despite a variety of criticisms of its effectiveness , peer review is a fundamental mechanism for validating the quality of the research that is published in today s scientific literature .it is a complex , multi - phase process and there appear to be some growing concerns regarding how to improve its functioning . given the growth of scientific journals , the increasing number of submitted articles , and the limited pool of reviewers , acquiring a good and timely review is becoming progressively more challenging .reviews can take even a year , depending on the complexity of the topic , the number of reviewers involved , and the details of the editorial procedures .  in face of these problems ,many suggestions have been proposed to make the peer review and editorial process more efficient and equitable . in particular , the role of editors in the process of selecting and managing reviewers has been increasingly discussed .the main focus of these discussions are ethical issues and general , qualitative recommendations for both the editors and the reviewers . while such issues are certainly practical and significant , there is still the lack of quantitative suggestions that could point out possible measurable improvements to the peer review process .do the editors send out a sufficient number of reviewer invitations to obtain two or three timely reviews of a manuscript ?how often should they draw on expertise of the same reviewers consuming their time and energy ?how long should they wait for a review before they can repeat an invitation or assume that a response is unlikely ?what is the statistical chance that reviewers will respond ?does it depend on whether they were previously reviewers for the same journal ?although all editors try to answer these and other questions while optimizing their work on their own , they do it somewhat in the dark . without an intensive discussion that could help to answer the aforementioned questions in a more systematic way one can be sure that editorial lags will be increasing in the years to come .our paper is meant to fill this gap with the help of quantitative analysis .we examine selected aspects of peer review and suggest possible improvements . to this end , we analyse a dataset containing information about 300 papers submitted to the biochemistry and biotechnology section of the journal of the serbian chemical society ( jcsc ) . after separating the peer review process into stages that each review has to go through , we use a weighted directed graph to describe it in a probabilistic manner and test the impact of some modifications of the editorial policy on the efficiency of the whole process .the paper is organized as follows :  section 2 describes the dataset used in the paper as well as the methodology employed to analyse the data .section 3 is devoted to the data driven theoretical analysis of the review times .simulations of various editorial policy scenarios and their impact on the efficiency of the process are presented in section 4 . in section 5we provide some concluding remarks and describe open problems that may be researched within the presented methodology in the future .the sample we studied contains information about reviews of 58 manuscripts submitted to one of the editors of jcsc between november 2011 and july 2014 .each of 323 members of the sample corresponds to a single reviewer and comprises the group the reviewer belongs to , the i d of the reviewed manuscript and dates associated with phases of the review process .reviewers were divided into two groups - 65 * trusted * reviewers are known personally by the editor while 258 * other * reviewers were chosen through various different means .the review process itself is separable into distinct phases that mirror interactions between the editor , authors and reviewers .it begins when the editor , after receiving a new submission , sends out invitations to a number of reviewers ( 5 on average - 4 * other * and 1 * trusted * ) and waits for their responses . if any of the invited reviewers does not respond , then after about 7 days an inquiry is sent .if that inquiry also remains without an answer for 10 days , then the review process for that particular reviewer is considered finished with a negative outcome . after receiving the initial invitation or the inquiry , reviewers who do answer either confirm their willingness to write the review or decline . in the latter case , much like for reviewers who did not answer at all ,the review process is considered finished with a negative outcome . in the former, the editor waits for the report for 25 days before sending an inquiry .this may result in either the reviewer finishing the review and sending the report - which is the only outcome of the process that is considered positive - or a lack of answer . to sum it up, there are three possible outcomes of the review process - * report * , * no response * or * decline*.        a directed graph in which nodes correspond to phases and edges connect subsequent phases can be used as a visual representation of the review process .graphs that describe our sample can be found in figures [ fig : bdiag - all]-[fig : bdiag - trusted ] .the value expressed in percent next to each edge is the probability that a realisation of the review process will pass through the edge - that is , the number of members from our sample for which the transition between nodes connected by the edge occurred divided by the size of the sample . widths of edges were scaled proportionally to that probability .what is striking is that only 43% of all invitations actually result in a finished review ( figure [ fig : bdiag - all ] ) .most of reviewers - that is 64% - do not even respond to the initial invitation and 42% ignore the inquiry .these poor results are mostly driven by reviewers that belong to the * other * group ( figure [ fig : bdiag - other ] ) , which constitutes the majority of all reviewers .only 31% of * other * reviewers finish the review , 73% ignore the initial inquiry , 51% do not answer at all and 16% reject the invitation . on the other hand , * trusted * reviewers - who are in minority - are far more reliable .most of them , 74% , respond to the invitation and 89% finish the review .only 3% do not answer and 8% reject . as we will show in the following sections , this disparity between * trusted * and * other * reviewers may play a crucial role in the review process and is the key factor that determines its effectiveness .review time , that is the number of days between the * invitation * phase and * report * phase , is the most direct and tangible measure of the efficiency of the review process .since our sample contains information about the beginning and end of each phase , we were able to acquire distributions of review time for * trusted * and * other * reviewers , as well as partial distributions of days between all intermediate phases .these partial distributions are especially interesting , as they can serve as building blocks with which one can create a simulation of the entire review process and recreate the cumulative distribution of review time under various assumptions .the distribution of review time can be reassembled using partial distributions in the following way .to each node ( phase ) of the review process graph ( figures [ fig : bdiag - all]-[fig : bdiag - trusted ] ) one can assign the probability that a realisation of the process will pass through node and the probability distribution of days between the * invitation * phase and phase .similarly , each edge is characterised by the probability that the review process will pass from phase to and the probability distribution of days associated with such a transition . given all these probabilities , can be calculated as follows where the summation is over set of all predecessors of node and symbol represents the discrete convolution weights are defined as and the probability can be expressed as equations [ equ : gj]-[equ : qj ] are recursive .the distribution associated with node depends on the corresponding distributions associated with predecessors of node and probabilities exhibit similar dependence . as such, these equations can be solved recursively if one assumes appropriate initial conditions for nodes without parents ( in our case it is and for the node that corresponds to the * invitation * phase ) and acquires probabilities and from the sample .one last fact worth noting is that the quantity from the numerator in equation [ equ : wij ] is actually the same as the probability in figures [ fig : bdiag - all]-[fig : bdiag - trusted ] next to each edge .          using the aforementioned procedure we recreated the distribution of review times for both * trusted * and * other * reviewers which we then compared with the corresponding empirical distributions from the sample . according to our theoretical calculations based on equations [ equ : gj]-[equ : qj ] the average review time for * trusted * reviewers is 23 days with standard deviation of 12 days .average review time and standard deviation acquired from the sample are the same . as for * other * reviewers , the theoretical average review time is 20 days with standard deviation of 11 days and the sample , again , yields the same values . one - sample kolmogorov - smirnov test performed to compare the theoretical distribution with the sample gives p - value 0.88 for * trusted * reviewers and 0.97 for * other * reviewers .it means that the distributions of review times calculated using partial distributions are essentially the same as the ones obtained directly from data .this is an important and non - obvious observation , as the only underlying assumption behind equations [ equ : gj]-[equ : qj ] is that the review process is memoryless - that is partial distributions assigned to edges do not depend on the history of the process .results presented thus far seem to confirm this assumption and it is reinforced even further in the following section .other than the validity of theoretical distributions , there are two main conclusions that can be drawn from results presented in figures [ fig : totdist - trusted - theor]-[fig : totdist - other ] .firstly , the review time distribution is bimodal .reviewers who either confirmed or sent in their reviews after receiving the invitation are the ones who contribute to the first maximum ( and they are in the majority of those who actually completed the reports - 69% of * other * and 82% of * trusted * ) .secondly , distributions of review time are similar for * trusted * and * other * reviewers .the difference between means and standard deviations is negligible from any practical standpoint and two - sample kolmogorov - smirnov test for both empirical distributions gives p - value 0.40 .based on these fact one can make a very strong assumption that the distribution of review time is the same across the entire population of reviewers and does not depend on the type of reviewer .so far we have considered review times of a single reviewer . however , editors usually need more than one review in order to judge whether to publish an article . in the case of our data from jcsc ,the editor required two reviews per article and sent invitations to five reviewers on average - one * trusted * and four * other*. while this review strategy indeed resulted in two reviews per article on average ( 2.34 to be exact ) , 9 articles were published after receiving only one review , 24 after 2 reviews , 21 after 3 and 4 after 4 reviews .this discrepancy between the target number of reviews and the number of reviews actually received stems from the difference in the probability of finishing the report between * trusted * and * other * reviewers .we are going to call this probability the completion rate .    using partial distributionswe can easily simulate the effects of any editorial strategy and find the number of reviewers needed to achieve a certain number of reviews per article .we will use the average time of receiving two reviews as a measure of effectiveness of each strategy .figure [ fig : allways - finish ] shows these average times under the assumption that a reviewer always writes the report ( the completion rate is equal 1 ) for both * trusted * and * other * reviewers as a function of the number of reviewers .the average time decreases as the number of reviewers increases and results for * trusted * and * other * reviewers are very similar .this is intuitive and consistent with our prediction made in the previous section .but with the x axis rescaled for * other * reviewers.,width=302 ]  the assumption that reviewers always write the report is not realistic .if we want to take into account the fact that the actual completion rate of the review process for a single reviewer is much smaller , especially for * other * reviewers , then some additional strategy needs to be introduced to deal with situations when two reviews are not received at all . in our simulations we decided to use a very simple solution -if two reviews are not received , then invitations are resent to the same number of reviewers .this procedure is repeated if necessary until reviewers produce two reports in total .while this is not the most effective and time - efficient strategy , it still allows us to study the consequences of the difference between the completion rates of * trusted * and * other * reviewers .figure [ fig : fraction - finish ] is analogous to figure [ fig : allways - finish ] - in that it shows the average time of receiving two reviews - but this time we used the actual completion rates taken from the sample ( 89% for * trusted * , 31% for * other * reviewers ) and employed the policy described in the previous paragraph . as can be clearly seen , the difference in completion rates between * trusted * and * other * reviewers results in a completely different dynamics .* other * reviewers are far less effective and their average times are much higher - for example , two reviews can be received from 2 * trusted * reviewers after 32 days but 2 * other * reviewers finish the reviews after 70 days .even as the number of reviewers increases , this difference remains significant .however , in the last section we have shown that distributions of review time for * trusted * and * other * reviewers are very similar which suggests that the completion rate is the leading factor during the review process . this claim is partially supported by results presented in figure [ fig : allways - finish ] .if that is indeed the case , then one * trusted * reviewer should be worth 89%/31% * other * reviewers and conversely one * other * reviewer is worth 31%/89% * trusted * reviewers . by worth we mean that proportionally substituting one type of reviewer for another should yield the same results .figure [ fig : fraction - finish - rescaled ] , where the x axis for one type of reviewers was rescaled to match their worth in the other type of reviewers , confirms this prediction . the average number of days after which 2 reviews are acquired are similar and standard deviations , while not exactly the same - which is to be expected - are comparable .  .average number of days needed to receive two reviews from a group of reviewers with a given number of * trusted * ( columns ) and * other * ( rows ) reviewers .values for groups of reviewers smaller than two were omitted .[ cols=">,>,>,>,>,>,>,>,>,>,>",options="header " , ]   so far we have studied separately * trusted * and * other * reviewers , however the group of reviewers invited to review an article usually contains reviewers of both kinds .figure [ fig : mix ] shows the average time of acquiring two reviews when reviewer types are mixed . as one could expect , the average time decreases with the increasing total number of reviewers and * trusted * reviewers are far more effective than * other*. still , by rescaling the x axis - that is by expressing the worth of one kind of reviewer using another - we get similar results ( figure [ fig : mix - rescaled ] ) .information about average times in groups of mixed reviewers , expressed in a slightly different way in figure [ fig : mix-3d ] and summarised in table [ fig : mix - table ] can potentially be of great importance for editors and act as a guide in determining the optimal number of reviewers .for example , in order to receive two reviews after about 30 days , one needs to invite 7 * other * reviewers , 2 * trusted * or a mixed group of 4 * other * and 1 * trusted*. that last option is consistent with the choice made by the editor of jcsc who provided us with the data .it is important to note that while editors may be tempted to invite only * trusted * reviewers - which would lead to shortest review times - such a policy would not only be not realistic but also inadvisable .since the pool of potential * trusted * reviewers is limited , editors would be forced to invite the same reviewers multiple times within a short time frame .this , in turn , could discourage reviewers and make them more likely to turn down invitations .     but with rescaled x axis.,width=302 ]our results show that the distribution of review time is similar for all kinds of reviewers and it is the completion rate that is the main factor that determines the effectiveness of the review process . *trusted * reviewers , that is reviewers known personally by the editor , are far more reliable than * other * reviewers .their completion rate is very high , which means that they are much more likely to answer the invitation and finish the review . on the other hand , only a fraction of * other * reviewers answer the initial invitation and write the report .it means that * trusted * reviewers are objectively better than * other * reviewers and there is no advantage in choosing the latter over the former . in an ideal world , editors would invite only * trusted * reviewers , which , unfortunately , is not possible .  one question remains , then - who exactly is this mythical * trusted * reviewer ? what makes the difference between * trusted * and * other * reviewers ?in the case of jcsc , it was a personal relationship with the editor .one can easily imagine that this mechanism works in a very similar way in journals of comparable scope .what about bigger journals or ones in which editors do not choose reviewers themselves ? even without knowing the editor , reviewers invited by prestigious journals with high impact factor may be more inclined to write the review and thus act as * trusted*. in the end , it seems that the distinction between * trusted * and * other * reviewers is slightly artificial and was motivated mostly by the way our data is structured . instead , the completion rate is a much more intrinsic property that differentiates between reviewers .it is also important to notice that the completion rate is not a property of a reviewer , but of his relationship with other entities - be it journals , editors or even other reviewers .as such , the same reviewer can be treated as * trusted * by some journals and as * other * by others .also , since relations between people can change , the completion rate does not have to be constant and it may evolve with time .authors of manuscripts , reviewers and editors form a complex network of mutual connections , the structure of which have a direct influence on the effectiveness of the review process . however , since editors are the ones who actually manage the entire process , it would seem that their workflow is equally , if not even more important . with the right kind of workflow onecan potentially overcome many shortcoming of the behaviour of both authors and reviewers .we have shown that through very naive and most certainly not optimal means - by sending invitations to a certain number of potential reviewers - it is possible to achieve almost any desirable average review time .while it is a very simple example , our results presented in this manuscript can be used as a foundation necessary to study the dynamics of the review process and determine the optimal workflow for an editor , which will be the subject of our future work .a.f . & p.f . were supported by the foundation for polish science ( grant no .pomost/2012 - 5/5 ) and by the european union within european regional development fund ( innovative economy ) .this paper is a part of scientific activities in cost action td1306 new frontiers of peer review ( peere ) .99 wager e. , jefferson t. , _ the shortcomings of peer review _ , learned publishing , * 14 * , pp.257 - 263 ( 2001 ) .cooper m.l . , _ problems , pitfalls , and promise of the peer - review process :commentary on trafimow & rice ( 2009 ) _ , perspect .sci . * 4 * , 8490 ( 2009 ) .baker d. , _ the peer review process in science education journals _, research in science education , * 32 * , 171180 ( 2002 ) .publishing research consortium , _ peer review in scholarly journals : perspective of the scholarly community an international study _ , ( 2008 ) .bornmann l. , _ scientific peer review _ ,* 45 * , pp.199 - 245 ( 2011 ) .cawley v. , _ an analysis of the ethics of peer review and other traditional academic publishing practices _ , int ., * 1 * , 205 - 213 ( 2011 ) .resnik d.b , gutierrez - ford c. , peddada s. , _ perceptions of ethical problems with scientific journal peer review : an exploratory study _* 14 * , 305 - 310 ( 2008 ) .schwartz s.j . , zamboanga b.l ., _ the peer - review and editorial system : ways to fix something that might be broken _ ,, * 4 * , 54 - 61 ( 2009 ) .kravitz r.l . , franks p. , feldman m.d ., et al . , _ editorial peer reviewers recommendations at a general medical journal : are they reliable and do editors care ?_ , plos one , * 5 * , e10072 ( 2010 ) .newton d.p . ,_ quality and peer review of research : an adjudicating role for editors _ , account ., * 17 * , 130145 ( 2010 ). committee on publication ethics , _ cope ethical guidelines for peer reviewers _ , http://publicationethics.org/files/ethical_guidelines_for_peer_reviewers_0.pdf , ( 2013 ) .wager e. , _ ethics : what is it for ?_ , nature : web debate peer - review , http://www.nature.com/nature/peerreview/debate/nature04990.html , ( 2006 ) .

Abstract: we examine selected aspects of peer review and suggest possible improvements . to this end , we analyse a dataset containing information about 300 papers submitted to the biochemistry and biotechnology section of the journal of the serbian chemical society . after separating the peer review process into stages that each review has to go through , we use a weighted directed graph to describe it in a probabilistic manner and test the impact of some modifications of the editorial policy on the efficiency of the whole process .  _ keywords : _ peer review , editorial process , weighted directed graph 0.5 cm


one of the motivations for establishing a computational grid is the ability to exploit unused computing cycles at remote facilities . in canada , there has been a significant injection of new funding for mid - size capability and capacity computational facilities .one of the conditions of the funding is that these facilities must make 20% of the resources available to outside users .a number of these facilities are associated with high energy physics ( hep ) centers or groups .however , the majority are facilities that are shared between many research fields .we would like to exploit these unused cycles for hep applications such as monte carlo simulations .this paper describes the grid canada testbed which consists of resources at both hep and non - hep sites .we demonstrate that hep simulations can be run without installing application - specific software at the remote site .we discuss the results of a series of tests we have run over the testbed and conclude with a discussion of our plans for the future .grid canada ( www.gridcanada.ca ) is an organization established by canarie inc .( www.canarie.ca ) , who provide the national research and educational network in canada ; the c3.ca association ( www.c3.ca ) , which is an organization that represents the user community of high performance computing ( hpc ) facilities in canada ; and the national research council of canada ( nrc ) ( www.nrc.ca ) .the goal of grid canada ( gc ) is to foster collaboration on grid activities in canada .gc is responsible for the canadian certificate authority and has helped coordinate a number of demonstration activities such as the 1 tb high - speed file transfer project between the triumf laboratory in vancouver and cern and a grid test using a number of hpc ( shared memory machines ) computers across canada .in addition , gc has helped to establish the linux testbed that will be described in this paper .the gc linux testbed involves researchers at the university of victoria who are members of the babar and atlas collaborations .in addition , personnel at the nrc institute for information technology , canarie inc . and the british columbia ministry for management services have also made significant contributions to the testbed .the testbed currently includes 12 sites in canada ranging from a number of sites in british columbia to those 3000 km away in ontario .typically each site has between 1 and 8 computers .all sites are required to run globus 2.0 or 2.2 on their computers except for the victoria site which is described in the next paragraph .in addition , sites must also run an openafs client .latencies between the two most - distant sites vary between 50 and 100 milliseconds .the remote sites access the application - specific software and , for some tests , read the input and write the output data via afs .the victoria grid testbed is shown in fig [ uvictb ] .it consists of two servers for afs and objectivity . a head node ( grid.phys.uvic.ca )runs the globus software with a series of processing nodes ( grid1 , ... , grid6 ) hidden behind a firewall .jobs are distributed to the processing nodes using condor although pbs has been tested .the processing nodes have the ability to access the afs server through the firewall .access to the software via afs by many remote machines can cause significant degradation in the cpu utilization to the server and subsequently reduce the efficiency of the remote processing machines .afs has a faster , more efficient method of reading clones or read - only volumes .for example , if a volume is read - only , then the client only has to contact the afs server once to cache the volume .we tested afs performance using two clones and two replicated volumes on two separate machines .the afs server machine ( basilisk.phys.uvic.ca ) held the master and a cloned volume , with the objectivity server machine ( objy.phys.uvic.ca ) holding a replicated and a cloned volume .this configuration appeared to be sufficient for the size of the testbed so that no bottlenecks occurred as a result of the afs servers .initial tests of the atlas software using a local machine and a machine 1200 km distant showed that using a cloned volume increased the access to the software at the remote machine .real execution time at the remote machine dropped by about 40% whereas ( as expected ) no change was observed at the local machine . running simultaneous multiple jobs over the griddid not degrade the afs performance . we concluded that having cloned volumes significantly increased the afs performance .we plan to continue to monitor the afs performance as we continue to scale up the size of the gc testbed .jobs were submitted from victoria using simple scripts .no resource broker or portal was used however , we are examining the available tools ( such as gridport ) and plan to incorporate them into the testbed .monitoring of the gc testbed was done using the cacti package providing network traffic and cpu utilization .detailed descriptions of the victoria testbed can be found at http://grid.phys.uvic.ca .hep simulation applications begin by the generation of events which are collections of 4-vectors representing the trajectories of particles from an initial collision of two incident particles .the 4-vectors are then passed through a program that simulates the response of the experimental detector .the output is in a format that is usually identical to the format used to store the real collision data , but includes additional simulation information .after the detector simulation , the data is passed through an application that reconstructs the data into physical quantities such as tracks in the tracking chambers and energy in the calorimeters .it is now common practice to inject background events ( either real or simulated ) on top of the simulated physics events .we chose to examine the performance of the gc testbed using the simulations of the babar and atlas experiments .the main difference between the atlas and babar simulation applications is the manner in which they store their data .atlas uses conventional files in a zebra format developed at cern while babar uses the commercial objectivity database . in the following subsectionswe describe the results of running the babar and atlas simulations on the gc testbed .it is worth pointing out that neither the babar or the atlas simulation are optimized for operation over a wide - area grid .   the babar collaboration studies electron - positron collisions at the slac facility .in addition to collecting data from the experiment , the collaboration generates a significant amount of monte carlo simulated data in order to model the response of the detector and to help assess efficiencies and systematic errors in the physics studies .the simulation application is run in 3 phases for event generation , detector simulation and reconstruction .data is written to objectivity by the event generation application .the detector simulation reads the output of the event generation and writes output that is then used by the reconstruction .the reconstruction application writes out data that can be used for physics studies .the babar application accesses the database multiple times per event .the handshaking required between the database and application combined with the large latency resulted in relatively poor utilization of the remote processors . for example , we observed that cpu utilization was approximately 10% at sites 3000 km away from the objectivity server .a series of 1 day tests were run involving many of the gc testbed sites .a total of approximately 50,000 events were generated per test .the babar software was accessed from the afs server .the network traffic to the objectivity and afs servers is shown in figure [ f1 ] .approximately 0.5 mb / s of data was constantly read and written to the database .afs traffic was generally only a few kb / s with a peak during the start of the application .our initial tests showed that one of the areas that had to be addressed was the issuing and releasing of database locks .for example , a remote application locks the entire federation during a creation of a container .if a remote machine lost network connectivity while a global database lock was present then this resulted in the entire testbed being halted as none of the sites would be able to write to the database . as a result we developed a series of monitoring and cleanup utilities that would eliminate any problems associated with the database locks .we consider the test a success in that we could run the babar application on non - hep resources .it is clear that the efficiency at the remote sites was low and we believe a number of modifications to the babar application could improve the throughput . however , given the plan by babar and the lhc experiments to move away from the objectivity database , it was decided not to pursue this application further .the atlas collaboration will study high energy proton - proton collisions at the large hadron collider at the cern laboratory .atlas is expected to produce large volumes of data starting in 2007 .the atlas data challenge ( dc ) is a project to test and develop the ability to exploit remote computing resources for monte carlo simulation . for our tests, we used the application that generates background ( called pile - up ) events . input andoutput data are standard files in a zebra format .future atlas dc will use the root data format ; such a change will make no difference to the way in which the current test was performed .we tested three modes of operation on the testbed :  1 .both input data and output data transferred using afs 2 .input data transferred using gridftp and output data transferred using afs 3 .both input and output data transferred using gridftp  all software and log files use afs .it has been recognized that afs was not an ideal protocol for transfering large data files , however , we felt it was important to quantify the differences .we found afs to extremely slow for reading input data and resulted in cpu utilizations being less than 5% .afs caches its output ; as a result we tested a mode where the input was sent via gridftp to the remote site and let afs control the output .the results of this mode of operation were more encouraging , however the performance of afs is comparable to single stream ftp and using gridftp is a much more effective solution .the mode of operation we chose was one where the input files were tarred and compressed , and sent via gridftp to the remote site . at the remote site , the files would be untarred and uncompressed , and the job executed . at the end of the job , the output files would be tarred and compressed , and then transferred via gridftp back to the victoria disk server .this was found to be a successful mode of operation .access to software via afs proved to be reliable and efficient .we chose an application that would run extremely quickly on the processing nodes ( 30 minutes on a 2 ghz cpu ) .compression , transfer and uncompression was approximately 20 minutes for a 2 gb file .although the overall utilization of a remote cpu could be considered to be low if one includes the compression and transfer times , a more realistic application , such as simulation or reconstruction , would take hours rather than minutes to process data files of the same size .in this situation , we believe the cpu utilization would significantly improve .we have demonstrated that hep applications can be run on generic computing resources with relatively high efficiency . with ( modest ) design changes in the applications we expect that further gains in efficiency would be possible .further tests are planned using a sites with significantly larger resources with the aim of establishing a production level grid resource in canada .

Abstract: a grid testbed has been established using resources at 12 sites across canada involving researchers from particle physics as well as other fields of science . we describe our use of the testbed with the babar monte carlo production and the atlas data challenge software . in each case the remote sites have no application - specific software stored locally and instead access the software and data via afs and/or gridftp from servers located in victoria . in the case of babar , an objectivity database server was used for data storage . we present the results of a series of initial tests of the grid testbed using both babar and atlas applications . the initial results demonstrate the feasibility of using generic grid resources for hep applications .


the problem of distributing particles uniformly over a metric space has proved an inspiring question for mathematicians , and has also attracted the attention of biologists , chemists , and physicists working on crystallography , molecular structures , and electrostatics .we consider an interacting particle system with a repelling force between the particles . under influence of the force ,the particles arrange themselves in the most energy - efficient manner ( one that minimises the total amount of energy in the system ) .the rationale is that repelling particles tend to spread apart until there is as much distance between them as possible , which results in some sort of `` uniform distribution '' of the particles .we investigate the case in which the repelling force between any pair of particles is given by a function of their distance .this function can take the form , with .this is a generalisation of the _ inverse square law _ that is well known in physics , where it describes the behaviour of forces like electrical charge .it also contains the reduction in power density of an electromagnetic wave as it propagates through space , known as _path loss_. path loss plays a crucial role in the design of wireless networks , for which the exponent normally ranges from 2 to 4 ( where 2 is for propagation in free space , and 4 is for relatively lossy environments ) .note that , since is a decreasing function , we assume that the repelling force becomes stronger when the particles move closer to each other .denote the locations of the particles by .the -energy experienced by particle is defined as , where denotes the metric .our original motivation stems from the area of wireless networks , in which particles are mobile users , and the -energy of a user is its interference with all other users .when experiencing too much interference , a user is unable to transmit data . for a given maximal sustainable interference level , a natural question is to find the maximal packing of users that can be active simultaneously without violating the threshold , i.e. , while maintaining -energy at most for each user . in the case that we will deal with , this question is intimately related to the problem of minimising the total energy among all pairs of particles ; see section [ sec : framework ] .a lot of research in energy minimisation focuses on spheres . in dimension one ,the uniform distribution on the circle is simply given by the equally spaced points ( roots of unity in the complex plane ) , but in higher dimensions it becomes less obvious on what type of patterns the particles arrange themselves , and this presents al sorts of mathematical challenges .  in this paper , rather than spheres or other continuous metric spaces , we consider a -dimensional grid as possible locations for the particles .further , to avoid boundary effects , we wrap around the boundaries .this grid has a natural embedding on a -dimensional torus , see figure [ torus ] , which is why we call it the -dimensional _ toric grid_.  let be the size of the grid in dimension  , so that we have a total of possible locations for the particles .it seems reasonable to expect that the best way , in terms of minimal energy , to distribute particles over this space is to place them in a _ checkerboard pattern _ , by which we mean a pattern in which exactly one particle is placed at any two neighbouring points .of course , because of the wrapping around , such a pattern exists only when all are even .  for any toric grid , regardless of its dimensions ,there are only two such configurations ( see figure [ square2 ] ) , and the checkerboard pattern is a natural `` uniform distribution '' on a toric grid .it is also a maximal - size _ independent set _ in the graph whose vertices are the possible locations and whose edges connect locations differing by in one coordinate and not at all in the remaining coordinates . the lee distance between two locationsis defined as the length of the shortest path , in terms of edges , between the corresponding vertices on this graph .the following conjecture formalises , to some extent , our intuition that checkerboard patterns are optimal .  for any toric grid with all even , and for any reasonable function of the lee distance ,the arrangements of particles that minimise the maximal -energy experienced by any of the particles are the two checkerboard patterns , and only these .of course , the validity of this conjecture depends on what _ reasonable _ means .it will certainly imply _ decreasing _ , but more conditions will be necessary .for the example of wireless networks the checkerboard conjecture has the following implication .when the threshold is increased slowly , an increasing number of users is allowed to be active simultaneously , and there will be a critical value at which this number becomes precisely . at that critical threshold , we then know that active users can only be arranged in a checkerboard pattern a phenomenon that we have first observed in simulations of wireless networks . for a large toric grid it is of course infeasible to prove the checkerboard conjecture by exhaustive search through all possible configurations .-grid , the black and white points denote the checkerboard configurations.,width=144 ]  -grid on a -dimensional torus.,width=288 ]  in this paper we prove the checkerboard conjecture in a large number of special cases .we first derive a continuous relaxation of our energy minimisation problem in section [ sec : framework ] .then , as a first ( and known ) special case , we prove the checkerboard conjecture for the one - dimensional toric grid and in section [ sec : circle ] . in section [ sec : hypercube ] we prove the checkerboard conjecture for the toric grid that has size two in any dimension and functions whose -th forward difference has sign .section [ sec : four ] then gives our strongest result ( which however does not immediately imply any of the previous two results ) : a proof for the checkerboard conjecture in the case where each is either two or a multiple of four , now assuming that is completely monotonic ; see section [ sec : four ] for this notion . finally , in section [ sec : open ] we discuss some problems open for future research .in this section we formulate a general version of our energy minimisation problem , which belongs to the realm of discrete optimisation .we then derive a continuous relaxation of that problem . if all optimal solutions of the relaxation happen to be feasible for the discrete problem , then they are also the optimal solutions for the discrete problem .this is our strategy for proving special cases of the checkerboard conjecture in the following sections .let be a positive integer , the _ dimension _ of our toric grid .let be positive integers , and set , a finite abelian group .let be the diagonal in .let be a function that is _ symmetric _( for all ) and _ -invariant _ ( for all ) .later we will add the restriction on that it is a suitable ( and in particular decreasing ) function of some -invariant distance on , so that we may think of as a repelling force between particles located at and .but for deriving our relaxation this restriction is not needed .next let be a natural number less than or equal to .let be a subset of of cardinality ; this is the set of locations of our particles . given we define called the _ energy of experienced by _ , and called the _ maximal energy _ of .the checkerboard conjecture concerns the following optimisation problem with .minimise the maximal energy over all subsets of cardinality .further we define called the _ total energy _ of .we can now formulate a second optimisation problem .minimise the total energy over all subsets of cardinality .an important relation between these two optimisation problems is the following .if a set minimises the total energy and happens to have the property that for all , then also minimises the maximal energy indeed , any with would necessarily have .the condition that does not depend on is satisfied , in particular , when is a coset of a subgroup of .indeed , the set is then equal to for all , and hence , independently of , by the -invariance of .checkerboard patterns are examples of cosets . in view of this relation between maximal energy minimisation and total energy minimisation ,most of our paper focuses on total energy minimisation .we proceed to derive a continuous relaxation , which uses the space of real - valued functions on .we represent a subset by its _characteristic vector _ defined by the space has two important additional structures .first , it is equipped with a -action defined by for and ; here the minus sign is customary but not strictly necessary .second , it has a natural inner product that is -invariant in the sense that for all .now we define the key quantity in this paper : the _ energy kernel _ which lives in the group algebra and acts by a linear map on : alternatively , one may think of as the symmetric -matrix whose -entry equals , and perhaps this conceptually simplifies the following computations .for any subset of we have   thus we have identified the total energy of a set as the inner product of with its image under the energy kernel . moreover , if has cardinality , then has the further properties , where is the all - one vector in .this motivates the following optimisation problem .minimise the `` fractional total energy '' over all satisfying the constraints .note that if we add the additional constraint that be a -vector , then this problem is just total energy minimisation .thus a feasible solution of the relaxation can be thought of as a `` fractional '' solution to the original problem , though this is slight abuse of language for two reasons .first , the optimal solution to the problem just stated may very well have irrational coordinates , so that it is not a `` fraction '' .second , it may have coordinates that are not in the interval  ] , but neither of these is integral or even rational .of course , a brute - force computer search over all configurations of particles on is possible in this case .such a search reveals that , up to translations , the following three characteristic vectors are the ones minimising the total energy : note that the first two are each other s images under swapping rows and columns , and that they represent the cyclic subgroups of generated by and , respectively .the last one is not a coset of a subgroup , but still has the property that the energies experienced by all particles are the same .this means that these configurations also minimise the maximal energy .we conclude that for the optimal solution to the fractional energy minimisation problem has little bearing on the original discrete optimisation problem , and it would be very interesting to find a strengthening of our relaxation that does give the optimal solutions for .  on the other hand , consider now .then the optimal solutions for fractional energy minimisation are , and these are exactly the characteristic vectors of the two checkerboard patterns . since fractional energy minimisation is a relaxation of total energy minimisation , this proves that the checkerboard patterns also minimise total energy . andsince they are cosets of a subgroup , the argument given after the introduction of shows that the checkerboard patterns are also the ( unique ) minimisers of .we have thus _ proved _ our first instance of the checkerboard conjecture . in the following three sections we follow exactly the same strategy : we determine the minimal eigenvalue of the energy kernel to determine the optimal solutions of fractional energy minimisation , and when these are the checkerboard patterns , then we are done .this works in quite a number of cases in particular , when each is either two or a multiple of four , see section [ sec : four]but not in general , see section [ sec : open ] .we conclude this section by relating our techniques and results to existing literature on energy minimisation .the most relevant reference is , which is primarily concerned with energy minimisation of repelling particles on high - dimensional spheres .there are close parallels between our approach and the techniques there .in particular , both papers make essential use of the representation theory of the natural symmetry group of the problem . in our casethis is the group itself , while in the spherical case it is the orthogonal group .the fact that is abelian ( and hence diagonalisable ) makes the representation theory much easier than that required for the spherical problem .on the other hand , there are also important distinctions .first of all , makes essential use of the fact that the symmetry group acts distance - transitively , while our group acts only simply transitively on itself .second , while deals with continuous optimisation problems , our optimisation problem is inherently of a discrete nature .it could be strengthened into a continuous problem by letting particles move on the continuous torus .if the energy - minimising configurations for that problem are ( unique up to translation and ) equal to our checkerboard configurations , then that implies our results ( provided that one uses the -norm , which is the continuous analogue of the lee distance ) . it would be interesting to know if the techniques from can be used to prove such a stronger statement .note that the pre - image in of the particles positions form a periodic set .the paper does discuss optimisation problems for such sets , but in the context where the lattice of periodicity is allowed to vary , as well . in our case ,the lattice is fixed to .our minimisation problem is also reminiscent of certain instances of the _ quadratic assignment problem _ that are studied in . in that paperit is proved that the class of those instances is np - complete . in view of this, minimality of checkerboard configurations is an interesting result . on the other hand , in the corresponding _ maximisation _problem is proved to be solvable in polynomial time . in our setting, this would correspond to taking for some _ increasing _ function of the distance , which has an interpretation in terms of _ attracting _ particles rather than repelling ones .this problem , in turn , resembles the problem of _ how to build an optimal city _ . our attention , however ,is focused entirely on the setting where is some _ decreasing _ function of the lee distance .the first special case that we consider is the one - dimensional toric grid .that is , we consider , with a positive integer , and define a graph on by connecting elements that differ by .one can think of this as equally spaced points on a circle .further we define the function as , where denotes the lee distance between and and is a decreasing strictly convex function . in the continuous problem of letting particles move on a circle is considered and it is shown that total energy is minimised if and only if the particles are equally spaced .this validates the checkerboard conjecture for this special case .the proof in  is based on a direct comparison between the total energy in the configuration with equally spaced particles ( i.e. the checkerboard configuration and its translations ) and the total energy in any other configuration . to get a better feeling for the technique of section [ sec : framework ] we now assume and prove that fractional energy is uniquely minimised as well by the checkerboard vectors .that is , we will prove the following result .[ thm : circle ] assume that is a multiple of .then the fractional energy over all with is minimised by the characteristic vectors and of the checkerboard configurations and only by these . as a consequence ,both the total energy and the maximal energy among all subsets with are uniquely minimised by and .  by proposition [ prop : eigenvalue ] we know that set of optimal solutions of the fractional energy minimisation problem is determined by the smallest eigenvalue of the energy kernel . as discussed in section [ sec : framework ] the eigenvalues are functions on the dual group , with the group of complex -th roots of unity . and the fractional energy is uniquely minimised by the checkerboard vectors if the eigenvalue has a unique minimum at , which lives in as is even .thus the following proposition implies theorem [ thm : circle ]  the function , has a unique minimum at .as is even we can write now note that the elements of the group can be represented by for . with a slight abuse of notation we can thus write so , we need to prove that .  for this first define by .\ ] ] now note that all eigenvalues are real numbers , so for all .hence , implies .  to prove thislet us look at the derivative of .differentiating we get to simplify this expression note that as can be proved using the prosthaphaeresis formulas .we thus find hence , for and for .further , by lhpital s rule , . also , for and for .thus has a unique minimum at , which completes the proof .in the previous section we considered the one - dimensional toric grid with an arbitrary number of points . in this sectionwe consider the -dimensional toric grid , but now we will assume that the grid has size two in all dimensions .that is , we consider .further we define a graph on by connecting two elements if they differ by for some position of the .one can think of this graph as the -dimensional unit hypercube ; the corners of this hypercube are the points of the toric grid .in fact , one should construct a -torus from the -dimensional hypercube , but this only connects corners that are connected already , as our grid has size two in every dimension .let be such that its -th forward difference has sign , i.e. , we assume that ( x )  > 0\ ] ] for all . here denotes the forward difference , ( x ) = f(x+1 ) -f(x)$ ] .we now define the function as , where denotes the lee distance between and .we will validate the checkerboard conjecture for this case .that is , we will prove the following theorem .[ thm : hypercube ] the fractional energy over all with is minimised by the characteristic vectors and of the checkerboard configurations and only by these . as a consequence ,both the total energy and the maximal energy among all subsets with are uniquely minimised by and .  to prove theorem [ thm : hypercube ] we again capitalise on proposition [ prop : eigenvalue ] and determine the smallest eigenvalue of the energy kernel .as the toric grid has size two in all dimensions we know by the discussion in section [ sec : framework ] that the eigenvalues are functions of the dual group .we further know that the fractional energy is minimised by the checkerboard vectors if the eigenvalue has a unique minimum at .this we prove in the following proposition , which thus implies theorem [ thm : hypercube ] .the function , has a unique minimum at .because of symmetry it suffices to prove that if are characters that differ only in the first position , where , then . we therefore compute writing for the number of ones among the and using dummy for the number of indices with and dummy for the number of indices with and the above expression equals where the last inequality follows from the conditions on and the last equality follows from the well - known formula ( x ) = \sum_{k=0}^m \binom{m}{k } ( -1)^{m+k } f(x+k);\ ] ] see for instance ( * ? ? ? * , equation 1a ) .this proves the proposition .in this section we prove our strongest result about the checkerboard conjecture , concerning particles on the abelian group when each is either two or a multiple of four .define a graph on by connecting two elements if they differ by for some position of the .the lee distance is the shortest - path distance between in that graph , and denoted by .the energy will be measured with a function that we assume to be ( strictly ) _ completely monotonic _ ,i.e. , and with for all and for all .  typical examples of completely monotonic are for a positive real number .these functions appear prominently in the paper , as well .moreover , as mentioned in the introduction , these function generalise the inverse square law in physics , and describe the path loss for electromagnetic waves .note that if is completely monotonic , then so is , because for all .iterating , we find that is a positive function , so that the restriction of to satisfies the condition on . in particular , theorem [ thm : hypercube ] implies the special case of the upcoming theorem [ thm : fourfolds ] where all are equal to .define the function as .the maximal energy , the total energy , the energy kernel , and the fractional energy are defined using this function .[ thm : fourfolds ] assume that each of is either or a multiple of .then the fractional energy over all with is minimised by the characteristic vectors and of the checkerboard configurations and only by these . as a consequence ,both the total energy and the maximal energy among all subsets with are uniquely minimised by and .  by proposition [ prop : eigenvalue ]it suffices to find the smallest eigenvalue of the energy kernel .recall that the eigenvalues are functions on the dual group , which in our present setting we may identify with , where is the group of complex -th roots of unity .since all are even , contains the real character , with character space spanned by the vector defined by .the checkerboard configurations have characteristic vectors .thus the following proposition implies theorem [ thm : fourfolds ] .[ prop : fourfolds ] the function sending to has a unique minimum at .  the completely monotonic function can be written as where is non - decreasing and the integral converges for ( for this theorem of bernstein see ( * ? ? ?* chapter iv , theorem 12b ) ) .thus , after interchanging integral and ( finite ) sum the function that we seek to minimise is seen to equal for this function to have a unique minimum at it suffices that for each fixed the function has a unique minimum at . at this point , there is no harm in including in the sum , which adds a constant term independently of .writing , we want to minimise over all characters .write ; then the lee distance equals , where we use the notation also for the lee distance in the individual .hence we have which factorises as the product of the factors for .thus we are done if we can show that each of these factors is positive for all , and minimal at .what remains is an easy calculation .simplify notation by fixing and writing . as a warm - up , consider the case where .then the trivial character of is mapped to , while the character of is mapped to .the latter value is smaller than the former , as desired .next assume that is divisible by , and consider the function sending an -th root of unity to now equals .if it equals , then this expression reduces to since , this is a positive number for any , and its smallest value is attained for the -th root of unity furthest away from in the complex plane , which equals since is a multiple of .next , if equals , then the expression above reduces to which is again positive for all with and minimal for the furthest away from in the complex plane ( which equals ) .it remains to compare and .for this , note that the factor in the expression for is smaller than the factor in the expression for , while moreover is further away from than .hence the minimum is attained at , as desired .this concludes the proof of the proposition , and hence the proof of theorem [ thm : fourfolds ] .the problem in extending this argument to the case of general even is that in the proof of the proposition , when is odd and at least , can very well be _ larger _ than . in other words ,proposition [ prop : fourfolds ] does not extend to that situation for general completely monotonic functions .extensive numerical evidence with and up to suggests that the proposition _ does _ extend to the case where ( and probably even for with ) , in which case also theorem [ thm : fourfolds ] extends .of course , the checkerboard conjecture may still very well hold for general completely monotonic and general even , even when proposition [ prop : fourfolds ] does not . to prove this, one would like to have a combinatorial / algebraic argument why the eigenspaces corresponding to characters having some entries equal to the relevant with odd are no good for finding -vectors . at this momentwe have no such argument .[ re : dft ] note that the table of eigenvalues of contains entries , and evaluating each individually involves a summation over , so that a straightforward implementation would require ( floating - point ) operations .however , the table of eigenvalues is nothing but the _ fourier transform _ of the table of values , so that algorithms for ( -dimensional ) _ fast fourier transform _ may be used to compute the table of eigenvalues more efficiently .we have used mathematica s built - in function fourier in our numerical experiments .for instance , figure [ fig : n10 ] shows the eigenvalues of the energy kernel for and and as a function of , standing for the character .the `` rough edges '' are related to the even / odd effect in the proof above , but they smooth out in the middle , so that the minimum is attained at , which corresponds to the character .in this paper we have proved the checkerboard conjecture for toric grids and energy functions for which the unique minimal eigenvalue of the energy kernel is uniquely attained at the character in the dual group .indeed , the minimal eigenvalue of _ always _ governs the solution to fractional energy minimisation ( proposition [ prop : eigenvalue ] ) , and if it is uniquely attained at , then the minimisers of fractional energy minimisation are -vectors and hence minimisers of the original problem .this motivates the following open problems .one would like to extend the results of section [ sec : four ] to the case where some of the are larger than but equal to modulo .computer experiments with two - dimensional grids up to suggest that for ( and perhaps for general inverse power laws ) the minimal eigenvalue of the energy kernel is still uniquely attained at . however , a proof of this fact would require more sophisticated analytical methods than the factoring into one - dimensional instances that we used there .alternatively , one might try and find a combinatorial argument why the minimisers of total energy minimisation are necessarily perpendicular to the eigenspaces of corresponding to the `` undesirable '' characters , thus sharpening the relaxation .the question remains for which metrics other than the lee distance the checkerboard conjecture will hold .for the euclidean metric the analogue of proposition [ prop : fourfolds ] does not hold for general completely monotonic functions .the first steps of its proof go through when one replaces the lee distance with the square of the euclidean distance .this holds in particular for the all - important factorisation step .one is then lead to minimise over the -th roots of unity , where stands for the euclidean metric on the one - dimensional toric grid , and where is a real number greater than .however , for close to the minimum is _ not _ in general attained at ; see figure [ fig : n8euclid ] . on the other hand , extensive numerical evidence for -dimensional grids up to suggests that the analogue of proposition [ prop : fourfolds ] does hold when the energy is given by an inverse power law of the euclidean distance ( and if these computations were done in suitable interval arithmetic , they would _ prove _ the checkerboard conjecture for those grids ) .perhaps one can prove such a statement by bounding the contribution , in the bernstein expansion of these inverse power laws , of the bit where is small .the checkerboard conjecture is not true for _ every _ metric however .for example , for the chebyshev ( or ) metric one can compute that the maximal energy of the patterns in figures [ square2ndbest ] and [ square3rdbest ] is lower than the maximal energy of the checkerboard pattern in a -grid .it is unknown what properties a metric should have in order for the checkerboard conjecture to be true .it is also interesting to consider _ nearly optimal _ configurations of particles in toric grids . when considering _ total energy _ , these configurations are probably given by small perturbations of checkerboard patterns .however , nearly optimal configurations for _ maximal energy _ seem to exhibit beautiful , regular patterns .for example , for a -grid we have computed the maximal energy of all possible configurations for the function and for both the lee metric and the euclidean metric .this computation shows that the checkerboard conjecture holds ( a fact that one can prove more efficiently using the discrete fourier transform as in remark [ re : dft ] ) , but also that the second and third best configurations agree for the lee and euclidean metrics ( see figures [ square2ndbest ] and [ square3rdbest ] ) .the fourth best configurations are different for the two metrics though , see figures [ square4thbestlee ] and [ square4thbesteuclid ] .it is a widely open question how to prove that certain configurations are second or third best .rainer e. burkard , eranda ela , gnter rote , and gerhard j. woeginger .the quadratic assignment problem with a monotone anti - monge and a symmetric toeplitz matrix : easy and hard cases ., 82(12 ( b)):125158 , 1998 .

Abstract: we explore the minimum energy configurations of repelling particles distributed over possible locations forming a toric grid . we conjecture that the most energy - efficient way to distribute particles over this space is to place them in a checkerboard pattern . numerical experiments validate this conjecture for reasonable choices of the repelling force . in the present paper , we prove this conjecture in a large number of special cases most notably , when the sizes of the torus are either two or multiples of four in all dimensions and the repelling force is a completely monotonic function of the lee distance between the particles .  supported by microsoft research through its phd scholarship programme ] supported by a vidi grant from the netherlands organisation for scientific research ( nwo ) ; also centrum voor wiskunde en informatica , amsterdam ] supported by an erc starting grant and a top grant from the netherlands organisation for scientific research ( nwo ) ]