From Helmut Jürgensen's Former Students: The Game of Informatics Research
FFor submission to the Journal of Automata, Languages and CombinatoricsCreated on March 11, 2019
FROM HELMUT JÜRGENSEN’S FORMER STUDENTS:THE GAME OF INFORMATICS RESEARCH
Mark Daley ( A ) Mark Eramian ( B ) Christopher Power ( C ) Ian McQuillan ( B,D ) ( A ) Department of Computer Science, University of Western OntarioMiddlesex College, London, ON, Canada [email protected] ( B ) Department of Computer Science, University of Saskatchewan,110 Science Place, Saskatoon, SK, Canada [email protected] [email protected] ( C ) Department of Computer Science, University of York,Heslington, York, UK [email protected]
ABSTRACTPersonal reflections are given on being students of Helmut Jürgensen. Then, we attemptto address his hypothesis that informatics follows trend-like behaviours through theuse of a content analysis of university job advertisements, and then via simulationtechniques from the area of quantitative economics.
Keywords: informatics, trends, hiring practices, simulation
1. Personal Reflections
The four authors of this paper were students of Helmut Jürgensen, with the latterthree supervised by Helmut for all of our graduate studies. We start with personalreflections on this experience.
I recall sitting at a desk in the rotunda outside Helmut’s office reading Saunders MacLane’s
Categories for the Working Mathematician . Helmut stepped out of his office,regarded me for a moment, and then said: “It is certainly beautiful, but one mustbe careful not to lose one’s entire life to it.” While I was not officially a student ( D ) Supported in part by a grant from NSERC.Published at Journal of Languages, Automata and Combinatorics, 23, 2018, 127–141 DOI:10.25596/jalc-2018-127 a r X i v : . [ c s . G L ] M a r M. Daley , M. Eramian , I. McQuillan , C. Power of Helmut’s, I consider him my adoptive second Doktorvater nonetheless, and thisinteraction is illustrative of the thoughtful mentoring I received from him.Helmut and I share many interests: computability, information, art, music, lan-guage, semigroups, typesetting, history, computing technology, and more; I have fondmemories of long conversations on these topics with Helmut, and his students, frommy time as a graduate student. Amongst all that I learned from Helmut, there aretwo lessons that I adopted as guiding personal philosophies and to which I believeI owe much of the good fortune I have had in my own career. The first:
Formalizeeverything.
When dealing with formal systems, it is too easy to fool oneself to in-correct conclusions with ad hoc informal reasoning. When I collaborated with him,Helmut always insisted on complete rigour in everything we did, and the end productwas always stronger for it. The second, and most important:
Be fearlessly inter-disciplinary . The fluidity with which Helmut moved between research questions anddisciplines solidified in my mind an exemplar of the type of scholar I aspired — andstill do aspire — to be.
When I think of my time as Helmut’s student I remember the deep discussions, theunwavering confidence he had in me even when I didn’t feel confident in myself, thesummer backyard BBQ’s Helmut held for his students at his house annually, and, ofcourse, the stories. I had the fortune of knowing Helmut before I even enrolled inuniversity. After my first undergraduate year, I approached him to ask if he knewof any professors who were seeking summer research assistants. He asked aroundand, finding none, offered to hire me himself. That summer project was my firstforay into research, and probably why I stuck with it. I recall spending that summerreading Helmut’s Pascal code (ported from Algol 60 of course) with a German-Englishdictionary at my side to decipher the variable names. Helmut kept me engaged inresearch throughout my undergraduate career with many interesting projects and ingraduate school allowed me to combine my interests in digital image processing andtheoretical computer science in a way that probably not many could. He taught methe thrill of success and that failure is normal. He cultivated in me a profound loveof L A TEX, a pedantic insistence for typesetting perfection, and a crippling sensitivityto poor typographic kerning.In supervising my own students I look to Helmut’s example of patience and sup-portiveness. Working with Helmut was one of the most inspirational and fun times ofmy life, and I am thankful for the experience. I am thrilled and proud to collaboratewith my contemporaries on this paper in Helmut’s honour.
I have very fond memories of my time as a graduate student working under thesupervision of Helmut Jürgensen. I first met Helmut while taking an advanced courseon automata and formal language theory as an undergraduate student. I was excitedby the foundational aspect of his emphasis; we learned about Gödel’s incompleteness rom Helmut Jürgensen’s Former Students: The Game of Informatics Research
My warmest memories of working with Helmut are of him encouraging me to pursuea research career at the end of my first year of my doctoral studies, when I waslost in a sea of proofs and theories, uninspired, and considering leaving. He kindlytook me aside, and said “There are some computer scientists who are inspired bythe infinite beauty of mathematics. There are others who are fascinated by creatingnew and wondrous things. You are that second kind, embrace it, and be happy.”Over a decade later, I still start my programming lectures with that story. Helmutencouraged me to work with people with disabilities, not only because it is a noblething to do, but also because of the challenge of thinking outside the traditionalboundaries of software design. He connected me with people such as the authors ofthis paper, who have been lifelong friends and colleagues. He introduced me to seniorresearchers in Canada and Europe and, as I found out years later, cold-called my firstboss to tell her the potential I had, and what an asset I would be to her team. I cansafely say, my life and my career would have been far less interesting and meaningfulif not for his friendship and guidance.In meetings, after sharing stories of new discoveries, bits of gossip from othergroups around the world, and lamenting languages he had forgotten over the years,Helmut would always say to me “Now go away, and come back and tell me somethinginteresting.” With my own students, I tell them the same thing, for that is possibly thebest encouragement a student can have: knowing that they have something important
M. Daley , M. Eramian , I. McQuillan , C. Power to say and that someone will listen. Hopefully, my friends and I have honoured hissentiment in this paper and have found something he will think is interesting.
2. The Game of Informatics Research
Helmut would frequently enter the student lab where we worked and tell stories aboutresearchers and academia in general. When we were reminiscing about this, we all re-called one particular analogy that he made relating computer science and informaticsresearch to the board game Clue. Clue (Parker Borthers, 1949) is a 3-6 player gamein which players control characters which they move from room to room in a houseattempting to solve a murder by guessing where, by whom and with what weapon themurder was committed, eventually coming to the solution by a process of elimination. “Informatics in those growing-up years was a field of fast-moving focus.Informatics then and even today reminds me of the game of Clue — orthe corresponding movie —, in which a Mr. Body has been murdered andthe remaining group of people investigates by running around in a panicfrom one room to another and back again — occasionally leaving someonebehind. Once the easy problems of a field have been solved, most peoplemove on to the next fashionable field, possibly even proclaiming the oldfield dead.” — H. Jürgensen, “People and Ideas in Theoretical Computer Science” [2].In relating this to us in person, Helmut would also add additional flavour to theanalogy. He would say that several very clever people would enter a room, say theconservatory, and start asking some clever questions. Then, upon everyone else inthe game hearing those questions, they would all run into the conservatory and startasking very similar questions, with small variations. The rope is replaced with thewrench. Miss Scarlet is replaced with Colonel Mustard. Eventually, you find thateveryone is asking the same questions. Then, the clever people who first were in theroom, move onto the dining room and begin asking new questions. The crowd thenraces behind them into the dining room and begins asking the same questions theyasked in the conservatory, because it is easy and comfortable. However, there aresome hard questions left in the conservatory, and some very clever people will staybehind and work to find and answer those questions. Helmut would say: “Your goalas a researcher is to be the first person in the room, or the last person in the room.”We wanted to test the hypothesis that informatics research does indeed largelyfollow this trend-like behaviour. Clue -like Behaviour in Hiring
When considering the game of
Clue in informatics research, it is first worth consid-ering whether this type of behaviour is actually prevalent in the research community.Certainly, there are trends that happen in funding regimes world-wide. It has beenthe experience of the authors that funding agencies such as NSERC in Canada, NSF rom Helmut Jürgensen’s Former Students: The Game of Informatics Research st century, and governments become more driven bya need to meet national industrial objectives, it is likely that these surges of fundingto specific areas will continue or become more pronounced. However, do the insti-tutions respond in kind? Do the hiring practices focus on broader areas, or do theyspecialize in ways that are comparable to the way funding is targeted at particularsubareas? Anecdotally, anyone who follows job advertisements for a period of morethan a couple of years will think there is a similar trend; however, to our knowledge,this question has never been empirically investigated. In this section, we undertake aqualitative study of job advertisements to answer the question as to whether trends inhiring seem to support the notion of a Clue -like game taking place in the ComputerScience academy.In order to answer this question, we undertook a content analysis of a set of jobadvertisements from Canada and the United States. Content analysis is a means ofmaking inferences about text that are both reliable and replicable by researchers [3].This is usually done by taking a collection of written source texts and producingmarkup codes for particular types of items contained within. In this case, we areinterested in identifying, coding, and making inferences about the types of researchersthat institutions hire over time. We are interested in identifying whether there is aprevalence of institutions moving rapidly into new “rooms” to chase research moneyand/or find trendy questions to ask, only to move on again soon thereafter.
We identified the Computer Research News (CRN) archive produced by the ComputerResearch Association (CRA) as an ideal set of documents for the purpose of answeringthese questions. The CRN is a broad-reaching publication, with a wide readershipby North American academics and beyond, that has been consistently published overthe last 25 years, originally 5 times a year and later moving to 10 times per year in2012.We selected a 20 year period from 1992 through to 2012 which captures a majorperiod of growth and diversity for the informatics discipline. Each publication has aset of job opportunities advertised as part of its main content, with the number ofadvertisements per issue ranging from 5 to 135. In terms of distribution, in generalthe first publication of each year (January) and the fifth publication (November)contained the largest proportions of job opportunities, corresponding with typicalhiring start dates of July or September at most institutions. Figure 1 shows thenumber of advertisements per issue over time. The number of ads increased a lot overthe first 34 issues in the dataset, corresponding to the period from 1992 to 1998, thenbecame fairly steady. The aforementioned hiring cycle is also evident from the peaksand valleys.
M. Daley , M. Eramian , I. McQuillan , C. Power A d . C oun t Number of Academic Job Advertisements in CRA Issues, 1992-2012
Figure 1: Number of academic job advertisements per CRA issue over time between1992 and 2012. The hiring cycle is evident from the peaks of advertisements in theNovember and January issues. Issues with a count of zero are missing from the archiveor were corrupted and unreadable.
We chose to examine each individual advertisement and code the topics of researchcandidates should pursue in order to be desirable or preferable for hiring. We in-cluded in our data collection all advertisements for academic research positions andindustrial research positions, including visiting professor positions if they requireda research component. Advertisements for postdoctoral fellows, department heads,administrative/director positions, teaching-only positions, and clearly non-researchindustrial positions were excluded. In all, 3248 of 4276 ads met our inclusion criteria.In place of having a completely open and emergent classification scheme, we ex-amined the first issue from each year over the 20 year period, and captured the mostcommon areas that were advertised for. This produced an initial list of 27 areas. Itwas noted during this process that there was a wide variety of different terms used bythe community for describing identical areas of study. We also included a category
Other to capture those items that did not seem to fit one of the original categories.When using this code, we recorded the exact words from the advertisement for pur-poses of later review. After coding was complete, this
Other category and its collectedterms were examined for common terms. Some terms were fit into existing categories(e.g. multicore was included in parallel and distributed computing ). For those areasremaining in the
Other , category, they were merged where there were recording dif-ferences (e.g. e commerce vs. e-commerce ) or where they described the same areain different ways (e.g. multi-agent systems and agent-based systems ). Coding to de-termine the list of categories as well as subsequent coding of the remainder of thedataset was performed manually by three of the authors (M.E., I.M., and C.P.).The complete list of categories used in the coding scheme were: Open (no spe-cific specialization was requested), Experimental Computer Science, Applied Com-puter Science, AI/Machine Learning (including related areas such as data mining),Big Data, Bioinformatics (including computational biology), Computer Architecture(including all hardware/computer engineering areas), Computer Graphics (includ-ing multimedia), Computer Vision (including image processing), Data Visualization, rom Helmut Jürgensen’s Former Students: The Game of Informatics Research
We undertook an inter-coder reliability task to ensure that the coding of the data wasdone in a consistent, repeatable, and valid way. Two researchers were given identicalsets of 40 job advertisements selected from across the sample and across the codes.Each researcher independently coded the sample using the coding scheme, and thesets were brought together for comparison. To determine inter-coder agreement weused Cohen’s kappa, defined as having p o as the relative observed agreement amongcoders, and p e is the probability of chance agreement by the coders. κ = p o − p e − p e With κ = 1 representing perfect agreement, the coders of the job advertisementsachieved κ = 0 .
83. When examining the results, many of the errors came from oneindividual coding two or more items within job advertisement separately, while theother merged these items into a single code. When removing these duplication errors,the inter-coder agreement was κ = 0 .
96, well above the threshold for having highconfidence that the coding of the advertisements was done reliably.
The recorded data were summarized in a matrix consisting of a row for each of the27 topic areas, and a column for each year. The entry in row i , column j was theproportion of areas mentioned in year j that were area i , denoted p ( i, j ). Formally,let A j ( k ) be the k -th ad in year j , N ( A j ( k )) be the number of uniquely coded areasmentioned in an ad, and N j = P k N ( A j ( k )) be the total number of topics mentionedin ads in year j . Then p ( i, j ) = |{ A j ( k ) | A j ( k ) mentions topic i }| N j . To get a visualization of the entire dataset, each row of the matrix p was plotted inan area line graph, shown in Figure 2.Many individual topics that have substantial proportions of job advertisements areshown separated out from the set in Figures 3 though 5. In Figure 3, we see a setof areas that show a dramatic boost at the beginning of the 1990s and then a steady M. Daley , M. Eramian , I. McQuillan , C. Power P r opo r t i on o f A nnua l M en t i on s . Trends in Computer Science Job Ad Area Preferences
Big DataOtherWeb Tech.TCSSoft. Eng.Social CompSecurityScientific Comp.Prog. Lang.Parallel/Dist.OSNetworksModelling/SimMobileHCIHPCGamesDatabasesData. Vis.VisionGraphicsArchitectureBinfoAI/M.L.AppliedExperimentalOpen
Figure 2: Overall results showing academic ad preferred area trends. The width of anarea i ’s band at year j represents p ( i, j ). drop off over the period of 20 years. Graphics peaked a little later, but still early inour dataset, and then steadily declines.In Figure 4 we see four areas that, aside from occasional peaks, are relatively stableand steady in their hiring. It is interesting that in the case of Theoretical ComputerScience (TCS), there is a slight increase over time though this may be an artefact ofthe code groups, with data structures and algorithms being particularly broad.Figure 5 shows six areas that seem to still be climbing in hiring trends. Securityand Artificial Intelligence/Machine Learning are both enjoying healthy surges in hir-ing, and we have separated mentions of Big Data to show a particular field that hasbecome popular in the last 5 years. Finally, the Other category in Figure 5 is inter-esting, as it has substantially increased over the time period. This category includesseveral interdisciplinary topics such as e-commerce, arts and computing, heritage andcomputing etc., plus some other specialized subareas that do not fit into any of the26 other topic areas. From the results above, there is an interesting story that emerges in relation to the
Clue hypothesis. We see a large number of areas that have a spike in hiring and thena steady decrease to a consistent level of hiring. These tend to be quite fundamentalresearch areas to computer science — when we were PhD students, Helmut wouldcall these “The very pipets and reagents we work with.” While it is very likely thatTheoretical Computer Science had an earlier peak, when giants strode boldly into rom Helmut Jürgensen’s Former Students: The Game of Informatics Research P r opo r t i on o f A nnua l M en t i on s Computer Graphics P r opo r t i on o f A nnua l M en t i on s Parallel and Distributed Computing P r opo r t i on o f A nnua l M en t i on s Operating Systems P r opo r t i on o f A nnua l M en t i on s Software Engineering P r opo r t i on o f A nnua l M en t i on s Programming Languages P r opo r t i on o f A nnua l M en t i on s Databases
Figure 3: Yearly proportion advertisements mentioning areas of Computer Science andInformatics that appear to have peaked around the beginning of our data set and aredeclining steadily. new domains, the early 1990s had spikes of hiring in systems focussed foundationalresearch. Core systems topics were invested in first by departments, specifically Oper-ating Systems, Parallel and Distributed Systems, Software Engineering, and Program-ming Languages. Following these areas, we see the
Clue -like behaviour in Networks,Databases, and Computer Graphics, which lag behind with their peaks, and then fol-low the same drop off trend in hiring. Younger fundamental areas, like HCI and DataVisualization, seem to miss this investment period, but have maintained a steadypresence in hiring.The data seems to match societal shifts that were happening at the time. Thisinvestment in core systems topics Computer Science by institutions coincides with0
M. Daley , M. Eramian , I. McQuillan , C. Power P r opo r t i on o f A nnua l M en t i on s Theoretical computer science P r opo r t i on o f A nnua l M en t i on s Human-Computer Interaction P r opo r t i on o f A nnua l M en t i on s Data Visualization P r opo r t i on o f A nnua l M en t i on s High-performance computation
Figure 4: Yearly proportion advertisements mentioning areas of Computer Science andInformatics that appear to have remained stable over a long period of time. the advent of reasonably inexpensive personal computers and just prior to the main-streaming of graphical user interfaces and internet access. Computing technologyexploded into the mainstream consciousness of society, and that paved the way forinvestment in these foundations just prior to our dataset. Given our sample startsat a notable peak in Computer Science research and practice, it is likely that we areseeing the end of a very long investigation of
Clue rooms that began in the 1970s withsteady growth on the back of advances in so many technologies, from the Xerox Starto ARPANET, and then a steady drop-off to a base level for the above fundamentalareas over 20 years.While we posit that some of this hiring is as a result of that increased availabil-ity of resources at institutions for Computer Science systems research as it becamemainstream and impactful, with another contributing factor for being the academyreacting to a steady increase in student numbers. After all, it would only be a fewshort years after these big periods of investment by institutions that the first dot-comboom and bust happened where teaching numbers bloomed, just as the authors wereentering their PhD programmes.After the ascendency of these foundational areas, we can see Security surges in 2005,which corresponds to the first time over 50% of the developed world had internet accessand the rise of Google [1]. For AI/Machine Learning, which many would consider afoundational area, we seem to have captured the end of the AI Winter [4] with thesteady climb in a variety of different contexts over the 20 years. Each of these areas rom Helmut Jürgensen’s Former Students: The Game of Informatics Research P r opo r t i on o f A nnua l M en t i on s Security P r opo r t i on o f A nnua l M en t i on s AI/Machine Learning P r opo r t i on o f A nnua l M en t i on s Bioinformatics P r opo r t i on o f A nnua l M en t i on s Big Data P r opo r t i on o f A nnua l M en t i on s Networks P r opo r t i on o f A nnua l M en t i on s Other
Figure 5: Yearly proportion advertisements mentioning specific rooms in the game ofinformatics that are currently increasing or have peaked and declined in a relativelyshort time. seem to be enjoying particularly long periods of targeted hiring.The question remains: why has hiring gone down in foundational areas after theyear 2000? The answer likely lies in the increasingly large number of areas of inves-tigation that emerged during the sample. Bioinformatics, Games, Web Technologies,and the myriad of research questions in the Other category, have led to an increasinglyfragmented field as evidenced in Figure 2. That fragmentation tends to lend evidenceto people dividing up into different rooms to ask questions for a period of time. Theserooms likely do contribute knowledge, to some extent, to mature foundational areasas well and to the game as a whole. For example, when someone is hired into con-vergent areas such as bioinformatics, computational neuroscience, or digital heritage,2
M. Daley , M. Eramian , I. McQuillan , C. Power there will be advances to the foundational areas in support of these new areas. It isalso likely the case that, as interdisciplinarity has grown, having people who are inareas that are malleable to application areas has been of benefit to departments asit potentially allows them to adapt to changing priorities in the research landscape,while still addressing the foundational teaching that can be delivered, decreasing theneed for targeted hirings in those areas as the pioneers retire. However, it is importantto note that many of specific areas appear and nearly vanish from the landscape veryquickly, giving weight to the
Clue analogy.One very interesting feature in the data is that, going back to 1992, there was arelatively low percentage of Open positions, ranging from approximately 10% downto almost nothing in any given year. This tends to indicate that academic institu-tions, in general, have always been quite specific in their Computer Science hiring,something that is often anecdotally attributed to modern hiring practices. While thedrivers behind hiring trends remain complex and difficult to interrogate, this con-tributes to the theory that informatics research is driven by specific needs at the timewithin the institutions and the funding landscape. The analysis of the academic jobadvertisements does seem give strong evidence that the
Clue -like behaviour positedby Helmut is alive and well in the academic community.Now that we have established that this behaviour is indeed happening in theacademy, we will investigate whether this is an optimal strategy for research.
4. The Game of Informatics
Reflecting Helmut’s broadly interdisciplinary approach to research, we now apply themodel of Neal [6] — exposited originally in the quantitative economics literature tomodel the dynamics of career choice — to investigating topic- and field-switchingamongst researchers. We make several assumptions, chief amongst them the assump-tion that researchers will seek to optimize their level of grant funding.Define total research grant income g t = θ t + (cid:15) t where θ t is funding due to the choiceof research field while (cid:15) t is funding due to choice of research topic . We proceed withdiscrete time modelling. At each time point t , a researcher has three options:( I ) Change nothing( II ) Select a new primary research topic, within current field ( (cid:15) t resampled)( III ) Switch research fields (both θ t and (cid:15) t are resampled)Observed grant funding levels allocated by granting agencies typically assume abroad range of values, with the grants at the extrema being relatively less common.In our model, it is necessary to select, a priori, distributions F and G from which wemay sample the funding level components θ t and (cid:15) t for each individual researcher. Inour investigation here, we will begin by grossly oversimplifying reality and assumingthat these distributions are uniform, but then move on to more realistic choices of F and G that match observed grant histograms for Canada’s NSERC.The game for each researcher now becomes one of maximizing lifetime grant in-come — keeping in mind that our researchers are only permitted to annually select rom Helmut Jürgensen’s Former Students: The Game of Informatics Research β ) for which values less than one expresscorrespondingly less certainty about the future.We draw θ t ∼ F, (cid:15) t ∼ G , with F and G independent and denote the future discountas β . Our goal is to maximize E ∞ X t =0 β t g t . (1)Our value function V ( θ, (cid:15) ) is the maximum of equation 1 over all feasible policies.The maximum is found computationally by iterating to convergence on the Bellmanequation . We implemented this calculation directly with a simple Python script.A full description of this process is beyond the scope of this paper; the details arepresented concisely in Neal [6] and the interested reader may refer to [5] for a gentlerexposition. We investigate optimal policies; θ and (cid:15) take values between 0 and 5 and, as per theexposition above, their sum represents the funding level of the researcher.Consider first a grossly oversimplified situation where F and G are strictly uniformand researchers are optimistic about the future ( β = 0 . θ , after which aresearcher will experiment with new topics until reaching a static condition with high θ and (cid:15) (Figure 6(a)). Though this policy is certainly consistent with the observed Clue -like behaviour discussed in this manuscript, the modelling assumptions are notparticularly realistic.We now consider a more realistic model in which the distributions F and G aresynthetic bimodal distributions consisting of a modified beta binomial with varyingparameters a, b investigated, and an additional mass at zero. The mass at zero rep-resents the risk of losing funding altogether when changing fields or topics. For F we begin with a beta binomial having parameters a = 10 . , b = 10 . G we choose a straight beta binomial having parame-ters a = 10 . , b = 10 .
0. The researchers remain optimistic with a future discount of β = 0 . viz., max( θ + (cid:15) + βV ( θ, (cid:15) ) , θ + R (cid:15) G ( d(cid:15) ) + β R V ( θ, (cid:15) ) G ( d(cid:15) ) , R θ F ( dθ ) + R (cid:15) G ( d(cid:15) ) + β R R V ( θ , (cid:15) ) G ( d(cid:15) ) F ( dθ )) M. Daley , M. Eramian , I. McQuillan , C. Power (a) (b)
Figure 6: Discrete modelling results (a) when F and G are strictly uniform, β = 0 . F and G are modified beta binomial, β = 0 .
95. In (a), the policy space isdominated by the strategy of switching fields, whereas it is less so in (b).Figure 7: Discrete modelling results when F and G are modified beta binomial, β = 0 . fields replaces a dominant field-switching strategy with a combination of a within-fieldtopic switches and simply settling for what one already has.If we fix F and G as above but our researchers develop pessimism about the futurein a post-Trumpian dystopia — modelled with a steep future discount β = 0 . Clue -like field switching is an optimal policy for all but the rom Helmut Jürgensen’s Former Students: The Game of Informatics Research
5. Conclusions
A preliminary exploration of Helmut Jürgensen’s hypothesis on the fast-changingnature of informatics research is presented. For this purpose, first, a content analysisof university job advertisements is performed for a 20 year period ending in 2012.Many areas do indeed demonstrate a spike in hiring, followed by a steady decrease.Theoretical computer science remained relatively consistent throughout this entireperiod, which may be the end-result for the other foundational areas of computerscience that have declined during this period. Other more specific areas seem to spikeand descend to very low numbers quite rapidly. Future work will apply statisticalanalysis to the determine the statistical significance of the observed trends.Then, simulation techniques from quantitive economics were used. It was foundthat as optimism regarding funding levels increases, this seems to increase the paceof switching research areas, as an optimal strategy.
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