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# The TransitMatters Rail Electrification Report

At TransitMatters, we’ve just released a report about the costs and benefits of rail electrification. It’s anchored to our proposal to electrify and modernize the commuter rail system in the Boston area, but much of the analysis is broader than that. The non-Bostonian reader may still be interested in the description of construction costs of electrification and the short case studies of Israel, Denmark, Norway, New Zealand, Britain, Canada, and the United States. The latter two, covering Toronto and the Bay Area, are unusually expensive and we go over why that came to be and how it is possible to avoid them. The section on alternatives and why they are all inferior to stringing wire and running EMUs is of general interest as well, and I hope European policymakers read over and take it as a sign they should electrify more lines (ideally, all of them, as is being done right now in South Korea, India, and China).

The Toronto problem

When we came up with the cost range of $800 million to$1.5 billion, there was a lot of skepticism. The Reddit thread‘s two most common kinds of comment are “great, this can’t happen fast enough” and “it will cost billions because of unspecified MBTA problems.” As I said in responding to one of the comments, the higher-cost comparison cases all have specific reasons for their higher costs: Britain has clearance restrictions that do not exist anywhere else in the world, and Caltrain had unusual managerial incompetence regarding the related signaling project where the MBTA is actually doing well. But Toronto still looms large.

As I said on Reddit,

I’m not too worried about Caltrain’s errors, which were truly bespoke. Toronto worries me more, because while the specifics are avoidable, the ultimate cause is reproduced: Toronto and Boston are both huge cities with heavy peak commuter rail traffic and should have electrified generations ago, so now the benefits of electrification are so high that managers can afford to be careless about costs and still have above-water benefit-cost ratios.

So it is important to be careful and avoid Toronto’s problems with cost control. This means baking cost control into the program from the start, and aggressively protecting the budget from use by other actors as OPM:

1. The budget should be set at a standard level with standard contingencies. Do not aim for the ceiling; aim for average. Nor should anyone include 100% contingency as used by Toronto; if you budget money for the project it will be used, so optimize for minimizing overall cost rather than for just-in-case funding.
2. Designs should be standard, and variations should be accommodated only based on cost minimization. Basically, if it’s good enough for Germany, France, Denmark, Norway, Israel, etc.,, it’s good enough for the United States.
3. If NIMBYs push back, the state should fight back. They want noise walls? Nope, EMUs are a lot quieter than diesels, quality of life will improve. They want trenches? Nope, that’s too expensive.
4. Under no circumstances should passenger rail electrification money be used for corporate welfare for freight rail companies. They can pay their own way for clearance for double-stacked containers.

The importance of maximum electrification

Based on the observations that the lifecycle costs of DMUs are about twice those of EMUs, and that operating and capital costs are both driven by the peak rather than off-peak, it’s possible to establish financial rates of return on electrification. Not counting the speed and reliability benefits to passengers, the ROI is around 0.3-0.5% per US-size car per hour at the peak. Lines that run 8-car trains every 15 minutes at rush hour run 32 cars per hour and so have an ROI of 10-16%; this is why outside the US and Canada, cities that run such long trains at such frequency have long electrified their tracks.

The problem is that electrification is relatively unfamiliar in North America. It exists, but is sporadic, and there have been very few recent projects, so managers think it’s a Herculean task. In Boston I’ve seen reticence to wire more track due to institutional conservatism, even in plans that spend comparable amounts of money on things the region is more used to, like station platform upgrades and extra tracks. Worse, I’ve seen this in New Jersey, which is largely already electrified but uninterested in finishing the job.

Against such conservatism, it’s important to remember that failure to undertake a high-value investment isn’t any more moral than a large investment that goes to waste. When your ROI hits double digits, you waste public benefits by avoiding or even just delaying the project – and the above calculation comes just from savings on operating, maintenance, and capital acquisition costs, without the large benefits to passengers, the environment, etc.

Can large cities afford not to electrify? Yes. They have money for many kinds of waste, including for forgoing the benefits of commuter rail electrification. But just because they can afford to waste money and social benefits doesn’t mean they should. So, please, no talk of DMUs, or bi-modes, or pilot programs, or batteries – just wire your system already and import some high-quality EMUs.

# Early Commitment

I want to go back to the problem of early commitment as I explained it two months ago. It comes out of research done by Chantal Cantarelli and Bert van Wee about Dutch cost overruns, but the theory is more generally applicable and once I heard about it I started seeing it in play elsewhere. The short version is that politically committing to a megaproject too early leads to lock in, which leads to compromised designs and higher costs. The solution, then, is to defer commitment and keep alternatives open as much as possible.

The theory of lock in

The papers to read about it are Cantarelli-Flyvbjeerg-Molin-van Wee (2010), and Cantarelli-Oglethorpe-van Wee (2021). Both make the point that when the decision to build is undertaken, it imposes psychological constraints on the planners. They are not long or difficult papers to read and I recommend people read them in full and perhaps think of examples from their own non-Dutch experience – this problem is broader than just the Netherlands.

For example, take this, from the 2010 paper:

Decision-makers show evidence of entrapment whenever they escalate their commitment to ineffective policies, products, services or strategies in order to justify previous allocations of resources to those objectives (Brockner et al, 1986). Escalating commitment and justification are therefore important indicators of lock-in. The need for justification is derived from the theories of self-justification and the theory of dissonance which describe how individuals search for confirmation of their rational behaviour (Staw, 1981; Wilson and Zhang, 1997). This need arises due to social pressures and “face-saving” mechanisms. The involvement of interest groups and organizational pushes and pulls can also introduce pressures into the decision-making process, threatening the position of the decision-makers, who may feel pressure to continue with a (failing) project in order to avoid publicly admitting what they may see as a personal failure (McElhinney, 2005). “People try to rationalize their actions or psychologically defend themselves against an apparent error in judgment” (Whyte, 1986) (“face-saving”). When the support for the decision is sustained despite contradicting information and social pressures, the argumentation for a decision is based on the need for justification.

The focus on face-saving behavior leading to escalation is not unique to the literature on transportation. In international relations, it is called audience cost and refers to the domestic backlash a political leader suffers in case they back down from a confrontation they were involved in earlier; this way, small escalations turn into bigger ones and eventually to war, or perhaps to a forever occupation.

There are a number of consequences of lock in:

1. Projects will follow designs set long ago, especially ones that were hotly contentious. For example, California High-Speed Rail has stuck with the decision to build its alignments via Palmdale and Pacheco Pass, since the possibilities of changing Palmdale to the Grapevine/Tejon alignment and Pacheco to Altamont Pass both loomed large (there was a NIMBY lawsuit trying to force a change to Altamont). However, at the same time, there are plans to potentially run the partially-built system without electrification, since that issue was never in contention and is not part o the audience cost.
2. There are unlikely to be formal cancellations. California is again a good example: high-speed rail lives as a hulk, not formally canceled even when the governor said of the idea to complete it, back during the Trump administration, “let’s be real,” defending the initial construction segment between Bakersfield and Fresno as valuable in itself. Formal cancellation is embarrassing; a forever construction project is less visible a failure.
3. Prioritization is warped to tie into real or imagined connections with the already-decided project. California is not as clear an example of this as of the other two points, but in New York, once the real (if not yet formal) decision to go forward with Second Avenue Subway was made in the 1990s, the Regional Plan Association tied in every proposed expansion plan to that one line.

Surplus extraction

Cantarelli-van Wee treat early commitment as a problem of bad planners, who become psychologically wedded to potentially incorrect solutions. However, it is instructive to shift the locus of moral blame to surplus extraction by political actors, such a local politicians, power brokers, and NIMBYs.

In the story of HSL Zuid, much of the extra cost should be blamed on excessive tunneling. In the flat terrain of Holland and near-coastal Brabant, no tunneling should have been needed. And yet, the line is 20% underground, partly to serve Schiphol, partly to avoid taking any farmland in the Groene Hart. The Groene Hart tunneling has to be understood in context of rural NIMBYism (since at-grade solutions to habitat loss exist in France).

In this formulation, the problem with lock in is not just at the level of planners (though they share most of the blame in California). It’s at the level of small actors demanding changes for selfish reasons, knowing that the macro decision has already been made and the stat cannot easily walk away from the project if costs rise. These selfish actors can be NIMBY, but they can equally be local power brokers wanting a local amenity like a detour to serve them or a station without commercial justification. In Germany, an extra layer of NIMBYism (albeit not on connected with lock in – we have late commitment here) is demands to include freight on high-speed lines, in order to take it off legacy lines, which design forces gratuitous tunneling on high-speed lines in order to moderate the grade.

California is a good example of a non-NIMBY version of this. The state politically committed to building high-sped rail in the 2008 election, for which it showed clear maps of the trains detouring via Palmdale and going to San Francisco via Pacheco Pass. By the time further environmental design showed that the Los Angeles-Palmdale route would require tens of km more tunneling through Soledad Canyon than anticipated to avoid impact to an ecologically sensitive area, the state had already pitched Palmdale as a key high-speed commuter suburb, and Los Angeles County made housing plans accordingly. The county subsequently kept agitating for retaining Palmdale even as other alignment changes in the area were made, turning Palmdale into its pet project.

The planning literature undertheorizes and understudies problems arising from localism. In conversations with people in the European core as well as the United States, there’s an unspoken assumption that the community is good and the state is bad. If the community demands something, it must represent correction of a real negative externality, rather than antisocial behavior on behalf of self-appointed community leaders who the state can and should ignore. It doesn’t help that the part of Europe with the least community input is the Mediterranean countries, which Northern European planners look down on, believing any success there must be the result of statistical fudging.

The solution: late commitment

To reduce costs and improve projects, it’s best to delay political commitment as late as possible. This means designing uncertain projects and only making the decision to build at advanced stages of design – maybe not 100% but close enough that major revisions are not likely. The American situation in which there is no regular design budget so agencies rely on federal funding for the design of the projects they use the same federal funding for leads to bad outcomes over and over. California, which went to referendum without completing the environmental design first, takes the cake.

Late commitment is thankfully common in low- and medium-cost countries. Germany does not commit to high-speed rail lines early, and, judging by Berlin’s uncertainty over which U-Bahn extensions to even build, it doesn’t commit to subways early either. Sweden is investigating the feasibility of high-speed rail but rail planners who I talk to there make it clear that it’s not guaranteed to happen and much depends on politics and changes in economic behavior; overall, Nordic infrastructure projects are developed by the civil service beyond the concept stage and only presented for political negotiation and approval well into the process. Southern European planners com up with their own extension programs and politically commit close to the beginning of construction.

# Do Costs Run Over or Are They Underestimated?

The literature on cost overruns for infrastructure projects is rich, much more so than that for absolute costs. The best-known name in this literature is Bent Flyvbjerg, who in the early 2000s collated a number of datasets from the 1980s and 90s to produce a large enough N for analysis, demonstrating consistent, large cost overruns, especially for urban rail. Subsequently, he’s written papers on the topic, focusing on underestimation and on how agencies can prospectively estimate costs better and give accurate numbers to the public for approval. This parallels an internal trend in the US, where Don Pickrell identified cost overruns in 1990 already, using 1980s data; Pickrell’s dataset was among those analyzed by Flyvbjerg, and subsequent to Pickrell’s paper, American cost overruns decreased to an average of zero for light rail lines.

But a fundamental question remains: are cost overruns really a matter of underestimation, or a true overrun? In other words, if a project, say Grand Paris Express, is estimated to cost 22.6 billion € in 2012 (p. 7) and is up to 35.6 billion € today (p. 13), does it mean the cost was 35.6b€ all along and the 2012 analysis just failed to estimate it right? Or dos it mean the cost was 22.6b€ then, and then the budget ran over due to failures of planning that could have been avoided?

Transit agencies that just want to avoid the embarrassment of media headlines saying “they said it costs X but it costs 2X” care mostly about underestimation. This is also true of both generic project managers and political appointees, two groups that do not care about the details of how to build a subway, and think of everything in abstract terms in which a subway might as well be a box of shampoo bottles.

However, the concrete examples that I have seen or heard of for cost overruns look like overruns rather than underestimation. That is, those projects could have been done at the original cost, but planning mistakes drove the budget up, or otherwise created conditions that would enable other forces to drive the budget up.

The Netherlands: early commitment

Bert van Wee is among the world’s top researchers on cost overruns, even if he’s less well-known to the public than Flyvbjerg. He spoke to me about the problems of early commitment in Dutch planning, in which politicians commit to a project before design is finalized. Once the political decision has been made, it is easy for actors to extract surplus, because the state or city cannot walk away easily, while a 20% cost overrun is much easier to explain to the public. This problem plagued 2000s investments like HSL Zuid. To deter this, after 2009 the Netherlands passed reforms that attempt to tackle this problem, aiming to defer the formal political decision to later in the process.

This factor seems to correlate with absolute costs, if not with overruns. American planning is extremely politicized; Canadian planning is fairly politicized too, with individual subway projects identifiable as the brainchildren of specific politicians or parties; Southern European and Nordic planning is highly bureaucratized, with design driven by the civil service and politicians making yes or no decisions late in the process.

Sweden: changes in rules

According to a senior planner at Nya Tunnelbanan, the project has run over from 22.506 billion kronor in 2013 to 31.813 today, both in 2016 price levels; in US dollars, this is $2.551b/19.6 km to$3.606b/19.6 km, all underground. The reasons for the escalation come largely from tighter regulations as well as litigation:

• Safety requirements have been tightened midway through the project, requiring a service tunnel in addition to the two track tunnels, raising excavation volume almost 50%
• An environmental court ruling slowed down excavation further
• Consensus with stakeholders took longer than expected
• Excavated rock was reclassified midway through the project from useful building material to waste that must be disposed of

Focusing on underestimation is not really germane to what’s happened in Stockholm. The problem isn’t that early 2010s engineers failed to anticipate regulations that were not in force at the time. It’s that regulations were changed later. The rock removal process today actually increases greenhouse gas emissions, just because of the need to freight it away, let alone the systemwide effects on climate of making it harder to build subways.

California: scope creep and change orders

California High-Speed Rail is such a big project that its cost overruns, in multiple stages, were amply discussed in the media. The original announcements in the early 2010s, for example here, were largely about scope creep. At-grade segments turned into viaducts; above-ground segments, particularly in the Bay Area, were turned into tunnels. The reasons were mostly about agency turf battles.

Only in one case was the problem more about underestimation than overrun: the Central Valley segment had originally been planned to follow railroad rights-of-way, but had to be redesigned to have more viaducts and swerve around unserved small towns. This was bad planning, at two points: first, the original designs assumed trains could go at 350 km/h through unserved towns, which they don’t anywhere; and second, once the redesign happened, it was so rushed that land acquisition was time-consuming and acrimonious. Even then, much of the overdesign as identified by a Deutsche Bahn postmortem could have been prevented.

The second stage is more recent: the Central Valley construction contracts have long busted their budgets due to change orders. Change orders are a common problem in California, and in this case, it involved not only the change order king Tutor-Perini, but also the usually reasonable Dragados. The situation here must be ascribed to overrun rather than underestimation: a transparent process for handling changes, based on itemized costs, is an emerging best practice, known since the early 2000s to people who cared to know, and more recently seen in the economics literature for general infrastructure. That California failed to follow this practice – which, again, was available already in the late 2000s – is the source of malpractice. The original bids could have held if the process were better.

Absolute costs and cost overruns

Cost overruns are not the same as absolute costs. They are not even obviously correlated: witness the way the US eliminated most overruns on surface light rail projects in the 1990s and 2000s, to the point that projects with large overruns like the Green Line Extension are exceptional, while absolute costs have skyrocketed. But if we understand the problem to be about cost overruns from an ambitious but achievable budget rather than about underestimating a final cost that could not be improved on, then the study of the two topics is inherently intertwined.

Problems that recur in postmortems of cost overruns are not just about estimation. They’re about building better and cheaper. A bureaucratized planning process in which politicians retain the right to make yes-or-no decisions on complete design reduces cost overruns by reducing leakage and surplus extraction; the overruns such a process prevents are preventable extra costs, rather than higher initial estimates. The same is true of avoiding overbuilding, of not introducing extraneous regulations, of treating environmental questions as systemic and quantitative rather than as local under a do-no-harm principle. Even the question of change orders is more transparently about reducing absolute costs in the literature, since the overruns prevented tend to be seen in higher risk to the contractor leading to higher profit margin demands.

The upshot is that this makes the study of absolute costs easier, because we can reuse some of the literature for the related problem of cost overruns. But conceptually, it means that agencies need to be more proactive and treat early budgets as standards to be adhered to, rather than just blow up the budgets preemptively so that it’s easier to stick to them.

# Hire In-House, Don’t Use Consultants

I recently found two presentations, one from 2017, the other from earlier this week, both underscoring the importance of in-house expertise for efficient construction. This is layered on top of interviews Eric and I did for our Boston case study and a few additional interviews I did in other American and European cities. It is my professional opinion that agencies that engage in major capital projects, even if they involve rolling stock acquisition rather than the construction of new lines, ought to hire in-house, and make sure to have long-term capital programs.

The presentations

Both presentations concern rolling stock. The one from 2017 is by Stadler, regarding the challenges of the American market. On slide 32, it mentions that Caltrain was a demanding customer, with all expertise outsourced and yet managers engaging in micromanagement. The micromanagement is in line with what we’ve heard from contractors for other capital expansions, like Second Avenue Subway, especially contractors with experience in both the US, where this practice is common, and Europe, where it isn’t.

Thanks to the factors mentioned by Stadler as well as the Buy America requirement to set up a new factory with a new supply chain for a midsize order, the cost is $551 million/96 cars, or$5.74 million/car; the typical cost of a KISS is 300 million €/90 cars, and the €:$ratio is not 1.72, far from it. The other presentation, from this week, concerns the MBTA’s slow approach to electrifying its commuter rail network. It wishes to begin with a pilot on the already-electrified Providence Line, but is running against the problem of having no in-house expertise, just as Caltrain does not. The presentation on this says, on slide 3, that it takes 6-9 months to onboard consultants, and another 6-9 to develop performance requirements for a kind of vehicle that is completely standard in high-performance regional rail networks in Europe. Instead of hiring experienced professionals (who must come from Europe or East Asia and not the US), the MBTA plans to piggyback on either the overpriced Caltrain order, or an obsolete-technology order by New Jersey Transit. The Caltrain order, moreover, is stretched for the generous loading gauge of the Western US, but does not fit the catenary height on the East Coast, even though European KISSes would easily and are around 13 cm lower than existing MBTA rolling stock. Prior Northeastern examples This combination of political and managerial micromanagement with outsourcing of technical expertise to consultants is common enough in the United States. In the Boston report on the Green Line Extension, we were told by multiple sources that the MBTA only has 5-6 engineers doing design review. Thus, they have the capacity to handle small projects but not large ones. Small-scale projects like building a new infill station or taking an existing low-platform commuter rail station and converting it to an accessible high-platform one usually have limited cost premium: in Berlin, infill stations are 10 million € outside the Ring, whereas in Boston, infill stations and high-platforming projects (which are very similar in scope) are around$20-25 million – and Boston platforms are longer. This is also the case in Philadelphia, where headline costs are lower because the stations are smaller, but overall the unit costs are comparable to those of Boston.

But large projects are beyond the ability of a 6-person team. The required permanent staffing level is likely in the teens for a team whose job is just to score design and construction contracts. This choked the original Green Line Extension, leading to bottlenecks in design and contributing to the project’s extreme cost. The restarted version is still extremely expensive – it’s getting some good press this week for running slightly under a $2.3 billion/6.3 km budget, but said budget,$360 million/km, is well above the international norm for a subway, let alone trenched light rail. The current project has sunk costs from the previous ones, and a combination of in-house and consultant design about whose efficacy we’ve heard conflicting reports, but the team is much larger now.

In areas that don’t even have the skeletal design review staff of Boston, costs are high even for small projects. Connecticut deserves especial demerit: its department of transportation relies exclusively on consultants for rail design (perhaps also road design but I do not know), and infill stations cost not $20-25 million but$50+ million. The Hartford Line, compromised from the start, even displays this state-by-state difference: the one Massachusetts project, a single high platform in Springfield, cost $10 million/100 meters, a fraction of comparable projects in Connecticut. Larger Connecticut stations, such as those for Metro-North, have seen extreme scope creep, amounting to a$106 million total cost.

Consultants and design

American agencies speak of design-bid-build contracts, in which design and construction are separate, and design-build ones, where they are combined into a single contract. Design-bid-build is superior. But really, contracts in low-cost countries are often neither of those, but just build contracts, with design done mostly in-house. A procurement official in Stockholm explained to me that Swedish contracts tend to be build contracts; design-bid-build can sometimes be used with supplemental consultants helping with design, but it’s not the norm. Moreover, in Oslo, the use of design consultants instead of in-house design has not been good: consultants tend to engage in defensive design because of how Norway structures risk allocation, leading to overbuilding.

In Spain and (I believe) Italy, contracts are design-bid-build. But there’s so much in-house involvement in design that it’s more accurate to call these build contracts. The in-house design teams are not huge but they’re enough to work with private design firms and score proposals for technical merit. In Istanbul, the system is somewhat different: preliminary design at the 60% level is contracted out separately from the combination of final design and construction, which may possibly be called des-bid-ign-build, but the design part is extensively scored on technical merit, at 60-80% of the total weight. The construction contracts in Istanbul are lowest-bid, but contractors can be disqualified, and since Turkey has so much infrastructure construction, contractors know that they need to behave well to get future work.

Unfortunately, American consultants believe the opposite: they believe in the superiority of design-build and are not even aware of pure build, only design-bid-build. Sources from that world that I generally think highly of have told me that directly. But that is because the sort of projects that they are most likely to be involved in are ones that use consultants, which definitionally are not build contracts. The ongoing expansion projects in Stockholm, Madrid, Barcelona, Milan, Rome, and Berlin have no use for international consultants, so international consultants are not familiar with them, and end up knowing only about high-cost examples like London or the occasional medium-cost one like Paris. In effect, to rely on consultants is to ascertain one largely learns worst industry practices, not best ones.

Hire in-house

The alternative to paying consultants is to obtain public-sector expertise. Agencies are obligated to hire sufficient-size teams, and pay them competitively. Engineers in Italy and Spain have a lot of social prestige, much as in France and Germany; even in medium- rather than low-cost countries in Europe, like France, we were told by UITP planners that the people planning metro systems are hired from the engineering elite (in France, this would be Grandes Ecoles graduates), and paid appropriately.

In the US, there is no such prestige. Humanities professors speak of STEM privilege routinely, but by Continental and East Asian standards, the US and UK have no STEM privilege: the elites are generalist and are not expected to know the specific industrial fields they oversee. The public sector thus treats the planner and the engineer as a servant to the political appointee. Senior management routinely ignores the advice of younger planners who are more familiar with present-day research.

The pay, too, is deficient. In absolute numbers, planners at American transit agencies get paid better than their European counterparts – but American white-collar wages are generally higher than European ones. The MBTA pays project managers $106,000 a year as of a few years ago, which is a nice wage, but the Boston private sector pays$140,000 in transportation and more in other fields. The public sector, through budget-cutting officials, sends a clear price signal: we do not want you to work for us.

There is another way, but it requires letting go of the idea that private consultants are better than long-term in-house experts. It is obligatory to hire in-house at competitive wages to grow the design review teams, and listen to them when they say something is desirable, difficult, or impossible. Instead of onboarding consultants, agencies should immediately staff up in-house with plans for long-term investments. Moreover, senior management should back the planners and engineers when they engage in value engineering, even if it annoys politicians and local activists. The role of elected politicians is to review those in-house plans and decide whether there is room in the budget for the megaprojects they recommend, and not to micromanage. This way, and only this way, can the United States shrink its procurement costs to typical Continental European levels.

# Australian Construction Costs

There’s a report just released by the Grattan Institute called Megabang for Megabucks, talking about high construction costs in Australia. Our transit costs project is quoted as an international comparison, pointing out that Australia is near the global high end. I encourage people to read the report itself, which says interesting things about problems with Australian construction and procurement. I am especially happy to see that the recommendations for the most part accord with what we are learning from other cases – of course, our Boston case is out and the report authors have likely read it, but the recommendations are in line with things we see from yet-unpublished cases, so this is not just me looking at a mirror.

The issue of competition

Australian megaproject contracts have insufficient competition. Only three firms are Tier One, the largest infrastructure contractors in Australia; those get most contracts for the largest infrastructure projects, and when mid-tier firms bid, it’s often in partnership with a Tier One company. Moreover, in the largest size category, higher than $1 billion, even the Tier One firms often partner with one another, leading to monopoly. International firms do access the Australian market, but it is inconsistent. Australia overweights the importance of local experience, and has some unusual rules, such as requiring firms to engage in more prior design than is typical. This is consistent with what I’ve seen in Israel. In short, the electrification contract in Israel was won by Spanish contractor SEMI, which had extensive European experience but none in Israel. This was criticized domestically, and some people blamed it for the schedule slips on the electrification project, but such blame is unfair. The bulk of the delays are not the fault of SEMI but come from a lawsuit launched by Alstom, which competed for the contract and lost out on price; Alston employed industrial espionage to create FUD about the bid, and the lawsuit delayed works by three years. Despite this, the costs have not run over much, and the absolute per-km costs remain on the low side, net of extras like Haifa’s demand for a trench. Thus, even in a situation of extensive domestic complaints about the winning bidder’s lack of local experience, said lack did not materially create problems. This is also consistent with lessons from Turkey. In Turkey, there must be a minimum of three bidders. If there are only one or two, the state or municipal government must rebid. Absolute costs in Turkey are low and so are cost overruns; the extensive competition helps discipline the contractors, as does the political consensus in favor of rapid infrastructure construction, credibly promising firms that there will be more work in the future and if they behave they will get some of it. Procurement The study discusses different contracting regimes. It does not talk about the design-build issue; I do not know whether it is as prevalent in Australia as in Canada, and regrettably there is no cost history, thus no way for me to confirm my suspicion that Australia resembles Canada and Singapore in only having had a cost explosion in the last 20 years. However, it does talk about change orders. Change orders are a notable problem in California. Low bids followed by renegotiation are common there; Tutor Perini is notorious for this behavior. The study goes over strategies to deal with this issue, though it does not talk explicitly about itemization as in Spain and Italy, where the unit prices are public and then if more is needed (e.g. more labor due to slower progress) then the change is already pre-agreed, avoiding litigation. Sweden avoids litigation as well. Finally, the study talks about rushing. This was an issue in Boston, so this may be me learning from a mirror, but, in brief, American funding for infrastructure encourages agencies to rush the preliminary design to apply for federal funding early. This leads to compromised designs and premature commitment, since there is no ongoing funding for long-term design. Learning from good examples I think the one drawback of the study is the list of comparisons. Sourced partly to us and partly to Read-Efron, they say, The empirical evidence is incomplete, but what there is shows that rail construction costs in Australia are in the top quarter of 27 OECD countries studied. They are higher than in numerous other rich countries: 26 per cent higher than in Canada, 29 per cent higher than in Japan, and more than three times as high as in Spain (Figure 1.2 on the following page). And road and rail tunnels cost more in Australia than elsewhere in the world, according to an international study. The comparison with Canada has a problem: the Canadian costs in our database go back 15-20 years, and back then, costs were much lower than today. The latest costs do not show an Australian premium over Canada – Toronto is more expensive to build in than Sydney and almost as much as Melbourne. It is critical to understand that high costs are really a pan-Anglosphere phenomenon, and thus Australia should learn from Continental European and East Asian examples (except very high-cost Hong Kong), and not from countries that in the last 10 years have had the same problems as Australia or worse. Spain is always good, as are common features to low-cost Spain, Italy, Turkey, South Korea, and the Nordic countries, and even common features to those and medium-cost countries like France, Germany, China, and Japan. # Tilting Trains and Technological Dead-Ends The history of tilting trains is on my mind, because it’s easy to take a technological advance and declare it a solution to a problem without first producing it at scale. I know that 10 years ago I was a big fan of tilting trains in comments and early posts, based on both academic literature on the subject and existing practices. Unfortunately, this turned into a technological dead-end because the maintenance costs were too high, disproportionate to the real speed benefits, and further work has gone in different directions. I bring this up because it’s a good example of how even a solution that has been proven to work at scale can turn out to be a dead-end. What is tilting? It is a way of getting trains to run at higher cant deficiency. What is cant deficiency? Okay. Let’s derive this from physical first principles. The lateral acceleration on a train going on a curve is given by the formula a = v^2/r. For example, if the speed is 180 km/h, which is 50 m/s, and the curve radius is 2,000 meters, then the acceleration is 50^2/2000 = 1.25 m/s^2. Now, on pretty much any curve, a road or railway will be banked, with the outer side elevated above the inner side. On a railway this is not called banking, but rather superelevation or cant. That way, gravity countermands some of the centrifugal force felt by the train. The formula on standard-gauge track is that 150 mm of cant equal 1 m/s^2 of lateral acceleration. The cant is free speed – if the train is perfectly canted then there is no centrifugal force felt by the passengers or the train systems, and the balance between the force on the inner and outer rail is perfect, as if there is no curve at all. The maximum superelevation on a railway is 200 mm, but it only exists on some Shinkansen lines. More typical of high-speed rail is 160-180 mm, and on conventional rail the range is more like 130-160; moreover, if trains are expected to run at low speed, for example if the line is dominated by slow freight traffic or sometimes even if the railroad just hasn’t bothered increasing the speed limit, cant will be even lower, down to 50-80 mm on many American examples. Therefore, on passenger trains, it is always desirable to run faster, that is to combine the cant with some lateral acceleration felt by the passengers. Wikipedia has a force diagram: The resultant force, the downward-pointing green arrow, doesn’t point directly toward the train floor, because the train goes faster than the balance speed. This is fine – some lateral acceleration is acceptable. This can be expressed in units of acceleration, that is v^2/r with the contribution of cant netted out, but in regulations it’s instead expressed in theoretical additional superelevation required to balance, that is in mm (or inches, in the US). This is called cant deficiency, unbalanced superelevation, or underbalance, and follows the same 150 mm = 1 m/s^2 formula on standard-gauge track. Note also that it is possible to have cant excess, that is negative cant deficiency. This occurs when the cant chosen for a curve is a compromise between faster and slower trains, and the slower trains are so much slower the direction of the net force is toward the inner rail and not the outer rail. This is a common occurrence when passenger and freight trains share a line owned by a passenger rail-centric authority (a freight rail-centric one will just set the cant for freight balance). It can also occur when local and express passenger trains share a line – there are some canted curves at stations in southeastern Connecticut on the Northeast Corridor. The maximum cant deficiency is ordinarily in the 130-160 mm range, depending on the national regulations. So ordinarily, you add up the maximum cant and cant deficiency and get a lateral acceleration of about 2 m/s^2, which is what I base all of my regional rail timetables on. You may also note that the net force vector is not just of different direction from the vertical relative to the carbody but also of slightly greater magnitude. This is an issue I cited as a problem for Hyperloop, which intends to use far higher cant than a regular train, but at the scale of a regular train, it is not relevant. The magnitude of a vector consisting of a 9.8 m/s^2 weight force and a 2 m/s^2 centrifugal force is 10 m/s^2. Okay, so how does tilt interact with this? To understand tilt, first we need to understand the issue of suspension. A good example of suspension in action is American regulations on cant deficiency. As of the early 2010s, the FRA regulations depend on train testing, but are in practice, 6″, or about 150 mm. But previously the blanket rule was 3″, with 4-5″ allowed only by exception, mocked by 2000s-era advocates as “the magic high-speed rail waiver.” This is a matter of carbody suspension, which can be readily seen in the force diagram in the above secetion, in which the train rests on springs. The issue with suspension is that, because the carbody is sprung, it is subject to centrifugal force, and will naturally suspend to the outside of the curve. In the following diagram, the train is moving away from the viewer and turning left, so the inside rail is on the left and the the outside rail is on the right: The cant is 150 mm, and the cant deficiency is held to be 150 mm as well, but the carbody sways a few degrees (about 3) to the outside of the curve, which adds to the perceived lateral acceleration, increasing it from 1 m/s^2 to about 1.5. This is typical of a modern passenger train; the old FRA regulations on the matter were based on an experiment from the 1950s using New Haven Railroad trains with unusually soft suspension, tilting so far to the outside of the curve that even 3″ cant deficiency was enough to produce about 1.5 m/s^2 of lateral force felt by the passengers. By the same token, a train with theoretically perfectly rigid suspension could have 225 mm of cant deficiency and satisfy regulators, but such a train doesn’t quite exist. Here comes tilt. Tilt is a mechanism that shifts the springs so that the carbody leans not to the outside of the curve but to its inside. The Pendolino technology is theoretically capable of 300 mm of cant deficiency, and practically of 270. This does not mean passengers feel 1.8-2 m/s^2 of lateral acceleration; the train’s bogies feel that, but are designed to be capable of running safely, while the passengers feel far less. In fact the Pendolino had to limit the tilt just to make sure passengers would feel some lateral acceleration, because it was capable of reducing the carbody centrifugal force to zero and this led to motion sickness as passengers saw the horizon rise and fall without any centrifugal force giving motion cues. Two lower cant deficiency-technology than Pendolino-style tilt are notable, as those are not technological dead-ends, and in fact remain in production. Those are the Talgo and the Shinkansen active suspension. The Talgo has no axles, and incorporates a gravity-based pendular system in which the train is sprung not from the bottom up but from the top down; this still isn’t enough to permit 225 mm of cant deficiency, but high-speed versions like the AVRIL permit 180, which is respectable. The Shinkansen active suspension is computer-controlled, like the Pendolino, but only tilts 2 degrees, allowing up to 180 mm of cant deficiency. What is the use case of tilting, then? Well, the speed is higher. How much higher the speed is depends on the underlying cant. The active tilt systems developed for the Pendolino, the Advanced Passenger Train, and ICE T are fundamentally designed for mixed-traffic lines. On those lines, there is no chance of superelevating the curves 200 mm – one freight locomotive at cant excess would demolish the inner track, and the freight loads would shift unacceptably toward the inner rail. A more realistic cant if there is much slow freight traffic is 80 mm, in which case the difference between 150 and 300 mm of cant deficiency corresponds to a speed ratio of $\sqrt{(80+300)/(80+150)} = 1.285$. Note that the square root in the formula, coming from the fact that acceleration formula contains a square of the speed, means that the higher the cant, the less we care about cant deficiency. Moreover, at very high speed, 300 mm of cant deficiency, already problematic at medium speed (the Pendolino had to be derated to 270), is unstable when there is significant wind. Martin Lindahl’s thesis, the first link in the introduction, runs computer simulations at 350 km/h and finds that, with safety margins incorporated, the maximum feasible cant deficiency is 250 mm. On dedicated high-speed track, the speed ratio is then $\sqrt{(200+250)/(200+130)} = 1.168$, a more modest ratio than on mixed track. The result is that for very high-speed rail applications, Pendolino-level tilting was never developed. The maximum cant deficiency on a production train capable of running at 300 km/h or faster is 9″ (230 mm) on the Avelia Liberty, a bespoke train that cost about double per car what 300 km/h trains cost in Europe. To speed up legacy Shinkansen lines, JR Central and JR East have developed active suspension, stretching the 2.5 km curves of the Tokaido Shinkansen from the 1950s and 60s to allow 285 km/h with the latest N700 trains, and allowing 360 km/h on the 4 km curves of the Tohoku Shinkansen. What happened to the Pendolino? The Pendolino and similar trains, such as the ICE T, have faced high maintenance costs. Active tilting taxes the train’s mechanics, and it’s inherently a compromise between maintenance costs and cant deficiency – this is why the Pendolino runs at 270 mm where it was originally capable of 300 mm. The Shinkansen’s active suspension is explicitly a compromise between costs and speed, tilted toward lower cant deficiency because the trains are used on high-superelevation lines. The Talgo’s passive tilt system is much easier to maintain, but also permits a smaller tilt angle. The Pendolino itself is a fine product, with the tilt removed. Alstom uses it as its standard 250 km/h train, at lower cost than 350 km/h trains. It runs in China as CRH5, and Poland bought a non-tilting Pendolino fleet for its high-speed rail service. Other medium-speed tilt trains still run, but the maintenance costs are high to the point that future orders are unlikely to include tilt. Germany has a handful of tilt trains included in the Deutschlandtakt, but the market for them is small. Sweden is happy with the X2000, but its next speedup of intercity rail will not involve tilting trains on mostly legacy track as Lindahl’s thesis investigated, but conventional non-tilting high-speed trains on new 320 km/h track to be built at a cost that is low by any global standard but still high for how small and sparsely-populated Sweden is. In contrast, trainsets with 180 mm cant deficiency are still going strong. JR Central recently increased the maximum speed on the Tokaido Shinkansen from 270 to 285 km/h, and Talgo keeps churning out equipment and exports some of it outside Spain. # No Cafe Cars, Please European and American intercity train planning takes it as a given that every train must have a car dedicated to cafeteria service. This is not the only way to run trains – the Shinkansen doesn’t have cafe cars. Cafe cars waste capacity that could instead be carrying paying passengers. This is the most important on lines with capacity limitations, like the Northeast Corridor, the West Coast Main Line, the LGV Sud-Est, and the ICE spine from the Rhine-Ruhr up to Frankfurt and Mannheim. Future high-speed train procurement should go the Shinkansen route and fill all cars with seats, to maximize passenger space. How much space do cafe cars take? Typically, one car in eight is a cafe. The standard European high-speed train is 200 meters long, and then two can couple to form a 400-meter train, with two cafes since the two 200-meter units are separate and passengers can’t walk between them. In France, the cars are shorter than 25 meters, but a TGV has two locomotives and eight coaches in between, so again one eighth of the train’s potential passenger space does not carry passengers but rather a support service. Occasionally, the formula is changed: the ICE4 in Germany is a single 12-car, 300-meter unit, so 1/12 of the train is a cafe, and in the other direction, the Acela has six coaches one of which is a cafe. A 16-car Shinkansen carries 1,323 passengers; standard class has 5-abreast seating, but even with 4-abreast seating, it would be 1,098. The same length of a bilevel TGV is 1,016, and a single-level TGV is 754. The reasons include the Shinkansen’s EMU configuration compared with the TGV’s use of locomotives, the lack of a cafe car in Japan, somewhat greater efficiency measured in seat rows per car for a fixed train pitch, and a smaller share of the cars used for first class. An intermediate form is the Velaro, which is an EMU but has a cafe and three first-class cars in eight rather than the Shinkansen’s three in 16; the Eurostar version has 902 seats over 16 cars, and the domestic version 920. The importance of the first- vs. second-class split is that removing the cafe from a European high-speed train means increasing seated capacity by more than just one seventh. The bistro car is an intermediate car rather than an end car with streamlining and a driver’s cab, and if it had seats they’d be second- and not first-class. A German Velaro with the bistro replaced by a second-class car would have around 1,050 seats in 16 cars, almost even with a 4-abreast Shinkansen even with four end cars rather than two and with twice as many first-class cars. How valuable are cafes to passengers? The tradeoff is that passengers prefer having a food option on the train. But this preference is not absolute. It’s hard to find a real-world example. The only comparison I am aware of is on Amtrak between the Regional (which has a cafe) and the Keystone (which doesn’t), and Regional fares are higher on the shared New York-Philadelphia segment but those are priced to conserve scarce capacity for profitable New York-Washington passengers, and at any rate the shared segment is about 1:25, and perhaps this matters more on longer trips. Thankfully, the Gröna Tåget project in Sweden studied passenger preferences in more detail in order to decide how Sweden’s train of the future should look. It recommends using more modern seats to improve comfort, making the seats thinner as airlines do in order to achieve the same legroom even with reduced pitch, and a number of other changes. The question of cafes in the study is presented as unclear, on PDF-p. 32: Put another way, the extra passenger willingness to pay for a cafeteria compared with nothing, 14%, is approximately equal to the increase in capacity on a Velaro coming from getting rid of the bistro and replacing it with a second-class car. The extra over a Shinkansen-style trolley is 3%. Of course, demand curves slope down, so the gain in revenue from increasing passenger capacity by 14% is less than 14%, but fares are usually held down to a maximum regulatory level and where lines are near capacity the increase in revenue is linear. Station food Instead of a bistro car, railroads should provide passengers with food options at train stations. In Japan this is the ekiben, but analogs exist at major train stations in Europe and the United States. Penn Station has a lot of decent food options, and even if I have to shell out$10 for a pastrami sandwich, I don’t think it’s more expensive than a Tokyo ekiben, and at any rate Amtrak already shorts me \$90 to travel to Boston. The same is true if I travel out of Paris or Berlin.

Even better, if the station is well-designed and placed in a central area of the city, then passengers can get from the street to the platform very quickly. At Gare de l’Est, it takes maybe two minutes, including time taken to print the ticket. This means that there is an even broader array of possible food options by buying on the street, as I would when traveling out of Paris. In that case, prices and quality approach what one gets on an ordinary street corner, without the premium charged to travelers when they are a captive market. The options are then far better than what any bistro car could produce, without taking any capacity away from the train at all.

# Poor Rich Countries and Isomorphic Mimicry

A curious pattern can be found in subway construction costs around the world, based on GDP per capita. On the one hand, poor countries that have severe cultural cringe, such as former colonies, have high construction costs, and often the worst projects are the ones that most try to imitate richer countries, outsourcing design to Japan or perhaps China. On the other hand, poor-rich countries, by which I mean countries on the periphery of the developed world, have similar cultural cringe and self-hate for their institutions, and yet their imitation of richer countries has been a success; for example, Spain copied a lot of rail development ideas from Germany and France. This can be explained using the development economic theory of isomorphic mimicry; the rub here is that a poor country like India or Ethiopia is profoundly different from the richer countries it tries to imitate, whereas a poor-rich country like Spain is actually pretty similar to Germany by global standards.

What is isomorphic mimicry?

In the economic development literature, the expression isomorphic mimicry refers to when a poor country sets up institutions that aim to imitate those of richer countries in hope that through such institutions the country will become rich too, but the imitation is too shallow to be useful. A common set of examples is well-meaning regulations on safety, labor, environmental protection, and anti-corruption that are not enforced due to insufficient state capacity. Here is a review of the concept by Andrews, Pritchett, and Woolcock, with examples from Mozambique, Uganda, and India, as well as some history from the American private sector. More examples using the theory can be found in Turczynowicz, Gautam, Rénique, Yeap, and Sagues concerning Peru’s one laptop per child program, in Evans’ interpretation of Bangladesh’s domestic violence laws, and in Rajagopalan and Tabarrok on India’s poor state of public services.

While the theory regarding institutions is new, analogs of it for tangible goods are older. Postwar developmental states engaged in extensive isomorphic mimicry, building dams, steel plants, and coal plants hoping that it would transform them into wealthy states like the United States, Western Europe, and Japan; for the most part, they had lower economic growth than did the developed world until the 1980s. The shift within international development away from tangible infrastructure and toward trying to fix institutions came about because big projects like the Aswan Dam failed to create enduring economic growth and often had ill side effects on agriculture, the environment, or human rights.

How does isomorphic mimicry affect public transportation?

The best example of isomorphic mimicry leading to bad transit that I know of is the Addis Ababa light rail system. This is funded by China, whose ideas of global development are similar to those of the postwar first and second worlds, that is providing tangible physical things, like railroads. Unfortunately, usage is low, because of problems that do not exist in middle-income or rich countries but are endemic to Ethiopia. Christina Goldbaum, the New York Times’ transit reporter, who lived in East Africa and reported from Addis Ababa, mentioned four problems:

1. Electricity is unreliable, so the trains sometimes do not work. In early-20th century America, electric railroads and streetcar companies built their own power supply and were sometimes integrated concerns providing both streetcar and power service; but in more modern countries, there is reliable power for urban rail to tap.
2. Not many people work in city center rather than in the neighborhood they live in. This, again, has historical analogs – there were turn-of-the-century Brooklynites who never visited Manhattan. Thus, a downtown-centric light rail system won’t get as much ridership as in a more developed city.
3. The train is expensive relative to local incomes, so many people stick with buses or ride without paying.
4. The railroad cuts through streets at-grade, to save money, and blocks off pedestrian paths that people use.

The Addis Ababa light rail system at least had reasonable costs. A more typical case for countries that poor is to build urban rail at premium cost, and the poorer the country, the higher the cost. The reason is most likely that such countries tend to build with Chinese or Japanese technical assistance, depending on geopolitics, and therefore import expensive capital for which they pay with weak currencies.

In India, the most functional and richest of the countries in question, there is much internal and external criticism that its economic growth is not labor-intensive, that is the most productive firms are not the ones employing the most people, and this stymies social development and urban growth. I suspect that this also means there is reluctance to use labor-intensive construction methods, that is cut-and-cover with headcounts that would be typical in New York, Paris, and Berlin in the early 20th century, or perhaps mid-20th century Milan and Tokyo. International consultancies are centered on the rich world and recommend capital-intensive methods to avoid hiring too many sandhogs at a fully laden employment cost of perhaps 8,000€ a month; in India, that is the PPP-adjusted gross salary of an experienced construction worker per year, and if capital is imported then multiply its cost by 3 to account for the rupee’s exchange rate value.

Poor-rich countries

Poor-rich countries are those on the margin of the developed world, such as the countries of Eastern and Southern Europe, Turkey, Israel, to a lesser extent South Korea, and the richer countries of Latin America such as Chile. These are clearly poorer than the United States or Germany. Their residents, everywhere I’ve asked, believe that they are poorer and institutionally inferior; convincing a Spaniard or an Italian that their country can do engineering better than Germany is a difficult task. Thus, these countries tend to engage in mimicry of those countries that they consider the economic center, which could be Germany in Southern Europe, Japan in South Korea, or the US or Spain in Spanish America.

However, being a poor-rich country is not the same as being a poor country. Italy is, by American or German standards, poor. Wages there are noticeably lower and living standards are visibly poorer, and not just in the South either. But those wages remain in the same sphere as American and German wages. The labor-capital cost ratios in Southern Europe are sufficiently similar to those of Northern Europe that it’s not difficult to imitate. Spain even mixed and matched, using French TGV technology for early high-speed rail but preferring the more advanced German intercity rail signaling system, LZB, to the French one.

Such imitation leads to learning. Spain imported German and French engineering ideas but not French tolerance for casual rioting or German litigiousness, and therefore can build infrastructure with less NIMBYism. Turkey invited Italian consultants to help design the early lines of the Istanbul Metro, but subsequently refined their ideas domestically in order to build more efficiently, for example shrinking station footprint and tunnel diameter to reduce costs. Seoul has a subway system that looks like Tokyo’s in many ways, but has a cleaner network shape, with far fewer missed connections between lines. As a result, all three countries – Spain, Turkey, Korea – now have innovative domestic programs of rail construction and can even export their expertise elsewhere, as Spain is in Ecuador.

Openness to novelty

Andrews-Pritchett-Woolcock stress the importance of openness to novelty in the public sector, and cite examples of failure in which bureaucrats at various levels refused to implement any change, even one that was proven to be positive, because their goal was not to rock the boat.

Cultural cringe is in a way a check on that. Isomorphic mimicry is an attempt to combine agenda conformity and closeness to novelty with a desire to have what the richest countries have. But in poor-rich countries, isomorphic mimicry is real imitation – there is ample state penetration in a country like Spain or Turkey rather than outsourcing of state capacity to traditional heads of remote villages, and education levels are high enough that many people know how Germany works and interact with Germany regularly. A worker who earns 2,000€ a month net and a worker who earns 3,000€ a month can exchange tips about how to apply for jobs, how to prepare food, what brands of consumer goods to buy, and where to go on vacation. They cannot have this conversation with a worker who earns 10,000€ a month net.

Within the rich world, what matters then is the realization that something is wrong and the solution is to look abroad. It doesn’t matter if it’s a generally poor-rich region like Southern Europe or a region with a poor-rich public sector like the United States – there’s enough private knowledge about how successful places work, but what’s needed is a public acknowledgement and social organization encouraging imitation and lifting voices that are most expert in implementing it.

And for all the jokes about how the United States or Britain is like a third-world country, they really aren’t. Their public-sector dysfunctions are real, but are still firmly within the poor-rich basket; remember, for example, that despite its antediluvian signaling capacity, the New York City Subway manages to run 24 trains per hour per track at the peak, which is better than Shanghai’s 21. Health and education outcomes in the United States are generally better than those of middle-income and poor countries on every measure. This is a public sector that compares poorly with innovation centers in Continental Europe and democratic East Asia, but it still compares; to try to do the same comparison in a country like Nigeria would be nonsensical.

The upshot then is that implementing best practices in developed countries that happen to be bad at one thing, in this case public transportation in the United States, can work smoothly, much like Southern Europe’s successful assimilation of and improvements on Northern European engineering, and unlike the failures in former colonies in Africa and Asia. But people need to understand that they need to do it – that the centers of innovation are abroad and are in particular in countries that speak English non-natively.

# Sorry Eno, the US Really Has a Construction Cost Premium

There’s a study by Eno looking at urban rail construction costs, comparing the US to Europe. When it came out last month I was asked to post about it, and after some Patreon polling in which other posts ranked ahead, here it goes. In short: the study has some interesting analysis of the American cost premium, but suffers from some shortcomings, particularly with the comprehensiveness of the non-American data. Moreover, while most of the analysis in the body of the study is solid, the executive summary-level analysis is incorrect. Streetsblog got a quote from Eno saying there is no US premium, and on a panel at Tri-State a week ago T4A’s Beth Osborne cited the same study to say that the US isn’t so bad by European standards, which is false, and does not follow from the analysis. The reality is that the American cost premium is real and large – larger than Eno thinks, and in particular much larger than the senior managers at Eno who have been feeding these false quotes to the press think.

What’s the study?

Like our research group at Marron, Eno is comparing American urban rail construction costs per kilometer with other projects around the world. Three key differences are notable:

1. Eno looks at light rail and not just rapid transit. We have included a smattering of projects that are called light rail but are predominantly rapid transit, such as Stadtbahns, the Green Line Extension in Boston, and surface portions of some regional rail lines (e.g. in Turkey), but the vast majority of our database is full rapid transit, mostly underground and not elevated. This means that Eno has a mostly complete database for American urban rail, which is by construction length mostly light rail and not subways, whereas we have gaps in the United States.
2. Eno only compares the United States with other Western countries, on the grounds that they are the most similar. There is a fair amount of Canada in their database, one Australian line, and a lot of Europe, but no high-income Asia at all. Nor do they look at developing countries, or even upper-middle-income ones like Turkey.
3. Eno’s database in Europe is incomplete. In particular, it looks by country, including lines in Britain, Spain, Italy, Germany, Austria, the Netherlands, and France, but even there it has coverage gaps, and there is no Switzerland, little Scandinavia (in particular, no ongoing Stockholm subway expansion), and no Eastern Europe.

The analysis is similar to ours, i.e. they look at average costs per km controlling for how much of the line is underground. They include one additional unit of analysis that we don’t, which is station spacing; ex ante one expects closer station spacing to correlate with higher costs, since stations are a significant chunk of the cost and this is especially notable for very expensive projects.

The main finding in the Eno study is that the US has a significant cost premium over Europe and Canada. The key here is figure 5 on takeaway 4. All costs are in millions of PPP dollars per kilometer.

However, the study lowballs the US premium in two distinct ways: poor regression use, and upward bias of non-US data.

Regression and costs

The quotes saying the US has no cost premium over Europe come from takeaways 2 and 3. Those are regression analyses comparing cost per km to the tunnel proportion (takeaway 3) or at-grade proportion (takeaway 2). There are two separate regression lines for each of the two takeaways, one looking at US projects and one at non-US ones. In both cases, the American regression line is well over the European-and-Canadian line for tunneled projects but the lines intersect roughly when the line goes to 0% underground. This leads to the conclusion that the US has no premium over Europe for light rail projects. Moreover, because the US has outliers in New York, the study concludes that there is no US premium outside New York. Unfortunately, these conclusions are both false.

The reason the regression lines intersect is that regression is a linear technique. The best fit line for the US construction cost per km relative to tunnel proportion has a y-intercept that is similar to the best fit line for Europe. However, visual inspection of the scattergram in takeaway 3 shows that at 0% underground, most US projects are somewhat more expensive than most European projects; this is confirmed in takeaway 4. All this means that the US has an unusually large premium for tunneled projects, driven by the fact that the highest-cost part of the US, New York, builds fully-underground subways and not els or light rail. If instead of Second Avenue Subway and the 7 extension New York had built high-cost els, for example the plans for a PATH extension to Newark Airport, then a regression line would show a large US premium for elevated projects but not so much for tunnels.

I tag this post “good/interesting studies” and not just “shoddy studies” because the inclusion of takeaway 4 makes this clear: there is a US premium for light rail, it’s just smaller than for subways, and then regression analysis can falsely make this premium disappear. This is an error, but an interesting one, and I urge people who use statistics and data science to study the difference between takeaways 2 and 3 and takeaway 4 carefully, to avoid making the same error in their own work.

Upward bias

Eno has a link to its dataset, from which one can see which projects are included. It’s notable that Eno is comprehensive within the United States, but not in Europe. Unfortunately, this introduces a bias into the data, because it’s easier to find information about expensive projects than about cheap ones. Big projects are covered in the media, especially if there are cost overruns to report. There is also a big-city premium because it’s more complicated to build line 14 of a metro system than to build line 1, and this likewise biases incomplete data because it’s easier to find what goes on in Paris than to find what goes on in a sleepy provincial town like Besançon. Yonah Freemark thankfully has good coverage of France and includes low-cost Besançon, but Eno does not – its French light rail database is heavy on Paris and has big gaps in the provinces. French Wikipedia in fact has a list, and all of the listed systems, which are provincial, have lower costs than Paris.

There is also no coverage of German tramways; we don’t have such coverage either, since there are many small projects and they’re in small cities like Bielefeld, but my understanding is that they are not very expensive. Traditionally German rail advocates held the cost of a tramway to be €10 million/km, which is clearly too low for the 2010s, but it should lower the median cost compared to the Paris-heavy, Britain-heavy Eno database.

# Who Should Bear the Risk in Infrastructure Projects?

The answer to the question is the public sector, always. It’s okay to have private-sector involvement in construction, but the risk must be borne by the public sector, or else the private sector will just want more money to compensate for the extra risk.

The biggest piece of evidence for this is emerging out of our construction costs project, so it will appear in the report and not in a blog post. But for now, I’d like to point out examples from media, the academic literature, and one interview of particular interest.

PPP, Gangnam style

A transportation planner in Korea named Abdirashid Dahir has been giving Eric and me a lot of detailed information about Korean construction costs. We were already aware that Line 9 in Seoul had been built as a PPP, but what we learned was more complicated.

Line 9 is a partnership – the last P in PPP. This means, part of the construction is done by the private sector, and part by the public sector, namely the Seoul Metropolitan Government. The private consortium, led by Hyundai, was responsible for the design and for the construction of the systems, including the tracks, signaling, and rolling stock. SMG was responsible for the civil infrastructure. The total cost of the first phase was 1,167.7 billion won for 25.5 km, split as 492.2 billion in municipal construction and 675.8 billion in private investment.

The importance of this split is that civil infrastructure is the least certain part of underground construction. There are always geotechnical surprises, most small, a few potentially leading to large cost and schedule overruns. These are especially likely during station construction – the tunnels in between tend to be simpler with modern TBMs. Systems, in contrast, are relatively straightforward. Installing rail tracks is the same task regardless of whether it’s in solid rock in an exurban area that has no significant archeology, or through sand that had to be frozen, partly underwater, in the oldest parts of Berlin.

The upshot here is that while low-cost countries do use PPPs, this project keeps the riskiest aspects of construction public and not private. Privatization is fine for less risky, more commoditized situations.

How private bidders respond to risk

Two examples come to mind, both from the United States.

First, in New York, Brian Rosenthal’s seminal New York Times article cited Denise Richardson of the General Contractors’ Association saying that the contractors are barely making any profit and are bidding high because of risks imposed on them by the public sector. I don’t think this is a very high-quality source – it’s extremely biased, for one – but in context, it makes some sense.

Second, we do have more quantifiable data on this, thanks to the work of the Stanford Graduate School of Business economist Shosh Vasserman and Hoover Institute economist Valentin Bolotnyy. They look at highway maintenance contracts in Massachusetts and compare scaling auctions, in which the contracts are itemized, with lump sum auctions, in which they are not. Based on actual differences in price and estimates of contractor risk-aversion, they estimate that itemizing saves 10% of the cost through lower risk.

Supporting structures for public-sector risk assumption

There’s always the problem of moral hazard. Of note, even with this problem, costs are lower with itemized contracts in Massachusetts than with lump-sum contracts. But this does suggest a number of ways to reduce costs through better risk management:

• Itemized contracts, in enough detail that changes do not need litigation.
• Fixed profit rates – Spanish contracts are done with a fixed profit rate over the items named in the bid.
• Public oversight – there needs to be tighter supervision of risky things, which most likely means no PPPs for civil infrastructure.

It is unfortunate that American trends in the last 20 years have been away from those principles and toward greater privatization of the state, and equally unfortunate that American (and British) soft power has led to similar reforms in the wrong direction in the rest of the Anglosphere. But it’s possible to do better and imitate Korean practices to get Korean costs.


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3: towers of Hanoi

There's a very good book by Hinz, Klávžar, Milutinović and Petr, called "Towers of Hanoi - Myths and Maths".
It collects all sorts of theorems and perspectives on the puzzle, and plenty of variants.
A Mastodon instance for maths people. The kind of people who make $\pi z^2 \times a$ jokes.
Use $ and $ for inline LaTeX, and $ and $ for display mode.

format: plain


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# Double integral : $\int_0^1 \int_0^1 \frac{x-y}{(x+y)^3}$

$$\int_0^1 \int_0^1 \frac{x-y}{(x+y)^3}dxdy \; and \; \int_0^1 \int_0^1 \frac{x-y}{(x+y)^3}dydx$$

and find the relation between my answer and Fubini's theorem.

But for the first integral I got $-\frac{1}{2}$ and the second $\frac{1}{2}$. I thought the integrals should gave the same answer, but I couldnt figure out what I was doing wrong.

Can someone give me a help?

• I know that this function is not defined on $(0,0)$, but I thought that it satisfies the Fubini's theorem, doesn't it? – Giiovanna May 10 '14 at 14:27
• With regards to expecting the result to be the same in both integrals, what happens if you just rename the variable $y$ as $x$ and the variable $x$ as $y$ in the second integral and then compare it to the first? – Graham Hesketh May 10 '14 at 14:30


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# How to copy excel file and change the file name?

Hello,

1. If there is no current date file, copy last month file.
2. Change the file name to yyyy-MM(This month)
3. Save

Directory.GetFiles(“D:\Users\01048398\Desktop\Treasury_CashReport_Final”,""+Today.ToString(“yyyy-MM”)+".xlsx")

You can use a copy file/move file activity and your desired file name. Don’t forget to include the file extension.

@kenneth.m Thank you for your comment.
I’ve tried to rename the target file with Move File activity but faced below error message.
which script should I change ?

Hello~
Could you please review which part is wrong?
FileSystem.Rename(“D:\Users\01048398\Desktop\Treasury_CashReport_Final\template”,“D:\Users\01048398\Desktop\Treasury_CashReport_Final\Today.ToString(“yyyy-MM”)”)

Please mention the file name in existing path details. I have attached screenshot for your reference.

Happy Learning

It should be coded like this. FileSystem.Rename(“D:\Users\01048398\Desktop\Treasury_CashReport_Final\template”,“D:\Users\01048398\Desktop\Treasury_CashReport_Final\" + now.ToString("yyyy-MM"))

You can see no error in the invoke code

FileSystem.Rename(“C:\Users\giris\Desktop\text.txt”,“C:\Users\giris\Desktop\text-" + now.ToString("yyyy-MM") + ".txt")


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• •

### 河南省火灾影响因素的空间分析

1. 南阳师范学院 环境科学与旅游学院,河南 南阳 473061
• 出版日期:2014-07-25 发布日期:2014-07-25
• 作者简介:

作者简介:张海军(1978-),男,河北滦平人,硕士研究生,讲师,主要从事自然灾害模拟、评估和预警监测研究,E-mail:hjzhangny@126.com

• 基金资助:
国家自然科学基金项目(41201099,30771744)

### Spatial analysis of fire-influencing factors in Henan Province

Haijun ZHANG()

1. School of Environmental Science and Tourism, Nanyang Normal University, Nanyang 473061, Henan, China
• Online:2014-07-25 Published:2014-07-25

Abstract:

The spatial relationships between fire events and fire-influencing factors have important implications for fire managers and scientifically revealing these relationships is therefore significant for management purposes. The spatial stationary relationships between fire events and fire-influencing factors considered by previous fire risk studies contradict the fact that fire events and their quantifiable influencing factors are always characterized by spatial heterogeneity. If the intrinsically non-stationary relationships between fire events and fire-influencing factors are modeled by some stationary models, misleading and even erroneous conclusions can be drawn, which hamper fire prevention operations. In this study, logistic geographically weighted regression (LGWR) that can account for local variations of spatial relationships between fire events and fire-influencing factors was employed to analyze the influences of different fire-influencing factors on fire events in the high risk season (September and October) from 2002 to 2012 in Henan Province. The independent variables of the model include altitude (Al), slope (Sl), distance to the nearest village (Dv), distance to the nearest path (Dp), land surface temperature (LST), Normalized Difference Vegetation Index (NDVI), and global vegetation moisture index (GVMI); and the binary dependent variable is monthly fire presence, with 1 representing presence and 0 representing absence. A training subset derived from spatial random sampling was created and potential multicollinearity among the independent variables was excluded, and then a LGWR fire probability model was developed using the GWR 4.0 software. The reliability and discrimination capacity of the developed fire probability spatial model was evaluated using a testing subset and an independent validation subset and the results show good model performance. The model was used for fire-influencing factor analysis in the next step. After delineating and overlaying the significant areas of the non-stationary fire-influencing factors, seven fire prevention regions were identified in Henan Province. The relative importance of the non-stationary fire-influencing factors was evaluated by comparing the absolute values of their estimated coefficients spatially. The results indicate that: I) The influences of Sl, Dv, LST, NDVI and GVMI on fire events present significant spatial variability, whereas the influences of Al and Dp exhibit insignificant spatial variability in Henan Province. II) The influences of LST and NDVI on fire events are significant globally in Henan Province, whereas the influences of Sl, Dv and GVMI are only significant locally. The sites most strongly influenced by LST are mainly Nanyang, Zhumadian, Xinyang and their contiguous areas. The sites most strongly influenced by vegetation cover (NDVI) are primarily Zhoukou, Xinyang, Luohe, Xuchang, Zhumadian and Shangqiu. In Xinyang and southeast Zhumadian, fire events are most strongly influenced by Sl, while in Luoyang this factor is Dv, and in Zhoukou and the adjacent area of Luoyang, Nanyang and Pingdingshan, it is GVMI. III) This study demonstrates the usefulness of LGWR for exploring local variations of fire-influencing factors and for examining the validity of a global fire probability model. The practical implication of spatial analysis of fire-influencing factors resulted from LGWR is that different fire prevention policies and emphases should be formulated for each of the seven fire prevention regions. Because of such heterogeneity, fire prevention policies need to take into consideration local conditions.

• X43


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Tag Info

17

Let us first restate the mathematical statement that two operators $\hat A$ and $\hat B$ commute with each other. It means that $$\hat A \hat B - \hat B \hat A = 0,$$ which you can rearrange to $$\hat A \hat B = \hat B \hat A.$$ If you recall that operators act on quantum mechanical states and give you a new state in return, then this means that with $\hat ... 16 There is a fair amount of background mathematics to this question, so it will be a while before the punch line. In quantum mechanics, we aren't working with numbers to represent the state of a system. Instead we use vectors. For the purpose of a simple introduction, you can think of a vector as a list of several numbers. Therefore, a number itself is a ... 12 Time is not a variable in Quantum Mechanics (QM), it's a parameter — much in the same way as it is in Classical (Newtonian) Mechanics. So, if you have a Hamiltonian, e.g., for the harmonic oscillator, you have$\omega$as a parameter, as well as the masses of the particle(s) involved, say$m$, and you also have time — even though it's not something that ... 12 There are observables corresponding to the light going through both slits. You can write down a basis: "it went through slit A + slit B", and "it went through slit A - slit B". Although maybe you can't detect these observables easily with an experiment, they're perfectly good observables, they're orthogonal, and a clever enough experiment should be able to ... 11 I don't have a complete answer, but maybe the following is useful for your purposes: Consider the Laplacian$\Delta$on a circular drum of unit radius. As explained on the wikipedia page, the axially symmetric eigenvectors$\Delta u(r) = -\lambda^2 u(r) $are Bessel functions$u(r)=J_0(\lambda r)$. Obviously, the boundary condition requires ... 11 Are we talking quantum mechanics? Then I'd say that a "measurement" is any operation that entangles orthogonal states of the system under consideration with orthogonal states of the environment. "Measurement" is the important thing in most formulations of QM. Colloquially speaking, an observer is something that performs measurements. The only other place ... 9 Several reasons: Orthogonal functions arise naturally in the study of Sturm-Liouville theory which includes many classical and quantum system mathematical models; More generally, it is the class of normal operators (and an important special case self adjoint operators) which the spectral theorem most readily works and is most complete for. The eigenvectors ... 8 A simple example of non-commutativity is rotations in 3D, cf. figure. Physically, the rotations around the$x$- and the$y$-axis are generated by angular momentum operators$\hat{L}_x$and$\hat{L}_y$, respectively, which do not commute. From the mathematical expressions for$\hat{L}_x$and$\hat{L}_y$, you may proceed with the mathematical derivation, ... 7 It's a very good question but the answer is No, there is nothing such as "it went through both slits" observable (i.e. no linear operator that would correspond to this Yes/No question). The reason is that such "information" cannot be observed, not even in principle and not even statistically. Much more generally, there don't exist any observables that would ... 7 There is quite a lot of very important information hidden in the term hermitian. For an operator$A$on a finite-dimensional Hilbert space$\mathcal H$, one can show that there exists an orthonormal basis for the Hilbert space consisting of eigenvectors of the operator$A$. Moreover, one can show that the eigenvalues corresponding to these eigenvectors ... 6 Yes, since it is the maximal set of compatible observables, it includes all observables for which$|a\rangle$,$|b\rangle$,$|c\rangle$, etc. are the eigenvectors (I'll use the notation$|\psi_1\rangle$,$|\psi_2\rangle$,$|\psi_3\rangle$etc instead). Hence this includes the observable$D = \sum_k k |\psi_k\rangle \langle \psi_k|$. However$D$has a unique ... 6 Assume that you have a maximal set$A,B,C,\ldots$and two states$\phi_1$and$\phi_2$with the same set of eigenvalues in that set. Then construct the operator$Z = |\phi_1\rangle\langle\phi_1|$. Convince yourself that it would distinguish between$\phi_1$and$\phi_2$, and that it would commute with all of$A,B,C,\ldots$--- i.e. your original set was not ... 6 The statement is that if$K$and$L$are Hermitian operators – which means $$K = K^\dagger, \quad L = L^\dagger$$ and it implies that the eigenvalues of$K,L$are real and the eigenvectors with different eigenvalues are orthogonal to each other, then$i(KL-LK)$(the same as yours) is also Hermitian. This is easily proved by computing the Hermitian ... 6 As Lubos has mentioned$QP-PQ=i\hbar$is one of the basic requirements of quantum mechanics. Classically observables are functions of variables$q$, and$p$and Poisson bracket relation read$\{q,p\}=1$(note that$\{q,p\}$is unitless quantity ) In QM observables are required to be hermitian operators (so that they can have real eigenvalues). In ... 6 This is a rough version of the summary of the complete answer I posted on math.stackexchange, where more details are discussed in a long digression, in particular mathematical motivations for your points 1., 3. and 4. (Any reader interested in more explanations and a longer updated list of references should check out that other answer in Math.SE). I eagerly ... 6 Every observable in the technical or mathematical sense (linear Hermitian operator on the Hilbert space) is, in principle, observable in the physical operational sense, too. That's why it's called this way. Magnetic fields may be measured, for example, by compasses. Analogous methods exist for electric fields, scalar fields, or any other fields. For ... 5 I would actually expect this to be rare, and only generically true when the state of the system corresponds to an eigenstate. This simply because, for a state$\psi = \sum a_{n}\lvert\phi_{n}\rangle$with eigenvalues$V_{n}$, you would have$\langle V\rangle = \sum V_{n}\lvert a_{n}\rvert^{2}$, which is not constrained to be equal to one of the$V_{n}$. ... 5 There exists a set of eigenstates,$\{ |\psi_\lambda\rangle \}$, such that$L|\psi_\lambda\rangle = \lambda|\psi_\lambda\rangle$where$\lambda$is a real eigenvalue and$|\psi_\lambda\rangle$is an eigenstate of$L$. The$\lambda$represents the value of a physical observable associated with the eigenstate$|\psi_\lambda\rangle$. There is currently no ... 5 If$\psi$is a normalized eigenvector of$L^2$and$\lambda$the corresponding eigenvalue then$\lambda=\psi^*\lambda\psi=\psi^*L^2\psi=(L\psi)^*(L\psi)$. Thus$\lambda$is manifestly real and nonnegative. This even holds if$L$is a vector of noncommuting real (i.e., Hermitian) quantities, such as angular momentum. Then we get in the last step$\sum_i ...

5

One problem with the given $3\times 3$ matrix example is that the eigenspaces are not orthogonal. Thus it doesn't make sense to say that one has with 100% certainty measured the system to be in some eigenspace but not in the others, because there may be a non-zero overlap to a different eigenspace. One may prove$^{1}$ that an operator is Hermitian if and ...

5

I don't think this question has been answered. The original poster asked: why is \begin{align} \int dp |p\rangle \langle p| = 1, \end{align} up to unimportant normalization issues that have been discussed extensively (but are off the point). The above statement is equivalent to the question of completeness of a set of states on an Hilbert space (which ahmed ...

5

There are many experiments, the most famous of them is probably the Cavendish experiment, done in 18th century by a British scientist. I believe it was the first one to measure the force acting between two masses in a laboratory. He calculated the attraction between two lead spheres. http://en.wikipedia.org/wiki/Cavendish_experiment So, I believe 'yes' is ...

5

There is no time operator in quantum mechanics. At least, there's no nontrivial time operator. You could have an operator whose action is just to multiply a function by $t$, but time is a parameter in QM, so the operator will never do anything more complicated than that. Its eigenfunctions wouldn't be terribly useful either because they would just be delta ...

4

The wave function is a solution of an equation. It is as subjective and as objective as all mathematical solutions to equations describing physical fields, whether classical or quantum mechanical. Certainly as a solution it is objective, a formula written on paper. Subjectivity enters in the choice of the equation to be solved and thus the choice of the ...

4

Transcendental numbers often pop out in higher-loop Feynman diagram calculations. One example is the spectrum of local operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory, where the anomalous dimensions at higher loops in general contain $\zeta$-functions. As an example, the dimension of the operator $\mathop{Tr} \phi^a\phi^a$ is given ...

4

Questions 1,2: An observable is an element that is obtained from experiments. You can take this as the definition of an observable. The fact that we make an operator and give it some properties does not change/influence the outcome of an experiment. It just so happens that the theory we have ascribes linear, hermitian operators to explain experiments. With ...

4

If I try to measure the field at one point in spacetime, I should get a real value which should be an eigenvalue of the quantum field, right? I guess the eigenvectors of the quantum field also live in Fock space? Yes, that's basically correct. If the value of the field at a point is observable, the eigenvalues of the operator representing it are the ...

4

If you are able to produce multiple copies of the same pure quantum state, then it is possible to reconstruct the wavefunction. In that case, you need a relatively precise experiment, as just measuring the position and building a histogram will only give you the mod-squared of the wavefunction. To get some information of the phase, you might try measuring ...

Only top voted, non community-wiki answers of a minimum length are eligible


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# Eigenvalue Estimates for Beltrami-Laplacian Under Bakry-Émery Ricci Curvature Condition

@article{Wu2021EigenvalueEF,
title={Eigenvalue Estimates for Beltrami-Laplacian Under Bakry-{\'E}mery Ricci Curvature Condition},
author={Ling Wu and Xin Song and Meng Zhu},
journal={Potential Analysis},
year={2021}
}
• Published 16 August 2021
• Mathematics
• Potential Analysis
On closed Riemannian manifolds with Bakry-Émery Ricci curvature bounded from below and bounded gradient of the potential function, we obtain lower bounds for all positive eigenvalues of the Beltrami-Laplacian instead of the drifted Laplacian. The lower bound of the kth eigenvalue depends on k, Bakry-Émery Ricci curvature lower bound, the gradient bound of the potential function, and the dimension and diameter upper bound of the manifold, but the volume of the manifold is not involved…

## References

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The Journal of Geometric Analysis
• 2021
We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on (m, 0) forms, i.e., sections of the canonical bundle of Kähler manifolds, where m
• Mathematics
• 2012
Let M be a complete Riemannian manifold with Riemannian volume volg and f be a smooth function on M. A sharp upper bound estimate on the first eigenvalue of symmetric diffusion operator $${\Delta_f = In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature • Mathematics • 2014 We derive a Harnack inequality for positive solutions of the f-heat equation and Gaussian upper and lower bound estimates for the f-heat kernel on complete smooth metric measure spaces with • Mathematics • 2011 We prove a comparison theorem on the modulus of continuity of the solution of a heat equation with a drifting term on Bakry-Emery manifolds. A direct consequence of the result is an alternate proof Let$${L=\Delta-\nabla\varphi\cdot\nabla}$$be a symmetric diffusion operator with an invariant measure$${d\mu=e^{-\varphi}dx}$$on a complete Riemannian manifold. In this paper we prove Li–Yau • Mathematics The Journal of Geometric Analysis • 2018 AbstractUnder the usual condition that the volume of a geodesic ball is close to the Euclidean one or the injectivity radii is bounded from below, we prove a lower bound of the$$C^{\alpha } \cap
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In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in Lp-norm for some $${p > n}$$p>n. Using this regularity theory, we
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We study both function theoretic and spectral properties of the weighted Laplacian $\Delta_f$ on complete smooth metric measure space $(M,g,e^{-f}dv)$ with its Bakry-\'{E}mery curvature $Ric_f$