:,2),'r.') hold off```

Create a Delaunay triangulation for a set of points.

```rng default; P = rand(10,3); TR = delaunayTriangulation(P);```

Compute the circumcenters of the first five tetrahedra in `TR`, and the radii of their circumscribed spheres.

`[C,r] = circumcenter(TR,[1:5]')`
```C = 5×3 13.2189 -2.3004 -0.4970 -0.4884 0.6741 -0.1140 0.3089 0.1067 -0.3349 0.2805 0.7532 0.5855 0.8514 2.1609 0.9824 ```
```r = 5×1 12.6978 1.1775 1.1135 0.3670 1.4112 ```

## Input Arguments

collapse all

Triangulation representation, specified as a scalar `triangulation` or `delaunayTriangulation` object.

Data Types: `triangulation` | `delaunayTriangulation`

Triangle or tetrahedron identification, specified as a scalar or a column vector whose elements each correspond to a single triangle or tetrahedron in the triangulation object. The identification number of each triangle or tetrahedron is the corresponding row number of the `ConnectivityList` property.

Data Types: `double`

## Output Arguments

collapse all

Circumcenters of triangles or tetrahedra, returned as a two-column matrix for 2-D coordinates or a three-column matrix for 3-D coordinates.

Data Types: `double`

Radii of the circumscribed circles or spheres, returned as a scalar or vector.

Data Types: `double`


text:
## 1. Introduction

Dialogue is a species of joint activity during which two or more people collaborate to make themselves understood to one another. While dialogue can be studied in its own right, it is often produced in the context of other joint activities, which it serves to coordinate (Bangerter & Clark, 2003; Clark, 1996; Gambi & Pickering, 2011). For example, participants may engage in dialogue to reach a common goal such as planning a trip, or deciding on how to move a bench. The fundamental unit of dialogue is a contribution (Clark & Wilkes-Gibbs, 1986; Clark & Schaefer, 1989; Clark & Brennan, 1991), which is composed of two phases, a presentation phase and an acceptance phase. In the presentation phase, a speaker produces an utterance. During the acceptance phase, the addressee either accepts the utterance as understood well enough for current purposes, for instance by saying okay or by nodding, or initiates a repair sequence (Drew, 1997), during which both partners attempt to determine what the meaning of the initial presentation was. Contributions to dialogue become part of participants’ common ground, or mutual knowledge (Brown-Schmidt, 2012; Clark, 1996; Clark & Marshall, 1981). As successive contributions to dialogue accumulate, then, participants’ common ground base is enlarged, and it becomes easier to engage in subsequent dialogue. This is most notably evidenced in a process called lexical entrainment (Garrod & Anderson, 1987; Van der Wege, 2009), whereby interaction partners progressively come to use the same words to refer to recurrent objects (e.g., tools in a manual task or patients in a hospital). On some accounts, lexical entrainment occurs because participants infer from their common ground that their current partner is capable of understanding these words. Lexical entrainment is a key phenomenon used to support prominent models of dialogue, although in different ways. In the interactive alignment model (Pickering & Garrod, 2004), it is evidence for priming mechanisms that serve to align representations of conversational partners. In the grounding model (Clark & Brennan, 1991), it corresponds to the establishment of conceptual pacts: Partners negotiate conventional agreements about how to refer to recurrent objects in a task. These conventions are normative; partners are expected to continue to use them, even when they may be overly informative in a novel context (Brennan & Clark, 1996).

Lexical entrainment has mainly been examined in experiments involving the matching task (or some kind of variation of it, e.g., Clark & Wilkes-Gibbs, 1986; Horton & Gerrig, 2005; Hupet, Seron, & Chantraine, 1991; Knutsen, Ros, & Le Bigot, 2018; Krauss & Weinheimer, 1966; Schober & Clark, 1989; Swets, Jacovina, & Gerrig, 2013; Tolins, Zeamer, & Fox Tree, 2018; Yoon & Brown-Schmidt, 2014). In this task, one participant (the Director) describes pictures (often abstract humanoid figures) to another participant (the Matcher), enabling the latter to rearrange these pictures in a predefined order. The task is repeated several times; the participants use the same set of pictures (in a different order) on each trial. Over trials, participants become more efficient, as the number of words and turns necessary to complete the task is reduced. This finding has been attributed to the participants negotiating conceptual pacts (i.e., specific labels to refer to the figures, such as the guy in the boat) in initial trials, thereby reducing the need for explicit negotiation in subsequent trials.

## 2. The Development of Procedural Coordination in the Matching Task

Mills (2014, p. 159) suggested that “experimental approaches that do study the emergence of conventions in dialogue typically restrict their analyses to the study of referring conventions, also eschewing analysis of how the interactive routines that yield these referring conventions are established and sustained”. He proposed (p. 158) that coordination in dialogue involves both “semantic coordination of referring expressions” and “procedural coordination of the timing and sequencing of contributions”. Procedural coordination develops via a similar conventionalization process as semantic coordination, but participants progressively converge on routines with complementary role structures (i.e., adjacency pairs, Schegloff, 2007). Building on Mills (2014), we distinguish two kinds of procedural coordination, specific and generic.

Specific procedural coordination concerns the efforts participants need to deploy to fulfill the requirements of a particular task. A case of specific coordination is Mills’ (2014) analysis of a dyadic maze game. Participants progressed through three stages of increasing coordination. First, they overtly negotiated complementary roles (e.g., you do X and I do Y) to create basic couplings of their actions. Then, they developed a finer-grained sense of the activity and established the sequential junctures (Schegloff, 2007) where particular contributions were relevant. Finally, there emerged a contracted set of often idiosyncratic terms to refer to particular moves in the task, also with particular instrumental actions (e.g., opening a gate in the maze) acquiring a communicative meaning. In the similar Map task setting, Doherty-Sneddon and colleagues (1997) described various procedural routines or “games” that participants could use to complete the task. More generally, procedural coordination routines emerge in a context-specific way whenever recurrent joint actions are performed (Fusaroli, Rączaszek-Leonardi, & Tylén, 2014). A primary site for this concerns work in organizations (Malone & Crowston, 1990). Recurrent work tasks in organizations are typically prepackaged via coordination mechanisms like plans and rules, physical objects, roles that enable division of labor, or physical proximity (Okhuysen & Bechky, 2009). This leads to a highly specialized system geared towards optimal performance. For example, pit stop crews in Formula One racing use dedicated equipment (e.g., signaling boards, pneumatic wrenches) and roles (e.g., tire changers, jack men, the lollipop man) to consistently attain top performance (i.e., completing refueling and tire change within seconds) within a complex, institutionalized task environment.

Beyond specific coordination germane to a particular task, however, any kind of joint action poses similar basic coordination problems; these problems are addressed by dialogue partners through generic procedural coordination. Because human beings have been coordinating joint action for a long time, language use has evolved to serve coordination (Clark, 1996; Levinson, 2006; Smith, 2010; Tomasello, 2008). As a result, natural languages provide users with procedures and conventional solutions for coordinating joint action. The turn-taking system (Holler, Kendrick, Casillas, & Levinson, 2015), for example, is a set of procedures for solving the problem of who is to speak when, i.e., avoiding too-long gaps in the floor, as well as overlap between speakers (Sacks, Schegloff, & Jefferson, 1974). Another example is the existence of universal procedures for repairing the ubiquitous problem of misunderstandings in conversation, as evidenced by the word huh which is used as an open-class repair initiator (Drew, 1997) in multiple languages (Dingemanse, Torreira, & Enfield, 2013). A further example relevant for the current analysis of the matching task is how discourse markers like oh, and, but, so or well or acknowledgment tokens like uh-huh, mhm, yeah, right, okay and all right form a conventional system of contrasts for signaling transitions within and between parts of an action structure (Bangerter & Clark, 2003; Schiffrin, 1987). Participants tend to produce okay and all right to signal transitions between large action units (i.e., to open and close actions), whereas they tend to use mhm, uh-huh or yeah to punctuate transitions from one step to the next within an action unit. Participants engaged in the matching task tend to use okay less and less often to mark the end of card description and placement sequences as they repeat the task. As their common ground accumulates and identifying cards becomes easier, the placement of each card becomes more and more like a brief step in an action sequence rather than an action in itself (Bangerter & Clark, 2003). Acknowledgment tokens used as signals of transitions from one task step to the next constitute efficient ways to solve a fundamental problem in all joint activities, namely coordinating progress.

To summarize, specific and generic procedural coordination likely constitute important demands on participants’ conversation in joint action. Currently, however, little research has been undertaken in order to understand the unique contribution of procedural coordination to reducing collaborative effort in dialogue, separate from that of semantic coordination (Clark & Wilkes-Gibbs, 1986). What is more, to our knowledge, the distinction between generic and specific procedural coordination has not yet been explored in the matching task.

## 3. This Study: Procedural Coordination in the Matching Task

With this study, we make three contributions to the literature on collaborative referring using the matching task. The first contribution is to quantify the amount of communication dedicated to procedural coordination. Given the ubiquity of the matching task in research on collaborative referring, it is important to attribute communication to the correct coordination demands, especially given that previous analyses have tended to implicitly assume that communication is exclusively dedicated to semantic coordination (but see Mills, 2014). The second contribution is to establish and explore a conceptual distinction between (task-) specific and generic forms of procedural coordination, and to quantify the relative amounts of communication dedicated to each of them. The third contribution is to explore the relation between procedural and semantic coordination in the matching task, that is, whether procedural and semantic coordination are independent from each other, or linked to each other. For example, if semantic coordination becomes more difficult, will this affect procedural coordination as well?

Because participants in the classic version of the matching task quickly converge on conceptual pacts, the development of procedural coordination is inescapably confounded with increasing semantic coordination. Investigating this third issue thus requires a dataset where semantic coordination can be varied systematically. We used a matching task corpus (transcripts from Experiment 1, Bangerter et al., in preparation) where participants completed the task in either of two conditions: The classic (or control) condition, where cards did not change over trials, and new cards condition, where they placed a new set of cards on each trial. In the new cards condition, participants are not able to establish conceptual pacts about recurring objects of reference. In other words, unlike in the classic condition, it is difficult to achieve semantic common ground, despite them being able to achieve procedural common ground (as they perform the same task in each trial). Bangerter et al. (in preparation) found that, although lexical diversity decreased somewhat over trials in the new cards condition, collaborative effort did not. Thus, the new cards condition offers an opportunity to compare procedural coordination development in two situations of differing difficulty of semantic coordination, and thus whether semantic and procedural coordination are independent from each other.

We operationalized four aspects of procedural coordination. First, (task-) specific procedural coordination was communication relative to placing the cards (hereafter card placement or CP). The experimental instructions required placing eight cards in a grid with two rows and four columns. Card placement thus involves agreeing on the order in which to proceed, or once this has been achieved, mentioning a card’s place. We operationalized generic procedural coordination as communication relative to progress within the task that would be similar in any kind of joint task. Generic procedural coordination has two sub-aspects. One is explicit generic coordination (EGC), i.e., queries and answers about whether both partners are ready to move on. The other is implicit generic coordination (IGC), involving the various acknowledgment tokens used to mark transitions from one step of the task to the next (Bangerter & Clark, 2003; by implicit we mean that the words used do not explicitly topicalize progress in the task). Each of these three forms of coordination can be produced in a discussion about a particular figure, and we thus coded the extent they were manifested in the participants’ talk. However, a fourth aspect concerns the fact that participants can also discuss coordination requirements in a general manner that is independent of a specific figure, e.g., they may discuss how to do the task in general. We also coded this fourth aspect (hereafter referred to as general procedural coordination, or GPC).

Procedural coordination involves the development of complementary roles (Mills, 2014). In the matching task, Directors and Matchers make different contributions to semantic coordination according to their roles (Clark & Wilkes-Gibbs, 1986). If they do so in procedural coordination as well, this may entail their making particular contributions more or less frequently. For example, Directors may be in a better position to discuss card placement, whereas Matchers may naturally communicate about whether they are ready to move on to the next card. For all analyses, we therefore distinguished between contributions made by Directors and by Matchers.

## 4. Method

### 4.1. Participants

Participants (N = 44 native French speakers, 25 women) were recruited from the student body of a Swiss university. They completed the experiment in dyads in exchange for compensation of 10 CHF each. They were scheduled to arrive together, and were randomly allocated to either the director or matcher role. Dyads were randomly allocated to either the classic condition or the new cards condition. As we expected more variance in the new cards condition, 14 dyads were allocated to it, whereas 8 dyads were allocated to the classic condition.

### 4.2. Procedure and materials

Participants read and signed informed consent forms upon arriving in the lab. They then arranged a set of eight cards depicting humanoid tangram shapes as used in other matching task experiments. These were displayed to participants on a computer screen in two rows of four columns using a program we developed in Flash (Action Script). While the directors’ view included cards already in placement slots, matchers saw their placement slots displayed above the cards. They moved cards to the slots by clicking and dragging them. Directors’ cards could not be moved. When they were done with a trial, they each pressed a blue button on their screen to move on to the next trial. Participants first completed a practice trial where they placed eight cards depicting everyday objects (e.g., sneakers), so that they could familiarize themselves with the task in both conditions. Then, in the main experiment, for 5 trials, they placed eight cards with tangram figures (the same set for both of them but in a different order). The main experiment used a pool of 40 different tangram figures. In the classic condition, participants arranged the same set of cards on each trial (cards were drawn randomly from the pool and the order of the cards was randomized at each trial). In the new cards condition, eight cards were drawn without replacement from the pool on each trial. After having completed the task, participants were debriefed, paid, and dismissed.

### 4.3. Experimental design and dependent variables

There were three main independent variables (IVs) in this study. The first one was condition, which had two levels (between-subjects): classic and new cards. The second was trial number (five levels; within-subjects). Both linear and quadratic trends of trial number were tested (both were centered to simplify the interpretation of the results). We included quadratic trends to be able to detect nonlinear phenomena (e.g., a particular coordination variable decreases over trials but then increases again at the end of the experiment), which are quite common in matching task data (e.g., Clark & Wilkes-Gibbs, 1986). The third independent variable was participant role (within-subjects), which had two levels: Director and Matcher.

Four dependent variables (DVs) were examined, each measuring a specific aspect of procedural coordination. The first DV was whether or not the participant used card placement (CP) talk (e.g., that one goes on the first row or it’s the second card) while discussing tangram figures during a trial. The second DV was whether or not the participant used implicit generic coordination (IGC) while discussing each tangram figure during a trial. This was defined as being largely analogous to the project markers investigated by Bangerter and Clark (2003), but included a wider range of words participants used to ground instructions and more generally mark progress in the task. Frequent examples (in French) include ouais, okay, mhm, alors, bon, donc, d’accord exactement, cool, or parfait. The third DV was whether or not the participant used explicit generic coordination (EGC), i.e., explicitly talked about progress while discussing a tangram figure. This category includes phrases like shall we start?, got it, I see it, or are you finished? It also includes single-word utterances explicitly related to coordination progress, e.g., then or next. Finally, it also includes elements of repair sequences relative to figure descriptions like I don’t understand or want me to repeat? For these three DVs, we coded the number of words used in talk about each tangram figure. The fourth DV was general procedural coordination (GPC), defined as procedural coordination of any of the above types that was not relative to a specific figure. Examples include suggestions about how to proceed in general (now second row or I think it’s easier if you tell me) or coordinating the end of the trial, after having placed the last card (blue button?, are we done?). Contrary to the three other DVs, we coded the number of words at the trial level rather than at the figure level.

To check interrater agreement, we double-coded data on CP, IGC and EGC from two dyads (one in each condition), and computed the correlations between the number of words coded by each coder for each turn (n = 422 turns). Because our primary measures (i.e., before transformation) are ratio-scale variables coded by two coders, we computed correlation coefficients as a measure of interrater agreement. Interrater agreement was generally high (r = .68 for CP, r = .97 for IGC, r = .87 for EGC, all ps < .001) Disagreements were resolved by discussion. A dialogue example illustrating how talk corresponds to the four aspects of procedural coordination is provided in Table 1.

Table 1

Dialogue Example Illustrating Card Placement Coordination, Implicit Generic Coordination, Explicit Generic Coordination and General Procedural Coordination.

Role Talk English translation CP IGC EGC GPC

M Ensuite j’en ai un qui est courbé ? Next I have one that’s bent over? Next
D Qui est courbé il est troisième, ligne en haut. That’s bent over he’s third, top row he’s third, top row
M Ouais Yeah Yeah
D Voilà y’en a un qui a un grand dos un peu That’s it. There is one with a large back kind of That’s it
M Ouais Yeah Yeah
D Qui baisse la tête Who’s lowering his head
M Ouais Yeah Yeah
D Celui-ci c’est quatrième case en haut. This one is fourth slot on top This one is fourth slot on top
M Donc ouais, ouais. So yeah yeah So yeah yeah
D Pis le dernier bizarre que j’essayais de t’expliquer… And the last weird one I tried to explain to you
M D’accord Okay Okay
D C’est le deuxième. Is the second one Is the second one
M On valide ? Shall we confirm? Shall we confirm?
D On valide. Let’s confirm Let’s confirm

Note: Example from Dyad 6, new cards condition, Trial 1. English translations of French acknowledgment tokens and discourse markers vary; in such cases, we chose to prioritize functional/colloquial equivalence over literal meaning. CP: card placement. IGC: Implicit generic coordination. EGC: Explicit generic coordination. GPC: General procedural coordination.

We performed initial analyses to relate the prevalence of each type of procedural coordination to the overall collaborative effort in terms of word count. We then transformed these word counts into binary data, i.e., whether or not, for each figure, a specific type of procedural coordination (CP, IGC or EGC) was used as highlighted above.1 Further, we computed whether or not, for each figure, general procedural coordination (GPC) was used by combining the binary data on CP, IGC and EGC in a trial that was not related to the identification and placement of a specific figure (for example, CP talk not related to a specific figure might include utterances like there are two cards left).

### 4.4. Data analysis

The data were analyzed using logistic mixed models in SAS 9.4 (GLIMMIX procedure). Mixed models allow including random intercepts (accounting for the potential variability across dyads, across participants and across items) and random slopes (accounting for the fact that dyads, participants and items may differ in their sensitivity to any within-units IVs in the design) (Baayen, Davidson, & Bates, 2008; Barr, Levy, Scheepers, & Tily, 2013; Jaeger, 2008). We used logistic models because the four DVs were binary (Agresti, 2002; Jaeger, 2008).

Four sets of analyses were conducted – one per DV. Each set followed a rationale similar to that used by Bangerter et al. (in preparation). Specifically, in each set, we started by running an analysis which included participant role as the only IV. The purpose of this was to determine whether one of the roles was more likely to resort to the kind of coordination considered in the analysis. We then analyzed the data separately for Directors and Matchers (we decided not to run a single analysis including participant role and all other IVs in order to make the results easier to interpret). Significant interactions were interpreted based on the corresponding b coefficient.

In line with Barr et al.’s (2013) suggestion, all models included the maximal random effects structure justified by the design. Here, the maximal random effects structure would include by-dyad, by-participant and by-item (i.e., by-figure) random intercepts, as well as random slopes corresponding to all within-dyad, within-participant or within-item IVs (although note that by-participant random effects were not included in the models when the participants’ data [Directors and Matchers] were analyzed separately). However, doing so often caused the models to fail to converge. Most convergence issues arising in mixed modelling are caused by random effects (random intercepts and/or slopes) that prevent the G-matrix of the model from converging. Removing these effects from the model usually solves all convergence issues (problematic random effects are identified automatically in SAS; Kiernan, Tao, & Gibbs, 2012). The results reported in this section thus correspond to the final models from which all problematic random effects were removed. The equation of the final model is provided for each analysis; a list of the symbols used in the equations is provided in Table 2.

Table 2

Symbols Used in the Equations.

Symbol Description

β0 Fixed intercept
β1 Fixed slope (role)
β2 Fixed slope (condition)
β3 Fixed slope (trial – linear)
β4 Fixed slope (trial – quadratic)
β5 Fixed slope (condition × linear)
β6 Fixed slope (condition × quadratic)
P0 By-participant random intercepts
I0 By-item random intercepts
D3 By-dyad random slopes (trial – linear)
P1 By-participant random slopes (role)
P2 By-participant random slopes (condition)
P3 By-participant random slopes (trial – linear)
P4 By-participant random slopes (trial – quadratic)
I1 By-item random slopes (role)
I2 By-item random slopes (condition)
I3 By-item random slopes (trial – linear)
I4 By-item random slopes (trial – quadratic)
p Participant
i Item
π Probability of an event occurring

Note: d, p and i are used as subscripts in the equations.

## 5. Results

### 5.1. Prevalence of procedural coordination in matching task conversations

As an initial descriptive analysis, Table 3 shows the mean number of words dedicated to each type of procedural coordination and the total amount of words produced to complete the task by condition. Together, the four types of procedural coordination make up 29.7% of the total amount of words in the classic condition and 28.9% of the total amount of words in the new cards condition. Thus, a substantial proportion of matching task conversation is dedicated to procedural coordination.2

Table 3

Mean Number of Words per Dyad (SDs) for Explicit Generic Coordination, Implicit Generic Coordination, Card Placement Coordination, General Procedural Coordination, and Task Completion in Total.

Classic condition New cards condition

Mean SD Mean SD

EGC 36.63 19.61 97.00 73.33
IGC 88.25 39.68 238.14 106.08
CP 83.00 39.70 250.21 152.24
GPC 43.50 42.55 72.57 40.62
Total 846.37 338.18 2273.28 857.89

Note: EGC: Explicit generic coordination. IGC: Implicit generic coordination. CP: card placement. GPC: General procedural coordination. Total: Total amount of words produced for task completion.

### 5.2. Card placement (CP) coordination

#### 5.2.1. Effect of role on card placement (CP) coordination

The probability of card placement coordination occurring was .69 (SD = .47) in the talk of Directors and .16 (SD = .37) in the talk of Matchers. The equation of the model used is

$\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{P}_{0p}+{\beta }_{1}{X}_{1}+{e}_{\mathit{\text{dpi}}}$

As shown in Table 4, Directors were significantly more likely to resort to card placement coordination than Matchers. Following this initial analysis, Director and Matcher data were considered separately.

Table 4

Model Parameters, F statistic and Odds Ratio for Card Placement Coordination.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F (fixed effects) OR (95% C.I.)

Random effects
By-participant random intercepts 1.56 (0.60)
Fixed effects
Intercept (fixed) –2.10 (0.36) <.001
Role: Director 3.40 (0.42) <.001 1, 21 66.71 <.001 30.01 (12.62; 71.36)

Note: Num: Numerator. Den: Denominator. OR: Odds ratio.

#### 5.2.2. Effect of condition and trial number on card placement (CP) coordination in Directors only

The data corresponding to this analysis are shown in Figure 1.

Figure 1

Director data – Probability of card placement coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+\left({\beta }_{2}+{I}_{2p}\right){X}_{2}+\left({\beta }_{3}+{D}_{3d}+{I}_{3p}\right){X}_{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{4}{X}_{3}^{2}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 5, only a significant negative quadratic trend was found.

Table 5

Model Parameters, F statistics and Odds Ratios for Card Placement Coordination – Director Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F (fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.22 (0.11)
By-item random slopes corresponding to condition 0.15 (0.14)
By-item random slopes corresponding to the linear trend 0.02 (0.05)
Fixed effects
Intercept (fixed) 1.81 (0.58) .005
Condition: C –1.14 (0.94) .228 1, 78 1.48 .228 0.32 (0.05; 2.07)
Linear trend 0.70 (0.49) .171 1, 18 0.62 .442 C: 0.93 (0.28; 3.12)
NC: 2.01 (0.77; 5.24)
Quadratic trend –0.13 (0.08) .092 1, 725 4.12 .043 C: 0.88 (0.73; 1.07)
NC: 0.88 (0.75; 1.02)
Linear trend × condition: C –0.77 (0.79) .326 1, 725 0.96 .326
Quadratic trend × condition: C <0.01 (0.13) .968 1, 725 <0.01 .968

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

#### 5.2.3. Effect of condition and trial number on card placement (CP) coordination in Matchers only

The data corresponding to this analysis are shown in Figure 2.

Figure 2

Matcher data – Probability of card placement coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{\beta }_{2}{X}_{2}+{\beta }_{3}{X}_{3}+{\beta }_{4}{X}_{3}^{2}+{\beta }_{5}{X}_{2}{X}_{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 6, card placement coordination was significantly less likely to occur in the classic condition than in the new cards condition. There was also a significant negative linear trend and a significant positive quadratic trend. Finally, there was a significant linear trend by condition interaction (the linear trend was significant in the classic condition only).

Table 6

Model Parameters, F statistics and Odds Ratios for Card Placement Coordination – Matcher Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
Fixed effects
Intercept (fixed) –1.54 (0.31) <.001
Condition: C –2.64 (0.74) <.001 1, 854 12.89 <.001 0.07 (0.02; 0.30)
Linear trend –0.74 (0.40) .064 1, 854 9.38 .002 C: 0.02 (<0.01; 0.33)
NC: 0.48 (0.22; 1.04)
Quadratic trend 0.06 (0.07) .372 1, 854 5.05 .025 C: 1.77 (1.04; 3.01)
NC: 1.06 (0.93; 1.21)
Linear trend × condition: C –3.39 (1.59) .034 1, 854 4.53 .034
Quadratic trend × condition: C 0.51 (0.28) .070 1, 854 3.30 .070

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

### 5.3. Implicit generic coordination (IGC)

#### 5.3.1. Effect of role on implicit generic coordination (IGC)

The probability of IGC occurring was 0.61 (SD = .49) for Directors, and .92 (SD = .28) for Matchers. The equation of the model used is

$\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{P}_{0p}+{I}_{0i}+{\beta }_{1}{X}_{1}+{e}_{\mathit{\text{dpi}}}$

As shown in Table 7, Directors were significantly less likely to resort to IGC than Matchers. Following this initial analysis, Director and Matcher data were considered separately.

Table 7

Model Parameters, F statistic and Odds Ratio for Implicit Generic Coordination.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-participant random intercepts 1.16 (0.49)
By-item random intercepts 0.07 (0.06)
Fixed effects
Intercept (fixed) 2.88 (0.32) <.001
Role: Director –2.30 (0.38) <.001 1, 21 37.61 <.001 0.10 (0.05; 0.22)

Note: Num: Numerator. Den: Denominator. OR: Odds ratio.

#### 5.3.2. Effect of condition and trial number on implicit generic coordination (IGC) in Directors only

The data corresponding to this analysis are shown in Figure 3.

Figure 3

Director data – Probability of implicit generic coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{I}_{0i}+\left({\beta }_{2}+{I}_{2i}\right){X}_{2}+\left({\beta }_{3}+{D}_{3d}+{I}_{3i}\right){X}_{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{4}{X}_{3}^{2}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 8, implicit generic coordination was significantly less likely to occur in the classic condition than in the new cards condition. Further, there was a significant linear trend by condition interaction (a negative linear trend which was significant in the classic condition only) and a significant quadratic trend by condition interaction (there was a negative quadratic trend which was significant in the new cards condition only).

Table 8

Model Parameters, F statistics and Odds Ratios for Implicit Generic Coordination – Director Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.01 (0.03)
By-item random intercepts 0.06 (0.15)
By-item random slopes corresponding to the condition 0.11 (0.17)
By-item random slopes corresponding to the linear trend 0.04 (0.04)
Fixed effects
Intercept (fixed) 1.34 (0.24) <.001
Condition: C –2.21 (0.39) <.001 1, 58 32.35 <.001 0.11 (0.05; 0.24)
Linear trend 0.78 (0.39) .064 1, 18 0.67 .424 C: 0.27 (0.10; 0.73)
NC: 2.17 (1.00; 4.70)
Quadratic trend –0.14 (0.06) .031 1, 725 0.13 .720 C: 1.11 (0.94; 1.30)
NC: 0.87 (0.77; 0.99)
Linear trend × condition: C –2.07 (0.63) .001 1, 725 10.68 .001
Quadratic trend × condition: C 0.24 (0.11) .025 1, 725 5.05 .025

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

#### 5.3.3. Effect of condition and trial number on implicit generic coordination (IGC) in Matchers only

The data corresponding to this analysis are shown in Figure 4.

Figure 4

Matcher data – Probability of implicit generic coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{\beta }_{2}{X}_{2}+\left({\beta }_{3}+{D}_{3d}\right){X}_{3}+{\beta }_{4}{X}_{3}^{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 9, all effects failed to reach statistical significance.

Table 9

Model Parameters, F statistics and Odds Ratios for Implicit Generic Coordination – Matcher Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.14 (0.12)
Fixed effects
Intercept (fixed) 3.28 (0.41) <.001
Condition: C –0.72 (0.66) .274 1, 834 1.20 .274 0.49 (0.14; 1.77)
Linear trend –0.36 (0.73) .628 1, 20 1.09 .309 C: 0.44 (0.08; 2.41)
NC: 0.70 (0.17; 2.92)
Quadratic trend 0.07 (0.12) .534 1, 834 0.34 .559 C: 1.03 (0.80; 1.32)
NC: 1.08 (0.85; 1.36)
Linear trend × condition: C –0.47 (1.14) .681 1, 834 0.17 .681
Quadratic trend × condition: C –0.05 (0.17) .786 1, 834 0.07 .786

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

### 5.4. Explicit generic coordination (EGC)

#### 5.4.1. Effect of role on explicit generic coordination (EGC)

The probability of explicit generic coordination occurring was .37 (SD = .48) for directors, and .30 (SD = .46) for matchers. The equation of the model used is

$\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{P}_{0p}+{I}_{0i}+\left({\beta }_{1}+{I}_{1i}\right){X}_{1}+{e}_{\mathit{\text{dpi}}}$

As shown in Table 10, no significant effect was found. Following this initial analysis, Director and Matcher data were analyzed separately.

Table 10

Model Parameters, F statistic and Odds Ratio for Explicit Generic Coordination.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-participant random intercepts 0.66 (0.25)
By-item random intercepts 0.09 (0.06)
By-item random slopes corresponding to role 0.01 (0.06)
Fixed effects
Intercept (fixed) –1.01 (0.26) .001
Role: Director 0.34 (0.27) .224 1, 21 1.57 .224 1.41 (0.80; 2.49)

Note: Num: Numerator. Den: Denominator. OR: Odds ratio.

#### 5.4.2. Effect of condition and trial number on explicit generic coordination (EGC) in Directors only

The data corresponding to this analysis are shown in Figure 5.

Figure 5

Director data – Probability of explicit generic coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{I}_{0i}+{\beta }_{2}{X}_{2}+\left({\beta }_{3}+{D}_{3d}\right){X}_{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{4}{X}_{3}^{2}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 11, EGC was significantly less likely to occur in the classic condition than in the new cards condition.

Table 11

Model Parameters, F statistics and Odds Ratios for Explicit Generic Coordination – Director Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.03 (0.03)
By-item random intercepts 0.13 (0.09)
Fixed effects
Intercept (fixed) –0.11 (0.30) .703
Condition: C –1.73 (0.50) .001 1, 795 12.03 .001 0.18 (0.07; 0.47)
Linear trend –0.26 (0.36) .470 1, 18 1.44 .245 C: 0.58 (0.19; 1.78)
NC: 0.77 (0.38; 1.55)
Quadratic trend 0.03 (0.06) .595 1, 795 0.12 .727 C: 1.01 (0.83; 1.23)
NC: 1.03 (0.92, 1.16)
Linear trend × condition: C –0.28 (0.68) .675 1, 795 0.18 .675
Quadratic trend × condition: C –0.02 (0.12) .854 1, 795 0.03 .854

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

#### 5.4.3. Effect of condition and trial number on explicit generic coordination (EGC) in Matchers only

The data corresponding to this analysis are shown in Figure 6.

Figure 6

Matcher data – Probability of explicit generic coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{I}_{0i}+\left({\beta }_{2}+{I}_{2i}\right){X}_{2}+\left({\beta }_{3}+{D}_{3d}+{I}_{3i}\right){X}_{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{4}{X}_{3}^{2}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 12, EGC was significantly less likely to occur in the classic condition than in the new cards condition. A significant negative linear trend and a significant positive quadratic trend were also found. Finally, there was a significant linear trend by condition interaction (the linear trend was significant in the classic condition only) and a quadratic trend by condition interaction (the quadratic trend was significant in the classic condition only).

Table 12

Model Parameters, F statistics and Odds Ratios for Explicit Generic Coordination – Matcher Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.02 (0.03)
By-item random intercepts 0.04 (0.14)
By-item random slopes corresponding to the condition 0.09 (0.16)
By-item random slopes corresponding to the linear trend 0.04 (0.04)
Fixed effects
Intercept (fixed) –0.68 (0.27) .021
Condition: C –1.03 (0.46) .029 1, 58 5.03 .029 0.36 (0.14; 0.90)
Linear trend –0.33 (0.36) .379 1, 18 8.96 .008 C: 0.19 (0.06; 0.56)
NC: 0.72 (0.35; 1.47)
Quadratic trend 0.02 (0.06) .717 1, 725 5.73 .017 C: 1.27 (1.06; 1.53)
NC: 1.02 (0.91, 1.15)
Linear trend × condition: C –1.34 (0.66) .044 1, 725 4.07 .044
Quadratic trend × condition: C 0.22 (0.11) .046 1, 725 4.00 .046

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

### 5.5. General procedural coordination (GPC)

#### 5.5.1. Effect of role on general procedural coordination (GPC)

The probability of general procedural coordination occurring is .78 (SD = 0.42) in the talk of Directors and .73 (SD = 0.45) in the talk of Matchers.

The equation of the model used is

$\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{\beta }_{1}{X}_{1}+{e}_{\mathit{\text{dpi}}}$

As shown in Table 13, no significant effect of participant role was found. Following this initial analysis, Director and Matcher data were considered separately.

Table 13

Model Parameters, F statistic and Odds Ratio for General Procedural Coordination.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
Fixed effects
Intercept (fixed) 1.20 (0.37) .004
Role: Director 0.34 (0.35) .325 1, 196 0.97 .325 1.41 (0.71; 2.81)

Note: Num: Numerator. Den: Denominator. OR: Odds ratio.

#### 5.5.2. Effect of condition and trial number on general procedural coordination (GPC) in Directors only

The data corresponding to this analysis are shown in Figure 7.

Figure 7

Director data – Probability of general procedural coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{\beta }_{2}{X}_{2}+\left({\beta }_{3}+{D}_{3d}\right){X}_{3}+{\beta }_{4}{X}_{3}^{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 14, GPC was significantly less likely to occur in the classic condition than in the new cards condition. There was also a significant linear trend by condition interaction (there was a negative linear trend which was significant in the classic condition only) and a quadratic trend by condition interaction (there was a positive quadratic trend which was significant in the classic condition only).

Table 14

Model Parameters, F statistics and Odds Ratios for General Procedural Coordination – Director Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.05 (0.26)
Fixed effects
Intercept (fixed) 2.60 (0.66) .001
Condition: C –1.98 (0.99) .050 1, 63 4.00 .050 0.14 (0.02; 1.00)
Linear trend 1.96 (1.62) .241 1, 20 0.97 .337 C: 0.01 (<0.01; 0.60)
NC: 7.12 (0.28; 182.24)
Quadratic trend –0.35 (0.27) .197 1, 63 0.42 .517 C: 1.84 (1.09; 3.34)
NC: 0.71 (0.42; 1.20)
Linear trend × condition: C –6.45 (2.57) .015 1, 63 6.30 .015
Quadratic trend × condition: C 0.95 (0.40) .020 1, 63 5.76 .020

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

#### 5.5.3. Effect of condition and trial number on general procedural coordination (GPC) in Matchers only

The data corresponding to this analysis are shown in Figure 8.

Figure 8

Matcher data – Probability of general procedural coordination occurring as a function of condition and trial number.

The equation of the model used is

$\begin{array}{l}\mathit{\text{logit}}\left(\pi \right)={\beta }_{0}+{D}_{0d}+{\beta }_{2}{X}_{2}+\left({\beta }_{3}+{D}_{3d}\right){X}_{3}+{\beta }_{4}{X}_{3}^{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}+{\beta }_{5}{X}_{2}{X}_{3}+{\beta }_{6}{X}_{2}{X}_{3}^{2}+{e}_{\mathit{\text{dpi}}}\end{array}$

As shown in Table 15, a significant negative linear trend and a significant positive quadratic trend were found. There was also a significant linear trend by condition interaction (the slope was steeper in the classic condition than in the new cards conditions) and a quadratic trend by condition interaction (the trend was stronger in the classic condition than in the new cards condition).

Table 15

Model Parameters, F statistics and Odds Ratios for General Procedural Coordination – Matcher Data Only.

b (SE) p value for b (fixed effects) df Num, Den (fixed effects) F p value for F(fixed effects) OR (95% C.I.)

Random effects
By-dyad random slopes corresponding to the linear trend 0.06 (0.23)
Fixed effects
Intercept (fixed) 1.59 (0.48) .004
Condition: C –0.17 (0.95) .860 1, 64 0.03 .860 0.85 (0.13; 5.63)
Linear trend –0.61 (1.18) .605 1, 20 8.70 .008 C: <0.01 (<0.01; 0.05)
NC: 0.54 (0.05; 5.65)
Quadratic trend 0.11 (0.19) .568 1, 64 8.59 .005 C: 3.82 (1.54; 9.48)
NC: 1.12 (0.76; 1.64)
Linear trend × condition: C –8.91 (3.44) .012 1, 64 6.71 .012
Quadratic trend × condition: C 1.23 (0.49) .016 1, 64 6.17 .016

Note: Num: Numerator. Den: Denominator. OR: Odds ratio. C: Classic condition. NC: New cards condition.

## 6. Discussion

The purpose of this study was to quantify and qualify the role of procedural coordination in dialogue (e.g., Mills, 2014) during the matching task (Clark & Wilkes-Gibbs, 1986), which is heavily used in dialogue research. This study has produced four main findings (see Table 16).

Table 16

Summary of the Results.

Effect of role Director data only Matcher data only

CP Director > Matcher
• Classic < New cards
• Negative linear trend in the classic condition
• Positive quadratic trend in both conditions
IGC Director < Matcher
• Classic < New cards
• Negative linear trend in the classic condition
• Negative quadratic trend in the new cards condition
• No significant effects found
EGC No significant effect found
• Classic < New cards
• Classic < New cards
• Negative linear trend in the classic condition
• Positive quadratic trend in the classic condition
GPC No significant effect found
• Classic < New cards
• Negative linear trend in the classic condition
• Positive quadratic trend in the classic condition
• Negative linear trend in both conditions
• Positive quadratic trend in both conditions

Note: CP: card placement. IGC: Implicit generic coordination. EGC: Explicit generic coordination. GPC: General procedural coordination.

First, although most researchers would probably agree that part of the participants’ talk in the matching task involves procedural coordination, the exact amount of talk dedicated to procedural coordination (rather than to semantic coordination) was previously unknown. The current study revealed that a substantial proportion of talk in matching task conversations (almost 30%) is dedicated to coordinating the activity itself and not to the establishment of referring conventions.

Second, a closer look at the results from the classic condition suggests that procedural coordination develops over trials. For Matchers, in this condition, where the establishment of conceptual pacts enables rapid completion of the task, explicit generic coordination, card placement coordination, and general procedural coordination decreased over trials. The only kind of procedural coordination that did not decrease for Matchers was implicit generic coordination, i.e., coordinating progress in the task via project markers (Bangerter & Clark, 2003). This remained at a high level (>0.90 probability of being used per figure) throughout the task, irrespective of experimental condition. It is noteworthy, however, that general procedural coordination and card placement coordination exhibited a quadratic trend in the classic condition. This may be due in part to explicit statements that the task was over at the end of the experiment (i.e., a kind of closing phase, as discussed in Bangerter & Clark, 2003).

For directors, findings in the classic condition were more complex. Directors’ talk about explicit generic coordination in this condition showed no trends over trials, while their use of card placement and implicit generic coordination decreased over trials. On the other hand, their use of general procedural coordination was similar to Matchers’ in the classic condition (i.e., decrease and an upswing in the last trial). Taken together, these findings suggest that in the classic version of the matching task, there are systematic trends in procedural coordination over trials. However, the trends depend on participants’ roles.

Indeed, and third, there is a division of labor in the accomplishment of procedural coordination according to participants’ roles, as suggested by Mills (2014). Because Directors’ cards are in the correct order, they tend to talk more about card placement than Matchers. Matchers typically acknowledge Directors’ descriptions, and so they produce more implicit generic coordination talk (and maintain high levels of such talk throughout). Directors typically enquire as to the possibility of continuing (ready?) or initiate discussion of the next card (next) once Matchers have acknowledged instructions, which should lead to high levels of explicit generic coordination. While their levels are not significantly higher than Matcher’s levels, they do not decrease over trials (while Matchers’ levels do). Thus, it seems that Directors and Matchers spontaneously take on responsibility for different types of procedural coordination, which is evidenced in the generally higher levels of talk relative to the specific type.

Fourth, procedural coordination is linked with semantic coordination. In the new cards condition, participants dealt with novel referents on each trial. This manipulation precluded the development of conceptual pacts (Brennan & Clark, 1996) and kept semantic coordination demands high over trials. In this condition, demands for several types of procedural coordination stayed high over trials, whereas they decreased over trials in the classic condition (except for general procedural coordination, which also decreased for Matchers in the new cards condition). Specifically, this difference between conditions was evidenced for card placement coordination (Matchers only), explicit generic coordination (Matchers only), and general procedural coordination (Directors only). These findings suggest that participants may trade off between demands of semantic and procedural coordination. When faced with recurrently novel referents (new cards condition), the risk that a card poses particular identification problems increases. Participants may then decide to temporarily suspend the placement of that card and focus on another card that may be easier to describe. This strategy decreases semantic coordination demands, but may require more effort to coordinate card placement. This is in part because the easier-to-describe card may be out of sequence, thereby requiring participants to talk about card placement, rather than simply proceeding to the “next” card. This may in turn require explicit coordination of suspension of a “next card” routine (e.g., let’s try one that’s easier to describe), further increasing procedural coordination costs.

Our findings have important implications for the experimental study of dialogue. First, in the matching task, the coordination problems participants must solve together are not only semantic, but also procedural. Reductions in collaborative effort in the matching task are not only due to the elaboration of conceptual pacts, but may reflect a range of coordination processes or even individual-level learning (see e.g., Bangerter, Mayor, & Knutsen, 2017). Because the matching task is the workhorse task for dialogue research, experiments using it should take into account the distinction between procedural and semantic coordination (Mills, 2014).

Second, the relation between procedural and semantic coordination needs further theoretical elaboration. As a first step, studies might focus on how the development of procedural coordination in the matching task is similar to or different from that of semantic coordination in other experimental dialogue tasks. The relative importance of semantic and procedural coordination may vary depending on the constraints of specific tasks, as suggested by Mills (2011), who used a task designed to make procedural coordination difficult and semantic coordination easy. Likewise, in our study, we manipulated the difficulty of establishing conceptual pacts, which allowed us to investigate whether procedural coordination is related to semantic coordination. However, some aspects of semantic and procedural coordination are difficult to conceptually separate in the matching task. Semantic coordination in the matching task in itself involves a procedure for negotiating conceptual pacts. This procedure is described in detail in Clark and Wilkes-Gibbs (1986) and consists of participants initiating a description of a tangram figure, refashioning it if necessary, and evaluating it. These steps also involve subprocedures. For example, refashioning can be accomplished via repair, expansion, or replacement. Thus, the improvement of semantic coordination in the matching task hinges in part on the increased efficiency of procedures for accomplishing collaborative referring, making it difficult to completely separate semantic from procedural coordination. We suggest that this will especially be the case for generic procedural coordination, which is based on universally shared interactional routines like turn-taking, adjacency pairs (Sacks, Schegloff, & Jefferson 1974), repair (Dingemanse et al., 2015), grounding (Clark & Schaefer, 1989) or transition marking (Bangerter & Clark, 2003). Another aspect where the two kinds of coordination may differ concerns the idiosyncratic paths taken in semantic coordination, which makes conceptual pacts increasingly opaque to overhearers (Schober & Clark, 1989). Because procedural coordination relies in part on task affordances or on routines that may be shared at least in part by all participants, its development may unfold faster and converge on less idiosyncratic solutions than semantic coordination. This may especially be the case for generic procedural coordination, which relies in part on the universal routines listed above. However, task-specific procedural coordination may converge more on a variety of idiosyncratic solutions. For example, in Garrod and Doherty’s classic (1994) maze game experiments, pairs of participants kept using a wide range of idiosyncratic schemes throughout the task.

Third, investigating differences between semantic and procedural coordination will have important implications for existing models of dialogue (see Brennan, Galati, & Kuhlen, 2010, for an overview). Our findings are largely consistent with the grounding model of dialogue. However, that model often implicitly focuses on semantic coordination. This leads to the observation, for example, that within-dialogue variability in wording and perspectives is lower than between-dialogue variability (Brennan et al., 2010). As suggested by the above discussion of the less idiosyncratic nature of procedural coordination, that observation may have to be qualified. Moreover, we document a division of labor between directors and matchers involving procedural coordination, similar to emergence of interactional routines involving complementary contributions (Mills, 2011, and Fusaroli & Tylén, 2016). Our findings thus converge with recent models of dialogue as interpersonal synergy (Fusaroli et al., 2014).

In conclusion, this study offers a better understanding of the role of procedural coordination in dialogue, and its interaction with semantic coordination. It sheds further light on the processes at play in the matching task, one of the most widely used tasks in dialogue research. Previous research has suggested that the decrease in collaborative effort usually observed in this kind of task reflects partners establishing and reusing conceptual pacts. The current findings nuance this claim by revealing that part of this decrease is in fact due to dialogue partners coordinating procedurally. We have also shown that all kinds of procedural coordination do not necessarily decrease as the interaction unfolds: this depends on whether coordination is general or specific, and on whether it is implicit or explicit. It also depends on the role in the dyad, and on whether participants can rely on semantic coordination as well.

## Data Accessibility Statement

Materials, transcripts, coded data and analytical scripts are available at https://osf.io/ua59z/.