While I had worked out a range of possible times for each of the ropes to complete its combustion, I went for a simulation based confirmation. The starting point is that a new fire can only be started when a burning rope ends up burning. Which only happens for a finite number of possibilities. I found 24 of them, consisting of

> total*prec [1] 0.000 0.5000 0.750 0.875 0.9375 1.000 1.125 1.1875 1.25 1.3125 [11] 1.375 1.4375 1.500 1.625 1.7500 1.875 2.000 2.1250 2.25 2.5000 [21] 2.750 3.0000 3.500 4.000

i.e., some combinations of 1, 2⁻¹, …, 2⁻⁴, with the comment that those times cannot all be obtained within a single arson experiment.

The simulation experiment consists in producing a random sequence of fire starts based on this principle. To reproduce the non-uniform burning rate I chose a Beta cdf although it has absolutely no relevance on the solution:

#safer beta quantile myqbeta <-function(x,a,b){ x=(x>0)*(x<1)*x+(x>=1) return(qbeta(x,a,b))} #burning rate, by side of the rope fuse <- function(t,side){ (side==1)*pbeta(t,2.0,1.7)+(side==2)*pbeta(1-t,2.0,1.7)} #time since start when at x infuse <- function(x,side){ (side==1)*myqbeta(x,2.0,1.7)+(side==2)*(1-myqbeta(x,2.0,1.7))}

then I defined R functions for proceeding on the time line and choosing starting points for new fires

#start a new burn light <- function(ropes,burns){ #check some are left if (max(ropes[,2]-ropes[,1])==0) return(burns) #pick number of new fires howmany=sample(0:sum((ropes[,2]-ropes[,1]==1)),1) if (howmany>0){ whichropes=sample(rep((1:N)[ropes[,2]-ropes[,1]==1],2),howmany) burns[whichropes,1]=TRUE} #ropes[whichropes,1]=fuse(prec,1)} #pick second end fire-start howmany=sample(0:sum(burns[,1]&!burns[,2]),1) if (howmany>0){ whichropes=sample(rep((1:N)[burns[,1]&!burns[,2]],2),howmany) burns[whichropes,2]=TRUE} #ropes[whichropes,2]=fuse(prec,2)} burns } #move fire along by one time step shakem whichones=(1:N)[burns[,1]] ropes[whichones,1]=fuse(infuse(ropes[whichones,1],1)+prec,1) whichones=(1:N)[burns[,2]] ropes[whichones,2]=fuse(infuse(ropes[whichones,2],2)+prec,2) #eliminate burnt whichones=(1:N)[ropes[,2]<=ropes[,1]] ropes[whichones,2]=ropes[whichones,1] burns[whichones,1]=burns[whichones,2]=FALSE list(ropes=ropes,burns=burns) } #completely burned ropes burnt <-function(ropes){ (1:N)[ropes[,2]==ropes[,1]]}

which can then be used repeatedly to record times at which a rope ends up burning, using a time discretisation of 1/2⁵ (which has no impact when compared with a finer discretisation):

N=4 prec=1/2^(N+1) ropes=cbind(rep(0,N),rep(1,N)) burns=cbind(rep(FALSE,N),rep(FALSE,N)) exhausted=NULL #start with at least one rope events=0 while (max(burns)==0) burns=light(ropes,burns) for (t in 1:(N/prec)){ update=shakem(ropes,burns) ropes=update$ropes burns=update$burns if (length(setdiff(burnt(ropes),exhausted))>0){ #one fire ended events=c(events,t) exhausted=burnt(ropes) #new firestart burns=light(ropes,burns) }

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In the RKHS pseudo-linear formulation, the prediction of a parameter value given a sample attached to this value looks like a ridge estimator in classical linear estimation. (I thus wonder at why one would stop at the ridge stage instead of getting the full Bayes treatment!) Things get a bit more involved in the case of parameters (and observations) of interest, as the modelling requires two RKHS, because of the conditioning on the nuisance observations. Or rather three RHKS. Since those involve a maximum mean discrepancy between probability distributions, which define in turn a sort of intrinsic norm, I also wonder at a Wasserstein version of this approach.

What I find hard to understand in the paper is how a large-dimension large-size sample can be managed by such methods with no visible loss of information and no explosion of the computing budget. The authors mention Fourier features, which never rings a bell for me, but I wonder how this operates in a general setting, i.e., outside the iid case. The examples do not seem to go into enough details for me to understand how this massive dimension reduction operates (and they remain at a moderate level in terms of numbers of parameters). I was hoping Jovana Mitrovic could present her work here at the 17w5025 workshop but she sadly could not make it to Banff for lack of funding!

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It may be that part of the interest in the paper is self-centred. I do not think analysing a similar dataset in another field like deconstructionist philosophy or Korean raku would have attracted the same attention. Looking at the clusters and the names on the pictures is obviously making sense, if more at a curiosity than a scientific level, as I do not think this brings much in terms of ranking and evaluating research (despite what Bernard Silverman suggests in his preface) or understanding collaborations (beyond the fact that people in the same subfield or same active place like Duke tend to collaborate). Speaking of curiosity, I was quite surprised to spot my name in one network and even more to see that I was part of the “High-Dimensional Data Analysis” cluster, rather than of the “Bayes” cluster. I cannot fathom how I ended up in that theme, as I cannot think of a single paper of mines pertaining to either high dimensions or data analysis [to force the trait just a wee bit!]. Maybe thanks to my joint paper with Peter Mueller. (I tried to check the data itself but cannot trace my own papers in the raw datafiles.)

I also wonder what is the point of looking at solely four major journals in the field, missing for instance most of computational statistics and biostatistics, not to mention machine learning or econometrics. This results in a somewhat narrow niche, if obviously recovering the main authors in the [corresponding] field. Some major players in computational stats still make it to the lists, like Gareth Roberts or Håvard Rue, but under the wrong categorisation of spatial statistics.

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However, as so often the case in Jacobin France, the move has been decided and supported by the State “top-down” rather than by the original institutions themselves. Including a big push by Nicolas Sarkozy in 2010. While the campus can be reached by public transportation like RER, the appeal of living and working on the campus is obviously less appealing to both students and staff than in a listed building in the centre of Paris. Especially when lodging and living infrastructures are yet to be completed. But the main issue is that the fragmentation of those schools, labs and institutes, in terms of leadership, recruiting, research, and leadership, has not been solved by the move, each entity remaining strongly attached to its identity, degree, networks, &tc., and definitely unwilling to merge into a super-university with a more efficient organisation of teaching and research. Which means the overall structure as such is close to invisible at the international level. This is the point raised by the State auditors. And perceived by the State which threatens to cut funding at this late stage!

This is not the only example within French higher educations institutions since most have been forced to merged into incomprehensible super-units under the same financial threat. Like Paris-Dauphine being now part of the PSL (*Paris Sciences et Lettres*) heterogeneous conglomerate. (I suspect one of the primary reasons for this push by central authorities was to create larger entities towards moving up in the international university rankings, which is absurd for many reasons, from the limited worth of such rankings, to the lag between the creation of a new entity and the appearance on an international university ranking, to the difficulty in ranking researchers from such institutions: in Paris-Dauphine, the address to put on papers is more than a line long, with half a dozen acronyms!)

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