Simulation method reference

PET expresses the selected body model's heat balance as a reference air temperature. It uses body parameters and local conditions you supply. Mathematical checks establish the equation solution; physiological validity remains unassessed.

1. Qualified conditional PETSolve the selected steady MEMI equations, retaining conditional root certificates or supported condensation diagnostics without a PET value.Solves the selected steady MEMI equations for supplied body parameters, posture and local weather. Eight frozen reference results and two supported condensation refusals qualify the implementation. Root enclosures certify the equations; they are not confidence intervals or general physiological validation. Reference condensation returns diagnostics without a PET value. Validity wording and evidence are versioned with each result.Under these stated body and weather conditions, what reference temperature does the selected PET model calculate?Measures: Available PET values; Reference condensation refusals; PET under supplied conditions

Water finds the low ground. The simplest useful question is which places sit below a given water level, and answering it needs terrain and a level and nothing else. Rain adds a second question: where the water the drains cannot take comes to stand, and where it runs once it is on the ground.

1. Bathtub inundationSimple bathtub inundation modelFills the terrain to a stated water level and marks every cell below it, whether or not water could reach it. With rain, it spreads the rainfall the drains cannot take over each block of the terrain grid and fills that block's low ground until the volume is held.If the water comes up a meter and a half, which streets and which doorways are under it?Measures: Flood Maximum Water Depth; Flood Mean Water Depth; Flooded Area; Flooded Buildings Percentage; Flood-Exposed Population
2. Connected bathtub inundationBathtub with hydraulic connectivity filteringApplies a stated water level but keeps only the flooded cells connected to where the water comes in, such as the coast, so that low ground cut off from the water stays dry.If the sea stands two meters higher along the south and west edges, which buildings can the water actually reach?Measures: Flood Maximum Water Depth; Flood Mean Water Depth; Flooded Area; Flooded Buildings Percentage; Flood-Exposed Population
3. Drainage-capacity screeningPluvial flood screening based on drainage capacityScreens for surface flooding from rain: rain falling faster than the drains can take it is held on the ground and settles in the low points of the terrain.If fifty millimeters of rain an hour falls for two hours on drains that take twenty-five, where does the excess stand?Measures: Flood Maximum Water Depth; Flood Mean Water Depth; Flooded Area; Flooded Buildings Percentage; Flood-Exposed Population
4. Diffusive-wave flowDiffusive Wave SWE solverLets the water move: it solves the diffusive-wave form of the shallow-water equations on the terrain grid, with flow driven by the slope of the water surface and resisted by Manning friction, under the time-step limit of the LISFLOOD-FP diffusive solver (Hunter et al. 2005). The water starts as a sea level or a layer of excess rain and spreads over the storm's duration.Once that water is on the ground, where does it spread and how deep does it settle?Measures: Flood Maximum Water Depth; Flood Mean Water Depth; Flooded Area; Flooded Buildings Percentage; Flood-Exposed Population

A stated condition; no terrain or hydraulic model is run.

Sometimes the question is not where the water would go but what happens once it is there. You state the water yourself: how deep, over which circle, and from what time. No terrain or drainage is worked out; every point inside the circle has the depth you set once it begins, so the result carries that condition as an assumption, not a forecast.

1. Prescribed street depthEvaluate an explicitly assumed flood forcing; no DEM is inferred.Sets the depth you state at every point inside a circle from the moment you state, and zero elsewhere. No terrain, rainfall or drainage enters; it supplies a stated flood to questions that depend on one, such as which streets close to traffic.If the streets inside this circle stand under half a meter of water from noon, which of these addresses are under water at two o’clock?Measures: Flood Maximum Water Depth

Traffic can be treated as a fluid with a density and a speed, or as individual vehicles following the one in front. Both produce queues and stop-and-go waves. They differ in what you can ask afterwards.

1. Cell transmission modelCell Transmission Model (Daganzo 1994): min(sending, receiving) cell transfers, proportional junction merge/diverge, CFL-sized cellsDivides each road into cells that traffic at free speed crosses in one step, and moves vehicles between cells as the lesser of what the upstream cell can send and the downstream cell can receive (Daganzo 1994), in the supply-and-demand form of Lebacque (1996). At junctions, merging flows share space in proportion to demand and diverging flows split in proportion to supply.When a lane closes, where does the queue form and how far back does it reach?Measures: Total Vehicle Hours; Realized Network Speed; Accepted Vehicle Distance; Street-End Crossings; Street-End Crossing Rate; Congested Link Fraction; Mean Travel Time
2. Intelligent driver modelIntelligent Driver Model - realistic car-followingFollows each vehicle with the Intelligent Driver Model (Treiber, Hennecke and Helbing 2000): every driver accelerates toward a desired speed and brakes to keep a gap that grows with speed and with how fast the gap is closing.How do individual drivers follow the car in front, and when does stop-and-go appear out of nothing?Measures: Mean Network Speed
3. Lighthill-Whitham-RichardsLighthill-Whitham-Richards first-order continuum: Godunov scheme with demand/supply interface fluxes and link-coupled boundary conditionsSolves the Lighthill-Whitham-Richards conservation law of traffic (Lighthill and Whitham 1955; Richards 1956) with a Godunov finite-volume scheme on cells of a chosen length, with the junction rules of the cell transmission model and a chosen relation between density and speed.How does a slowdown travel back up the road as a wave after the cause has gone?Measures: Total Vehicle Hours; Realized Network Speed; Accepted Vehicle Distance; Street-End Crossings; Street-End Crossing Rate; Congested Link Fraction; Mean Travel Time
4. Nagel-SchreckenbergNagel-Schreckenberg cellular automaton microsimulationRuns the Nagel-Schreckenberg cellular automaton (Nagel and Schreckenberg 1992) on roads of 7.5-meter cells in one-second steps: each vehicle speeds up, slows to the gap ahead, sometimes slows at random, and moves.Cell by cell, with drivers braking at random. How does phantom congestion come out of nowhere?Measures: Mean Network Speed

What a place feels like on a hot day is not the air temperature. It is temperature, humidity, wind and radiation acting together on a body standing in that spot.

1. Outdoor heat screening (UTCI)Universal Thermal Climate Index screeningComputes the Universal Thermal Climate Index with the operational polynomial of Bröde et al. (2012), using weather inputs adjusted empirically for building density, parks, canyon wind and radiant heat. The public workflow uses the full sunlit or supplied reference radiant span and models no building shade. These input adjustments are screening assumptions; nothing here is calibrated to measurements.Under the supplied weather and building conditions, what does the outdoor heat screening calculation estimate at this bus stop?Measures: UTCI Maximum Temperature; UTCI Minimum Temperature; UTCI Median Temperature; Moderate Heat Stress Area; Strong Heat Stress Area

Sound leaves a source and loses energy on the way: with distance, into soft ground, into the air itself, and around whatever stands in between. Modeling it means accounting for that loss from the source to a receiver you actually care about, which is usually somebody's window.

1. Residents exposed at each facadeConserved resident allocation from supplied incident facade levelsShares each building's supplied residents among its supplied facade receivers so that every resident is counted once, and reports how many people are associated with each supplied noise level. The facade levels are inputs; this method does not compute sound propagation.Given the noise level at each facade, how many residents of these buildings live behind each level?Measures: Residents represented; Residents in buildings with a quiet facade; Share in buildings with a quiet facade
2. ISO 9613-2 outdoor propagationISO 9613-2 outdoor sound propagationFollows the general method of ISO 9613-2 for outdoor sound: the level at each receiver is the source's sound power less the losses from spreading with distance, from absorption in the air (ISO 9613-1), from the ground and from screening by barriers, summed over every source, under the downwind conditions the standard assumes.Will a new rooftop plant push night-time noise at the apartments opposite past the limit in the planning condition?Measures: Maximum Equivalent Sound Level; Minimum Equivalent Sound Level; Mean Equivalent Sound Level; Area Above Noise Threshold
3. Road noise from a line of trafficOctave-band finite-line and period propagation over flat groundIntegrates the sound of road traffic along straight line sources to each receiver, octave band by octave band and period by period, with geometric spreading, air absorption by ISO 9613-1 and an approximate ground term over flat ground. Barriers, buildings and terrain between source and receiver are not modelled.How loud is the traffic on this road at that window, by octave band and time of day?Measures: Listening points represented; Highest supplied-period level; Highest day-evening-night level
4. Experimental sound reflectionsStochastic ray tracing with reflectionsTraces sampled sound paths with reflections from supplied building geometry. The experimental estimator has an uncalibrated absolute decibel scale and is not calibrated to the ISO distance-loss reference; it cannot establish compliance with a noise limit.How do modeled sound reflections change across these building layouts in the experimental estimator?Measures: Maximum Equivalent Sound Level; Minimum Equivalent Sound Level; Mean Equivalent Sound Level; Area Above Noise Threshold
5. Residents of each buildingPrepare building residents from supplied counts, volumes or floor spacePrepares the number of residents of each supplied building from supplied counts, building volumes or floor space, by stated rules, so that later noise-exposure steps count people. It computes no sound levels.How many people live in each of these buildings, from the counts or floor space I supply?Measures: Prepared residents; Residential buildings represented; Heights based on known storeys
6. Distance attenuationSimple distance-only attenuationKeeps only the loss from spreading with distance, the first term of the ISO 9613-2 method, and sums the sources: a quick estimate with no absorption by the air or the ground.Roughly how far back does a generator have to sit before it stops mattering? No barriers, no ground effect, distance only.Measures: Maximum Equivalent Sound Level; Minimum Equivalent Sound Level; Mean Equivalent Sound Level; Area Above Noise Threshold
7. Receiver points on building facadesPrepare receiver midpoints for supplied straight facades longer than 2.5 mPlaces receiver points on supplied straight facades longer than 2.5 m, following the European noise-mapping rule (Directive 2015/996, Annex II, section 2.8): one midpoint on a wall up to 5 m, and equal intervals of at most 5 m on longer walls. Shorter walls are refused. It computes no sound levels.Where on these building walls should noise be computed?Measures: Prepared facade receivers; Supplied wall length

Something released into the air is carried by the wind and spread by turbulence. Where it comes down depends on the release height, the weather, and the buildings in the way. The three methods trade cost against how much of that geometry they can honor.

1. Computational fluid dynamics2D steady-state advection-diffusion solver (upwind finite differences, vectorized Jacobi)Solves the steady two-dimensional advection-diffusion equation for concentration on a grid, with the wind slowed where buildings stand, turbulent diffusion set by the stability class and an optional deposition loss, by upwind finite differences iterated to convergence.Given the buildings actually standing around that stack, where does the plume come down?Measures: Maximum Pollutant Concentration; Affected Area; Maximum Plume Distance
2. Gaussian plumeSteady-state Gaussian plume model (Pasquill-Gifford)Computes the steady concentration downwind of each source with the Gaussian plume equation, reflecting the plume off the ground, with its spread set by the Pasquill (1961) stability class through the dispersion coefficients of Briggs (1973). Optional dry deposition depletes the plume with distance.A depot is proposed upwind of a school. Roughly what concentration reaches the playground on an ordinary day?Measures: Maximum Pollutant Concentration; Affected Area; Maximum Plume Distance
3. Lagrangian particleStochastic Lagrangian particle trackingReleases many particles and moves each with the mean wind plus a random turbulent velocity that remembers its last step, a first-order Lagrangian stochastic model (Thomson 1987; Wilson and Sawford 1996), reflecting particles at the ground and at the top of the mixed layer. Concentration is the time-averaged mass of particles near the receptor height.Smoke from a fire, followed as particles while the wind shifts. Where does it end up?Measures: Maximum Pollutant Concentration; Affected Area; Maximum Plume Distance

People in a crowd steer around each other. Model each person as pulled toward where they want to go and pushed away from everyone close by, and lanes, jams and bottlenecks appear without anyone having programmed them.

1. Agent-based pedestriansORCA velocity-obstacle collision avoidance with behavioral layersHas each person choose a velocity that avoids colliding with neighbors over the next few seconds, sharing the avoidance equally, by optimal reciprocal collision avoidance (van den Berg et al. 2011), with behavioral layers such as panic on top.In a crowded concourse, do people get through the gates, or does a jam form and hold?Measures: Evacuated Agents; Mean Evacuation Time; Maximum Crowd Density; Crush Events
2. Floor-field crowd movementGrid-based cellular automata (faster)Moves people on a grid toward reachable exits using a static distance field and a decaying, diffusing field of prior movement, following the floor-field cellular automaton (Burstedde et al. 2001; Kirchner and Schadschneider 2002). Each cell holds at most one person; the supplied seed controls stochastic choices.How do people reach the exits through this declared grid, and where do queues form?Measures: Evacuated Agents; Mean Evacuation Time; Maximum Crowd Density
3. Helbing social force modelClassic Helbing social force modelMoves each person by the social force model (Helbing, Farkas and Vicsek 2000): a driving force toward the destination, repulsion from nearby people and walls, and contact forces where bodies touch. Reports how many people get out, how long it takes, the highest crowd density and crush events.How does a crowd move down a corridor, and where does it bunch up?Measures: Evacuated Agents; Mean Evacuation Time; Maximum Crowd Density; Crush Events

Graph measures, not physics.

Streets, paths and connections form a graph. Its structure helps examine how far you can get, what is near, which junctions connect many paths, and which places form closely connected groups. People can examine what those patterns mean for access and neighborhood life. The same model reads tables about areas and the people in them: which store people choose, how areas change between two years, where households move and how much groups share the places they visit.

1. Reach at each stated departureDirected accessibility for complete declared departure snapshots, best view and unionCalculates each supplied departure separately using its complete link-time multipliers. Reports each departure, the earliest best departure and the union of reached places separately.How does the area I can reach change across these departure times?Measures: Reachable network points
2. Access at different departure timesTime-varying accessibility with temporal profilesFinds the places reachable from one origin within a stated travel time at each declared departure, using supplied link-time multipliers. Each departure is evaluated separately; travel across departure intervals is not simulated.From this origin, which places are within twenty minutes at each supplied departure time?Measures: Reachable network points
3. Economic access between placesTravel times between zones on the network, access to economic mass (Graham, Gibbons & Martin 2009) and its appraisal value between two cases, and with a commuting table the Poisson gravity fit (Santos Silva & Tenreyro 2006), market access (Donaldson & Hornbeck 2016) and the hand-off to the spatial equilibriumComputes travel times between anchored work areas and access to their economic mass from actual jobs and supplied settings. Optional comparisons, commuting fits and market-access calculations remain conditional on those inputs; access alone does not prove a productivity gain.How does this travel-time change alter access to jobs and economic activity under these settings?Measures: Zones analyzed; Reachable zone pairs
4. Borrowed sizePopulation potential / borrowed size (van Oort/Burger)Adds up the population of every other place within a stated travel time, each divided by the time it takes to get there, a population potential after the borrowed-size idea of van Oort and Burger. It shows how much population a place can draw on beyond its own.A small town sits beside a big one. How much nearby population or activity is within reach, and what opportunities could that connection provide?Measures: Mean Population Potential
5. Nearby population weighted by travel timeDirected access using complete declared evidence and canonical travel secondsSums destination populations divided by their travel times along reachable paths. This is a network potential measure, conditional on the supplied population and travel data.How much nearby population does each place connect to under these travel times?Measures: Mean Population Potential
6. Capability relatednessBipartite relatedness and adjacent-possible analysisFinds the activities in which each region specializes by revealed comparative advantage (Balassa 1965), measures how related two activities are by how often regions specialize in both (the proximity of Hidalgo, Klinger, Barabási and Hausmann 2007), and lists the activities a chosen region lacks that are related to those it has: its adjacent possible.This city already does these things. Which industries are genuinely adjacent for it, and which are a reach?Measures: Adjacent Possible Capabilities; Mean Capability Relatedness
7. Connections among stated capabilitiesDeclared binary or weighted incidence and focus-bound relatednessReads the supplied region-to-capability network to measure specialization and relatedness. Binary and weighted incidence keep their distinct declared meanings; unavailable means remain unavailable.Which capabilities occur together across these supplied regions?Measures: Mean Capability Relatedness
8. Street-network disconnectednessStreet Network Disconnectedness Index (SNDi/Boeing)Describes street-network disconnectedness from connections, dead ends and the detours between supplied coordinates. This is a heuristic indicator of urban form; it calculates no travel activity, fuel use or carbon emissions.How disconnected is this street layout, and how much do routes detour from straight lines?Measures: Carbon footprint form records
9. Street geometry in declared coordinatesDeclared-distance street form using CRS axes and bounded canonical OD pairsMeasures route circuity, intersections and dead ends with the declared coordinates and units. Sampling and unavailable values remain explicit. These are geometric indicators with no emissions calculation.How connected is this supplied street layout under its stated coordinate system?Measures: Carbon footprint form records
10. CentralityNode/edge centrality (betweenness, closeness, etc.)Measures how central each junction is: betweenness (Freeman 1977), how often it lies on the quickest paths between other pairs, and closeness (Bavelas 1950; Sabidussi 1966), how near it is to all the others. On large networks it estimates from a seeded sample of starting points (Brandes and Pich 2007) and says so.Which junctions lie on many network paths, and whose journeys could depend on them?Measures: Highest Betweenness
11. Connection scores from declared linksDeclared-role centrality on the supplied topologyCalculates the selected centrality measure with explicit weight meaning. Scores describe the supplied graph and do not by themselves establish the effects of changing a place.Which places score highest under this stated connection measure?Measures: Centrality Scores Returned; Highest Betweenness
12. How close network places areCloseness (Bavelas 1950; Sabidussi 1966) and harmonic centrality (Marchiori & Latora 2000) of every nodeScores each node by its distances to other nodes, including a harmonic score that gives unreachable nodes no contribution. It reads links in both directions and reports when a seeded sample estimates scores instead of an exact calculation.Which junctions are nearer to the rest of this network under the declared link costs?Measures: Ranked Nodes Returned
13. Commercial vacancy and how long occupancies lastSupplied occupancy snapshot and exact inception survival records.Reports the share of the supplied commercial premises that are vacant in a supplied snapshot, and estimates how long an occupancy lasts from the supplied start dates, counting occupancies that have not yet ended as still running (Kaplan-Meier, with Greenwood intervals). The estimates describe the premises supplied; the platform does not check the records against any register.From these records of who occupies which shops and offices, what share is vacant now, and how long do occupancies usually last?Measures: Vacancy streets measured
14. Community detectionCommunity detection (Louvain/label propagation)Divides a network into groups that are more strongly tied within than between, by the Louvain method (Blondel et al. 2008) or label propagation, and reports how many groups there are and how sharply the network divides (its modularity).Which parts of the street network hang together as neighborhoods, rather than on the map?Measures: Community Count; Network Modularity
15. Groups of closely connected placesCanonical Louvain communities with the actual fixed seedGroups the supplied graph using unweighted links or declared tie strengths. Unsupported controls are refused; the grouping is conditional on the supplied network.Which supplied places form closely connected groups?Measures: Community Count; Network Modularity
16. Displacement evidence and conditional riskMove records, denominators and optional held-out risk-model evidence.Reads records of households moving between areas by group and reports how often each group leaves each area, with 95 percent Wilson (1927) intervals, where they go, and whether moves lead toward lower-income areas (after Sampson and Sharkey 2008). With more evidence it estimates price spillovers from high-price areas (after Guerrieri, Hartley and Hurst 2013), fits and tests a risk model on held-out data, or turns a stated change in accessibility into a range of rent pressure.What do the declared household moves and supported risk evidence say about displacement under the stated household definition?Measures: Evidence levels reported
17. Who receives a burden or benefitHow a burden or benefit given per location is spread across groups of residents: population-weighted means, gaps, percentiles and shares above thresholds by group, the Kolm-Pollak index (Sheriff & Maguire 2020), the concentration index (O'Donnell et al. 2008), response functions and screening indices from settings, and the change under a scenarioCombines a burden or benefit recorded for each place with resident-group counts. Reports group means, gaps, percentiles and threshold shares, with optional supplied response rules and scenario comparisons; those rules determine the meaning of any derived screening index.How is this measured noise burden distributed among the resident groups in these areas?Measures: Resident groups compared
18. Specialization across places and industriesEconomic and product complexity indices from job counts (Hidalgo & Hausmann 2009)Reads job counts by place and industry to measure specialization and how industries relate through that employment mix. The signed standardized indices describe the supplied table; they are not forecasts of growth or proof of an industry's suitability.What specialization patterns and related industries appear in this place-by-industry job table?Measures: Locations measured; Industries measured
19. Segregation in a declared visit panelDeclared visits and group assignment, with disclosed panel limitations.From a table of visits by home area to places, measures how much groups share the places they spend time in, by the experienced income segregation of Moro et al. (2021) or the experienced isolation of Athey et al. (2021), beside the residential figure for the same areas. Home areas below the panel's minimum group size are left out and counted.How much group exposure occurs in the declared visit panel, given its privacy bounds and population limits?Measures: Home areas measured
20. People within reach of facilitiesPopulation within a travel time of facilities, and the most the same number could cover (maximal covering location, Church & ReVelle 1974)Counts residents within a stated travel time of the supplied facilities and searches for better coverage with the same number of candidate sites. It reports whether optimality was proved and any remaining gap; network reach does not establish service capacity or quality.How many residents can reach these clinics in fifteen minutes, and could the same number of sites cover more?Measures: Population Within the Coverage Standard; Facilities Counted
21. Fifteen-minute cityPOI accessibility within walking isochrones (Moreno)Checks, for each junction, which of four kinds of everyday destination (education, health, food and leisure) can be reached on foot within a stated time, after the fifteen-minute city of Moreno et al. (2021), and reports the average share of the four within reach.From this doorstep, what can you reach on foot in fifteen minutes: school, doctor, groceries?Measures: Mean Fifteen-Minute Coverage
22. Coverage of four destination kindsDirected access using complete declared evidence and canonical travel secondsMeasures coverage of supplied education, health, food and leisure destinations within 15 minutes, following the declared links and travel costs. It is conditional on complete supplied counts.Which of these destination kinds can each place reach within 15 minutes?Measures: Mean Fifteen-Minute Coverage
23. Street drainage pathwaysThe street drainage network a one-dimensional solve reads: links with slopes, SWMM 5.2 street sections and Manning n, junctions with inverts, rims and branch bearings, sinks and spill paths by fill-spill-merge (Barnes, Callaghan and Wickert 2021), subcatchments, candidate inlets and the utility's sewer, every field marked measured, derived or assumed; no water is movedAssembles street slopes and sections, junctions, low-point sinks, spill paths, catchments and supplied sewer connections for a drainage calculation. Fields retain whether they are measured, derived or assumed. This preparation method moves no water and predicts no flood depth.Which street low points, spill paths and sewer connections would a drainage solver need for this area?Measures: Flood pathways records
24. Reaching food sourcesDistance from residents to the nearest food source of the counted categories, the sources within each threshold of an access rule setting, and the residents and areas beyond itFinds residents' distances to the nearest food sources of the counted categories, counts sources within the supplied access thresholds, and reports residents and areas beyond them. The categories and thresholds come from the declared rule.Which residents are beyond the supplied walking-distance rule for the food-source categories we counted?Measures: Food sources counted
25. Green space accessibility2SFCA park/green space accessibility (benchmark: 0.5 ha per 1,000 residents)Measures park access with a two-step floating catchment: each park's area is divided among the people who can reach it within a stated travel time, and each home adds up the shares of the parks it can reach. Reports the share of residents with at least 5 square meters of park each, a benchmark of 0.5 hectares per 1,000 residents.Does this neighborhood meet a benchmark of 0.5 hectares of park per 1,000 residents, once you count everyone competing for the same parks?Measures: Share of residents meeting 0.5 ha per 1,000 residents
26. Park access from supplied area and populationDirected access using complete declared evidence and canonical travel secondsUses supplied park area, population and travel times to calculate catchment ratios. The fixed area-per-person threshold is a disclosed proxy and establishes no external access standard.How much supplied park area is accessible relative to the people sharing it?Measures: Park Access Scores Returned
27. Street-canyon geometryStreet canyon H/W ratio and Sky View FactorUses supplied building heights and street widths to calculate canyon height-to-width ratios and an approximate visible-sky fraction. These are geometry proxies, not computed air temperatures or measurements of a heat island.Which streets have the deepest building canyons and the least visible sky under this geometry approximation?Measures: Heat island proxy records
28. Street canyon geometryComplete declared street-canyon geometry and sky-view approximationReports height-to-width ratios and a geometric sky-view proxy from the supplied observations. These geometric measures establish no temperature estimate.What do the supplied building heights and street widths say about canyon geometry?Measures: Heat island proxy records
29. Inequality within and between areasGini, Theil and Atkinson inequality of a named quantity among the zones of a zone system, from values or bracket counts (Jargowsky & Wheeler 2018), its split between neighborhoods (Shorrocks 1980), and the spatial Gini decomposition (Rey & Smith 2013)Measures inequality in a named quantity using weighted values or bracket counts for a declared zone system. Reports Gini, Theil and Atkinson measures and supported decompositions between neighborhoods and across neighboring areas; results retain what the units and weights count.How unequal are the supplied household incomes, and how much of that difference lies between neighborhoods?Measures: Income units measured
30. Where an industry clustersDistances at which a declared set of codes is localised against its wider sector (Duranton & Overman 2005), link distance decay (Murata et al. 2014), and location quotients, Gi* hot spots and network kernel density on zonesTests where supplied industry-coded points cluster against a declared wider sector, with optional observed-link and spatial-unit analyses. It does not establish a cause or a spillover distance; the street-distance extension has not been compared with the published straight-line test.At which distances do the listed industry locations cluster compared with their declared wider sector?Measures: Analytical results returned; Points in the selected code set; Hot spot groups
31. Collaboration structure between placesSupplied collaboration structure with caller-declared graph conventions.Computes the supplied collaboration network's structure, including normalized harmonic centrality restricted to outside places, under the component, projection and normalization choices you state, which the result repeats beside each number. It is a graph measure, not a prediction of innovation, and it ranks no places.In this network of collaborations, how central are outside partners to each place?Measures: Collaboration places measured
32. IsochronesTravel-time isochrones / accessibility contoursSearches outward from a starting point until a stated travel time runs out (Dijkstra 1959), and reports which junctions can be reached and what share of the network's junctions that is.How far can you get from here in ten minutes, twenty, thirty?Measures: Isochrone Reachable Share; Isochrone Reachable Nodes
33. Reachable streets with map locationsDeclared directed travel-time reachability with optional CRS-aware node projectionFollows supplied link directions and declared travel-time costs. Reports reached nodes and their travel times, with map locations where the supplied coordinates support them.Which streets can I reach within this travel time, and where are they on the map?Measures: Isochrone Reachable Share; Isochrone Reachable Nodes
34. Jobs within reachJobs each node reaches, weighted by a negative exponential of travel time (Hansen 1959) and within 1,800 s and 3,600 s, and their spread over residentsCounts jobs reachable within 30 and 60 minutes and weights jobs by a supplied decay with travel time. It also describes how access is distributed over residents. Reaching jobs does not establish vacancies, eligibility or a person's chance of employment.How many jobs can residents reach in thirty or sixty minutes, and where is access weakest?Measures: Job Access Points Scored; Job Access Equity Ratio
35. Nodes whose removal changes network influenceKey player intercentrality (Ballester, Calvo-Armengol & Zenou 2006)Ranks candidate nodes by how much removing each would lower the network's modeled total influence, using supplied decay along connections. The result concerns that mathematical network model, rather than demonstrating a person's real-world influence.Which candidate node's removal most reduces the network's modeled influence under this decay setting?Measures: Highest Key-Player Intercentrality
36. Labor markets from commutingLabor markets from commuting flows by Louvain community detection (Blondel et al. 2008), and the commuting each market keepsGroups places by the strength of their observed commuting flows and measures how much commuting each resulting market keeps within its boundary. The grouping describes the supplied flow table, rather than imposing administrative boundaries.Which places form commuting groups, and what share of each group's commuting stays inside it?Measures: Labor market areas; Commuters staying within their market
37. Neighborhood change under a declared rule setTwo declared area-year systems and caller-provided classification rules.Applies a typology of neighborhood change that the question supplies as a rule set, such as comparisons of each area's change with the regional median, to area statistics from two years. It carries the earlier year onto the later boundaries and prices where needed, and gives each area the first category it meets.Which areas meet the supplied neighborhood-change categories between two declared observation years?Measures: Areas classified
38. Access after links close or slowLinks a condition field closes or slows under a response rule, and the change in reach from facilities within response standards, places cut off, travel times of named pairs and the largest connected piece (Pregnolato et al. 2017; Wang et al. 2019)Applies a supplied response rule to a condition field to close or slow network links. Compares facility reach, isolated places, named journeys and the largest connected piece before and after that declared disruption.Under the declared flood-to-road response rule, which journeys and facility catchments lose access?Measures: Network disruption records
39. Occupations with similar skillsOccupations whose skill content is most similar, by the cosine of importances scaled by revealed comparative advantage (Alabdulkareem et al. 2018), with shared and missing skills and local jobsCompares occupations by their weighted skill content and reports similar occupations, shared and missing skills and supplied local jobs. Skill similarity alone supplies no probability of a worker moving between occupations.Which occupations use similar skills, and which required skills differ in the supplied records?Measures: Similarity comparisons returned
40. Routes with competing prioritiesMulti-objective non-dominated routesFinds routes for the first declared origin and destination under several supplied link costs. It keeps routes for which no alternative costs as little on every objective and less on at least one; the method does not choose which tradeoff the traveler should prefer.Which routes trade journey time for exposure after removing options that another route improves without increasing either cost?Measures: Non-dominated Routes Returned
41. Trade-offs among examined routesNondominated routes within a declared first-objective candidate boundCompares routes within a bounded candidate search. Reports the examined routes, the returned trade-offs and whether search or output limits left alternatives unexamined.Among the routes examined, which offer different trade-offs across these costs?Measures: Candidate Routes Returned; Non-dominated Routes Returned
42. Network connectivity under targeted node removalNetwork resilience via adaptive targeted node removalRepeatedly removes the node on the most shortest paths, recomputing that ranking after each removal. Records how the largest connected piece shrinks, the number of pieces and a connectivity threshold; this is a network-removal experiment, not a physical failure model.How quickly does this network break into pieces when the node on the most shortest paths is repeatedly removed?Measures: Largest Component Fraction; Schneider Robustness Index
43. Connectivity through targeted removalsUnweighted targeted-removal curve from the shared engineRecomputes the targeted removal order as nodes disappear. Reports connectivity and the removal curve within its stated computational bound. This route requires a positive removal share.How does this network break apart as important nodes are removed?Measures: Largest Component Fraction; Schneider Robustness Index
44. Diversity within and across sectorsUnrelated and related variety of each location's jobs across and within sectors (Frenken, Van Oort & Verburg 2007)Measures how jobs are spread between sectors and between industries within each sector, using the supplied classification and its two named levels. It describes diversity in the employment table, without establishing knowledge spillovers or future growth.Do these places have diverse sectors, diverse industries within sectors, or both?Measures: Locations measured
45. How residential groups are distributedDissimilarity, isolation and information theory indices of residential segregation (Duncan & Duncan 1955; Bell 1954; Theil 1972), and the spatial information theory index over street distance (Reardon & O'Sullivan 2004)Measures how resident groups are distributed across supplied areas through dissimilarity, isolation and information measures. With a street network it also evaluates group mixing at stated distance scales; residential distribution does not describe every place people visit.How separated are the supplied resident groups across areas and at the stated street-distance scales?Measures: Resident groups compared
46. Retail catchmentHuff store choice: expected customers and market share of each store (Huff 1963)Estimates each store's expected customers and market share with the Huff model (Huff 1963, 1964): the chance that people at a place choose a store rises with its size and falls with travel time, each raised to an exponent. Customers are counted as people, not revenue.Given store sizes and travel times, how many customers is each store expected to attract?Measures: Focal Store Share of Residents; Focal Store Expected Customers
47. Retail catchment fitted to declared visitsObserved-panel calibration of Huff choice, with caller-defined stores.Fits the Huff model's distance exponent, and its size exponent where store sizes are known, to an observed panel of visits from home areas to stores by maximum likelihood, for each class of store. Reports the fit with McFadden's (1974) pseudo R-squared and the correlation of observed with predicted visits.What store-choice exponents fit these declared visits, and what conditional trade areas follow from that fit?Measures: Outlet classes fitted
48. Noise emitted by road trafficSound power per meter each street link emits from its traffic, by segment, octave band and period, under a named emission standard's coefficient table; links ranked, and the change between two traffic cases (Directive (EU) 2015/996, Annex II, section 2.2)Computes the sound power emitted per meter of street from supplied traffic and a named emission standard's coefficient table, by frequency band and period. It ranks links and can compare traffic cases; sound levels at receivers require a separate propagation calculation.Which street links emit the most sound under this traffic table and the chosen emission coefficients?Measures: Road noise emission records
49. Shortest pathSingle-objective shortest/cheapest pathFinds the quickest route between two points from the travel time on each link, following the direction each link allows, by shortest-path search (Dijkstra 1959).What is the quickest way from here to there, and how does it change when a road shuts?Measures: Quickest Route Travel Time
50. Routes with declared travel costsDeclared cost or hop-based shortest simple routes with canonical equal-cost orderingRanks actual routes using the supplied cost attribute and its declared unit. Returns the selected link identities and reports when no route connects the stated points.Which routes have the lowest declared travel cost between these two points?Measures: Returned Routes; Quickest Route Travel Time
51. Related work from observed movesSkill relatedness from moves between classes with a binomial test per pair (Neffke & Henning 2013), its stability, the flow network's recursive communities (Park et al. 2019), job connectivity per place (Moro et al. 2021), where displaced workers went, and unemployment after a shock (del Rio-Chanona et al. 2021)Measures relatedness from recorded moves between work classes, with pairwise tests, communities and supported local-job and shock analyses. The supplied periods, counts and settings determine which comparisons and conditional scenarios can be reported.Which work classes are linked by the observed moves, and how stable is that pattern across the supplied periods?Measures: Classes measured; Flow periods measured
52. Access to places that bring people togetherPlaces that bring people together within a walk of each node, by category, their Shannon diversity, and provision per 1,000 residents by the two-step floating catchment (Luo & Wang 2003); access to places, with no statement about social capitalCounts places that bring people together within a stated walk, their category diversity and provision relative to residents through overlapping catchments. It measures access to places, without establishing social capital or actual participation.Which residents have few meeting places within a walk, under the supplied categories and travel times?Measures: Social places counted
53. Access from supplied journey timesCaller-supplied OD samples; no timetable routing or verified source authority.Reduces supplied origin-to-destination journey samples with their stated weights, counting opportunities after travel-time quantiles. Missing journeys retain unreachable probability mass. It acquires no timetable and establishes no observed reliability.Which opportunities fall within the requested travel-time percentile and limit?Measures: Origins measured from supplied journeys
54. A heuristic score for access on footWalk Score-style composite walkability indexCombines counted everyday destinations, junctions and network connectivity into a 0-to-100 score using fixed heuristic weights. The proxy is uncalibrated and does not measure pedestrian safety, observed walking or personal accessibility needs.How do these areas compare under the fixed walking-access proxy, using our counted destinations and street connections?Measures: Points scored for walkability
55. Walkability from supplied streets and destinationsDirected access using complete declared evidence and canonical travel secondsCombines supplied destinations, intersections and local links under a disclosed scoring rule. The result is a descriptive proxy conditional on that rule and those data.How does this stated walkability rule score the supplied places?Measures: Points scored for walkability

Conditional economic and fiscal analysis; no physical solver is asserted.

Economic calculations compare a declared travel-time change under fixed worker totals, commuting flows and supplied elasticity sets. Fiscal calculations apply a supplied profile to development quantities for one accounting year and report each government tier separately. Both calculations depend on their stated inputs and assumptions.

1. Single-year fiscal impact by government tierRevenue and cost a development adds to each tier of government in one stated year, under a fiscal profile the caller supplies: rates, band schedules, shares of pools, grants and charges against driver times unit cost, average or marginalApplies a supplied fiscal profile, with its rates, bands, shares of pooled revenue, grants and unit costs, average or marginal, to a development's quantities, and reports revenue and cost for each tier of government in one stated year, never summed across tiers. It follows the fiscal impact methods of Burchell and Listokin (1978) and Kotval and Mullin (2006).What revenue and cost does this development add to each government tier in the stated accounting year under the supplied fiscal profile?Measures: Government tiers reported
2. Property effects from published ratesApply each selected rate with its published spread, measured source places/period and separate scoped comparisons; no local calibration, total, forecast or causal claim.Applies each rate you select from a published study, with its published spread and the places and years it was measured in, to the supplied properties, and reports each result separately beside the study's own scope. It does not fit anything to local sales, sum the results, forecast or claim a cause.If I apply the published effect of a new transit line on house prices to these properties, what range of changes does that give?Measures: Areas with supplied measure changes
3. Price changes around an announcementDescriptive single-announcement dose/event regression with preterms and independent-error HC0 intervals; unsupported causal labels refuse.Fits a descriptive regression of supplied sale prices on distance to one announced change and on time before and after the announcement, with terms for the period before, and reports coefficients with heteroskedasticity-robust (HC0) intervals that assume independent errors. A label that asks it to call the result causal is refused.Did sale prices near the announced site move differently after the announcement than before it?Measures: Event-study priced observations
4. Checking a property price model on held-out salesTraining-only log-price fits on identical features; report median absolute percentage error and share within10% on the same heldout observations, without calibrated scientific confidence.Fits log-price models on a training share of the supplied sales only, with identical features, and reports the median absolute percentage error and the share of predictions within 10 percent on the same held-out sales, with the seed that chose them. It measures prediction error on these sales; it assigns no scientific confidence.If I fit this price model on part of these sales, how well does it predict the sales it did not see?Measures: Held-out priced observations
5. Property price effects of a nearby changeOLS or supplied-weight spatial Durbin 2SLS with area/annual effects, exact direct/indirect effects and area-only bootstrap counterfactuals; no causal or forecast claim.Fits sale prices by ordinary least squares or by a spatial Durbin model estimated by two-stage least squares with neighbour weights you supply, with area and annual effects. It reports direct and indirect effects and counterfactual changes with intervals from resampling areas. It makes no causal or forecast claim.How are sale prices in this area associated with distance to the new park, here and in neighbouring areas?Measures: Supplied priced observations
6. Property price models with controlsDated OLS or supplied-weight Durbin 2SLS with optional repeated-property effects, categories, boundary groups and area-class slopes; exact class-origin effects and area-only scenario sensitivity. No causal claim or assessed interval coverage.Fits dated sale prices by ordinary least squares or a spatial Durbin model with optional effects for repeated sales of one property, categories, boundary groups and slopes by area class. It reports effects by class and the sensitivity of a scenario to area-level variation. It makes no causal claim, and the coverage of its intervals has not been assessed.Does the association between sale prices and the new line hold when I control for repeated sales of the same property and for boundaries?Measures: Retained dated priced observations
7. Closed-city spatial equilibriumJobs, residents, wages, floor prices and welfare after a change in travel times, by exact hat algebra (Dekle, Eaton & Kortum 2008) in the closed city of Ahlfeldt, Redding, Sturm & Wolf (2015), bracketed over elasticity sets and two closuresSolves for the new equilibrium after a change in travel times in the closed-city model of Ahlfeldt, Redding, Sturm and Wolf (2015), written in proportional changes by exact hat algebra (Dekle, Eaton and Kortum 2008). It runs under one to three supplied sets of elasticities and two closures, one without agglomeration and with fixed floor space and one with agglomeration and elastic floor space, and reports results as ranges.How would jobs and residents redistribute after this travel-time change under fixed worker totals and the supplied economic assumptions?Measures: Minimum jobs relocated

Travel demand is built in stages: how many trips a place produces, where they go, which mode they take, and which roads they end up on. The stages separate cleanly, which is why this has been the standard planning method for decades. Activity-based techniques build the same demand from each person's day of activities.

1. Activity-based travel from declared schedulesMode choice for supplied persons following supplied schedulesStarts from a population of people and each person's schedule of activities, makes a trip whenever a person moves between zones, and chooses each trip's mode with a multinomial logit model, offering only modes that fit the time before the next activity and driving only to people with a car.Given each person’s declared day of activities, which trips do they make, when, and by what mode?Measures: Total Trips; Average Trip Time; Average Trip Length; Total Vehicle Miles Traveled
2. Four-step travel demandTraditional 4-step model: generation, distribution, mode choice, assignmentGenerates trips from households, jobs and retail floor space, or grows a supplied base-year table of trips; distributes them between zones with a gravity model; divides them among modes with a multinomial logit model that weighs travel time by a value of time (Ben-Akiva and Lerman 1985); and assigns them to roads. These are the four stages of the four-step model (McNally 2000).A housing block goes in. How many trips does it generate, where do they go, by what mode, and which roads carry them?Measures: Total Trips; Total Vehicle Miles Traveled; Average Trip Length; Average Trip Time
3. Iterative replanning with Charypar-Nagel scoringIterative mode replanning for supplied persons following supplied schedules with Charypar-Nagel scoringStarts from declared schedules and, round after round, lets the worst-scoring travelers revise their plans, each keeping their best plan. Plans are scored after Charypar and Nagel (2005): time at activities earns utility and time traveling costs it.If people with these declared schedules reconsider how they travel, which mode choices score best against the supplied travel times?Measures: Total Trips; Average Trip Time; Average Trip Length; Total Vehicle Miles Traveled

Infection moves through a population that is not uniform. People mix mostly within their own age group, commute between places, and recover at different rates. These models follow the whole population moving between states rather than following individuals.

1. Metapopulation SIRDeterministic susceptible-infected-recovered flow across caller-supplied population groups.Follows susceptible, infected and recovered people in several connected populations, such as districts, with deterministic equations. Each population's infection pressure combines contact within it with contact carried from the others through weighted connections, such as commuting.An outbreak starts in one borough. How does it move between boroughs, given who commutes where?Measures: Most people infectious at once; When the infectious population peaks; Cumulative infections
2. Stratified SEIRDeterministic susceptible-exposed-infected-recovered flow across heterogeneous caller-defined strata.Adds an exposed stage between susceptible and infected, and lets groups such as age bands differ in how susceptible and how infectious they are, mixing through a directed contact matrix. The deterministic equations keep each group's population constant.How differently does the same outbreak run through children, working adults, and people over seventy?Measures: Most people infectious at once; When the infectious population peaks; Cumulative infections

Some questions are better asked of a model that someone has already published. This one is a published model of an outbreak that follows how many people are susceptible, infectious and recovered. The platform runs its equations exactly as the source states them, in steps of 1/32 of a day over 100 days, so its results can be checked against the published reference. You can change how easily the illness spreads and how long people stay infectious.

1. Published SIR, fixed-step EulerExact source equations and 1/32-day Euler reference recipe.Follows the susceptible, infectious and recovered people of one closed population with the published source's equations, stepped forward by Euler's method every 1/32 of a day for 100 days, as the source's reference recipe specifies. It reports the largest number of infectious people at the sampled times and the day it occurred, and how many people end in each state.If people stayed infectious for a shorter time, how much lower and how much later would the outbreak peak in the published model?Measures: sir sampled peak infectious people; sir sampled peak time days; sir final susceptible people; sir final infectious people; sir final recovered people

People move between states: waiting, being seen, finished. Following the flow between those states over time is what tells you where a backlog builds and how long it takes to clear.

1. Continuous four-stateContinuous flow across Idle, Queued, Active, and Cleared states.Moves each group's population from idle to queued to active to cleared with deterministic equations, so that people wait in a queue before they are served and the backlog shows where it builds.With a queue stage before service, where does the backlog at a vaccination center actually sit?Measures: Peak Active Fraction; Cumulative Shifted Fraction; Time of Peak Active Fraction; Final Active Fraction; Final Cleared Fraction
2. Continuous three-stateContinuous flow across Idle, Active, and Cleared states.Moves each group's population from idle to active to cleared with deterministic equations; the rate of becoming active depends on how active the group and the groups linked to it already are, and the rate of clearing is fixed.People waiting, being seen, done. How does the queue at a vaccination center drain across a day?Measures: Peak Active Fraction; Cumulative Shifted Fraction; Time of Peak Active Fraction; Final Active Fraction; Final Cleared Fraction
3. Stochastic three-stateStochastic flow across Idle, Active, and Cleared integer-unit states; does not represent individual attributes, schedules, movement, or explicit interaction events.Counts whole people instead of fractions: at each step the number moving between idle, active and cleared is drawn from a binomial distribution at the stated rates, from a seeded random generator. Repeating the run shows how much the outcome varies.The same flow counted in whole people rather than fractions, run many times, so you can see how much the day varies.Measures: Peak Active Fraction; Cumulative Shifted Fraction; Time of Peak Active Fraction; Final Active Fraction; Final Cleared Fraction

Something spreads across a network of connected places: heat, money, a rumor, a habit. Each method here makes a different assumption about what makes the next place catch it, and on the same graph they give you noticeably different answers.

1. Independent cascadeIndependent Cascade model for information/influence spreadingStarts from chosen seed nodes. Each newly active node has one chance to activate each inactive neighbor, with a probability scaled by the strength of their tie, and the spread stops when a round activates no one (Kempe, Kleinberg and Tardos 2003).One shop on the street goes contactless only. If each neighbor gets one chance to persuade the next, how far does it travel?Measures: Activation Fraction
2. Linear heat conductionHeat equation on graph LaplacianSolves the heat equation on the network's graph Laplacian: each node's value moves toward its neighbors' values at a rate set by the tie weights, and chosen nodes can be held at fixed values. Reports the lowest, highest and mean values at the end.Heat is dumped into one district. How does it even out across the connected districts over the next few hours?Measures: Final Mean Node Value; Final Lowest Node Value; Final Highest Node Value
3. Linear thresholdLinear Threshold model for opinion/behavior adoptionEach node takes something up once the share of its tie strength coming from neighbors that already have it reaches the node's threshold, which is fixed or drawn at random for each node; rounds continue until no one else adopts (Granovetter 1978; Kempe, Kleinberg and Tardos 2003).People join a recycling scheme only once enough neighbors already have. Does it reach the whole neighborhood, or stall halfway?Measures: Activation Fraction
4. Values returning toward a long-run meanOrnstein-Uhlenbeck for price/economic diffusionMoves each node's value toward a stated long-run mean while values also diffuse along network ties. A supplied volatility can add seeded random shocks. The resulting paths depend on these parameters and do not establish a calibrated economic forecast.How do these network values evolve under the stated long-run mean, tie strength and volatility?Measures: Final Mean Node Value; Final Lowest Node Value; Final Highest Node Value

When one part of an infrastructure network fails, the load it was carrying has to go somewhere. If its neighbors cannot absorb it they fail in turn, and the failure walks across the network.

1. Steady pipe-flow balancingSteady pipe-flow and head-loss screening; pressures are not solvedBalances signed pipe flows with continuity and Darcy-Weisbach friction corrections on a declared steady pipe network. Reports flow and friction head loss; absolute pressure heads are not solved.With these pipe dimensions and demands, what signed flows balance the pipe loops?Measures: Total Infrastructure Failures; Stressed parts; Stressed links; Largest final pipe flow; Largest final friction head loss
2. Dependence across infrastructure layersAggregate interdependent infrastructure cascade with persistent exposureShares load within declared infrastructure layers and reduces capacities through supplied dependencies. Reports failures and local cross-layer effects, with a post-failure repair-time estimate; it does not simulate repair or prove the effects of a full counterfactual rerun.Can loss of capacity in one infrastructure layer cause failures in another?Measures: Total Infrastructure Failures; Stressed parts; Stressed links; Model-necessary cross-layer failures; Aggregate exposure chain length; Heuristic repair estimate; Aggregate resilience score
3. Load redistribution cascadeLinearized load redistribution cascadeStarts from the components that have failed. Each failed component passes a stated share of its load to its working neighbors, in proportion to how easily load flows to each, and sheds the rest; any component pushed to its capacity fails in turn, until nothing more fails.One substation trips and its load moves to its neighbors. Do they trip too?Measures: Total Infrastructure Failures; Cascade Depth; Stressed parts
4. Nonlinear load screeningHeuristic nonlinear burden and attenuation cascade; not electrical power flowDistributes persistent base load scores through weighted links with quadratic burden and attenuation. Reports overloaded parts and final scores; these scores do not establish electrical power, voltage or physical losses.Under these declared load-score rules, which parts overload after a failure?Measures: Total Infrastructure Failures; Stressed parts; Stressed links; Largest final quadratic burden; Largest final node load score
5. Offered traffic screeningTelecom congestion cascade with queueing-style latency escalationSplits each sender’s offered traffic across available outgoing links and computes a capped utilization-based latency estimate. Traffic is not forwarded through later nodes; packet routing and end-to-end latency are not computed.How does each sender’s offered traffic load its available outgoing links?Measures: Total Infrastructure Failures; Stressed parts; Stressed links; Largest final offered link rate; Largest final latency proxy; Links at the latency proxy cap

Graph measures, not physics.

Take a network and start removing pieces. For a while very little happens, and then it comes apart. Where that threshold sits, and how far it moves between random loss and deliberate attack, is what these measure.

1. Random failureUniform random node removalRemoves junctions in a random order fixed by a seed and tracks the largest connected part as a share of the original network. Reports the robustness index R of Schneider et al. (2011) and the share removed when the largest part first falls below half.If parts of the network fail at random, at what point does it break into disconnected pieces?Measures: Largest Component Fraction (Percolation); Schneider R-Index (Percolation); Percolation Threshold
2. Targeted removalIterative highest-betweenness node removalRemoves the junction that most shortest paths pass through, recomputing after each removal, and reports the same measures. Compared with random failure, it shows how much faster a network breaks apart when its most central junctions go first.If someone takes out the most important junctions one at a time, how many before the whole thing comes apart?Measures: Largest Component Fraction (Percolation); Schneider R-Index (Percolation); Percolation Threshold

Materials and perishable cargo have a clock running on them. Heat speeds up chemical decay, and repeated loading accumulates fatigue. Both are cumulative, and neither shows until something fails, so the model keeps the running total rather than a snapshot.

1. Arrhenius temperature agingArrhenius kinetics for temperature-time (organs, food)Lowers a health index over time at a rate that rises exponentially with temperature, by the Arrhenius equation, from a reference rate, reference temperature and activation energy the question supplies. Reports the remaining health, the accumulated damage, spells well above the reference temperature and, by extrapolation, when health would run out.A donor organ sat in a broken cold chain for forty minutes. How much viable time did that cost?Measures: Final Health Index; Total Accumulated Damage
2. Cooling, melting and microbial thresholdsCold chain perishability with phase change and microbial growthFollows modeled item temperature, melting and microbial growth through the supplied conditions. Reports retained states and the declared microbial threshold being reached; the health and excursion indices do not establish food safety or biological viability.Under this temperature history, when does the modeled item melt or reach the declared microbial threshold?Measures: Final Health Index
3. Miner’s rule fatigue accumulationMiner's rule for cumulative fatigueAdds up fatigue damage by Miner's rule: each period of loading uses up its number of cycles divided by the number the material can bear at that stress, read from an S-N curve of Basquin form with a fatigue limit below which no damage accrues. A damage index of 1 marks the end of fatigue life.A bridge deck has taken twenty years of truck traffic. How much fatigue life is left in it?Measures: Total Accumulated Damage; Final Health Index
4. Combined heat and mechanical screeningUncalibrated coupled thermo-mechanical screening rulesCombines declared thermal and mechanical screening rules, retaining their separate damage increments, interaction and condition history. The coupled rules and failure index are uncalibrated; they do not establish failure probabilities or a safety assessment.How do the declared heat and mechanical rules contribute to this uncalibrated condition-loss history?Measures: Final Health Index
5. Condition after recorded shocksG-force shock damage (artwork, electronics)Applies the declared threshold rule to each recorded instantaneous acceleration peak and retains the resulting condition loss. Condition is an uncalibrated index, not a failure probability or a biological viability assessment.How much condition does the declared rule remove at each recorded acceleration peak?Measures: Final Health Index

Construction has geometry and it has shaking. A crane sweeps a volume that must not intersect anything; piling and demolition put vibration into the buildings next door. Both get checked against published limits.

1. Combined constraintsRun both crane clearance and PPV vibration in one passRuns the crane clearance check and the vibration screen together for one site and reports both.Run the crane clearance check and the vibration screen for one site in a single pass.Measures: Minimum Structural Clearance; Maximum Peak Particle Velocity; Clearance Violations
2. Crane clearance3D geometric crane clearance checkChecks in three dimensions whether the volume each crane's jib sweeps as it slews keeps the required clearance from the buildings around it, and flags each building that falls short.Can this crane slew without its jib crossing the neighboring building or the railway?Measures: Minimum Structural Clearance; Clearance Violations
3. Elastic strain and yield screening of a frameElastic trial normal strain and sourced member material-yield ratiosSolves the frame elastically and, for each member, reports the normal strain of that trial solution and the ratio of its stress to the yield strength of the member's stated material, with that material's source. A ratio above one means the elastic assumption does not hold for that member; the method does not follow the member beyond yield.Under these loads, how close does each member of this frame come to the yield strength of its material?Measures: Largest elastic trial normal strain; Largest normal-stress material utilization
4. Experimental ground-wave screeningFinite-difference ground-wave propagationPropagates vibration on a finite-difference grid in homogeneous soil and screens modeled peak motion at buildings. Despite its legacy method name, this is not a finite-element solver; it remains unvalidated against measurements or the empirical vibration method.Under this homogeneous-soil assumption, what ground motion does the experimental grid model estimate at nearby buildings?Measures: Maximum Peak Particle Velocity
5. Linear elastic frame analysisSmall-displacement planar Euler-Bernoulli frame stiffness solve with explicit member dataSolves a planar frame of straight, rigid-jointed members by the direct stiffness method with Euler-Bernoulli beam elements, and reports joint displacements, support reactions and member end forces. It assumes small displacements and elastic materials, and uses only the member data and supports you supply.How far does this frame move, and what forces does each member carry, under these loads?Measures: Largest planar joint displacement; Largest frame normal stress
6. Peak particle velocity vibrationPPV vibration screening (DIN 4150-3)Estimates the peak particle velocity of ground vibration at each building from the velocity at the source and the distance, decaying at a rate set by the soil, and screens each building against the limits of DIN 4150-3, in bands from negligible to severe.Will piling next door shake that landmark building past the DIN 4150-3 limit?Measures: Maximum Peak Particle Velocity

Graph measures, not physics.

A city rarely stops where its boundary says it stops. Delineation infers the real extent from where people are and where they travel, rather than from an administrative line.

1. Density clusteringDensity-based cluster delineationKeeps the grid cells at or above a population density threshold, joins touching cells into clusters by the City Clustering Algorithm, and keeps the clusters whose population reaches a stated minimum.Where does the built-up area actually end, going by where people are rather than by the city limits?Measures: Urban Cluster Count
2. Flow-based functional urban areasFlow-based FUA delineationStarts from the density clusters, merges cores linked by at least a stated share of their commuting (15 percent unless set otherwise), and attaches each surrounding area to the core that receives the largest share of its commuters, giving functional urban areas.Which towns commute into this city enough to count as part of it?Measures: Functional Urban Area Count; Urban Cluster Count; Largest Functional Urban Area Population
3. Settlement thresholds followed by commuting areasPercolation-detected threshold delineation chained with flow-based FUA grouping on the same supplied inputsSelects a settlement threshold through a sweep, then uses it to group cores and commuting areas from the same presence and flow inputs. The historical name does not mean additional data sources are combined; its confidence score is an uncalibrated heuristic.Which commuting areas follow after a threshold sweep identifies settlement cores in these data?Measures: Functional Urban Area Count; Urban Cluster Count; Largest Functional Urban Area Population
4. Settlement boundaries from a threshold sweepEndogenous threshold detection with percolation phase analysisSweeps settlement-density and flow thresholds and looks for a change in cluster size to select a boundary threshold. The result records a detected or fallback threshold; its confidence score is an uncalibrated heuristic, not a probability that a boundary is correct.Where does cluster size change sharply as the supplied settlement thresholds are swept?Measures: Urban Cluster Count

Many questions are about amounts that build up and run down: people waiting for a service, food in a pantry, money in a fund, water behind a dam. A stock-and-flow model, the method known as system dynamics, writes each amount as a stock, and each movement between stocks as a flow with an equation for its rate. You or your assistant write the model. The platform checks its units and equations before the run and then runs it as written. A model that runs cleanly is not thereby right about the place, and the platform states that with its results.

1. Stock and flowRun an exact admitted version 1, 2 or 3 source at capacity 2, retaining the series its invocation names, locating the switches of its rates and reporting how far its solves have got.Runs a model written as data: stocks, the flows between them, the equation for each flow's rate, and the unit of each amount. Every flow moves an amount between two stocks or across the model's edge, so nothing is created or lost between the stocks it connects. The platform checks units and equations before the run and integrates under the numerical limits stated for the run, which were set from measurements of the solver. A model may declare delays: a delay holds an amount for a stated time before passing it on, and the platform runs each delay as a chain of stages inside the model. The run keeps the time series of the stocks and flows it names; peaks, totals over time, threshold crossings and amounts moved can be computed for any stock or flow, whether or not its series is kept. When a rate switches from one formula to another, such as a release that starts when a reservoir passes a stated level, the platform finds the time of the switch to a stated tolerance and restarts the solver there, and it reports each switch it found and any interval in which it could not settle when a switch happened. A model whose amounts change on very different time scales, which is called stiff, such as a fast reaction beside a slow one, can run under the Radau or BDF method, and each of the two is checked against the other. A model may declare arrays: a stock, flow or other declaration over named dimensions, such as one per region or age group, with one equation for every element, exceptions for named elements, and sums, means, products and least or greatest values over a dimension; the platform runs each element as a declaration of its own. A run may be approved for up to a day of computing; while it runs it reports how far each solve has got in model time and how much of its work limit it has used, and that report is status, not a result. A run may be an ensemble: the same model run a stated number of times, each member drawing the inputs it names from stated distributions, each with its source, from one seed. The result lists the members by outcome and, for each observation, its spread over the members that finished; those values are conditional on the model and on the stated distributions. A run may be a sweep: the same model run at stated values of the inputs it names, either every combination of each input's values or a list of stated points, each input with its source. The result lists the points by outcome and each observation at every point; the points were chosen, not drawn, so those values describe the stated points and are conditional on the model.Our food pantry takes in donations and gives out food every day. If donations fall by a third, how many weeks until the shelves are empty?Measures: the stocks and flows the model lists as its observations

Some questions are about something passed from one person or thing to another through contact: a task, a status, a signal. This model gives each identifier one state, idle, active or cleared, and lets an active one make an idle contact active with a stated probability on each step. The contacts are a fixed list you supply, so the result depends on that list and on the probability, which the platform does not calibrate.

1. Idle, active and cleared states over contactsPrivate Idle, Active and Cleared states over fixed typed contacts.Gives every identifier one private state, idle, active or cleared, and on each step lets an active identifier make idle contacts active through independent trials with the supplied probability. Contacts of three types use fixed trial counts of 10, 5 and 8 and fixed weights of 1.5, 1.0 and 1.2, which are not calibrated. The contact list stays fixed during the run, and steps are ordinal, not clock time.If one of these units becomes active, how many others along these contacts become active, and when do they clear?Measures: contact state flow final idle count; contact state flow final active count; contact state flow final cleared count; contact state flow peak active count

An illness passes between particular people who live, work or study together, not between averages. This model follows each person through susceptible, infectious and recovered over whole days, with contact trials along a household, workplace or school graph you supply. People who recover stay recovered. The trial counts and contact weights are fixed settings that have not been compared with any outbreak.

1. Infection between people on a contact networkRun the existing native contact-network SIR model with fixed infectious duration and per-day repeated contact trials.Follows each person on a supplied household, workplace or school contact graph through susceptible, infectious and recovered, day by day, with repeated contact trials each day and a fixed number of infectious days. People who recover do not become infectious again. The trial counts and contact weights are fixed settings, not calibrated.If this person is infected, how many people in these households, workplaces and schools become infected, day by day?Measures: Peak infected population; Cumulative infections

Some infections give no lasting immunity, so a person who recovers can be infected again. This model follows each person over whole days on a fixed contact graph you supply: an infectious person stays infectious for a stated number of days and then becomes susceptible again. Its contact settings have not been compared with any outbreak.

1. Recurring infection on a contact networkSeeded repeated contact trials with fixed infectious whole days.Follows each person on a supplied fixed contact graph through susceptible and infectious states, day by day, with seeded contact trials. An infectious person stays infectious for a fixed number of whole days and then becomes susceptible again. The trial counts and contact weights are fixed settings, not calibrated.If immunity does not last, how many people on this contact network are infected each day, and does the infection persist?Measures: epidemic sis peak infected; epidemic sis new infection events; epidemic sis recovery events; epidemic sis final infected

Before asking where something is crowded, it helps to count where it is. This model lays a grid over a stated area and counts the supplied positions that fall in each cell. It counts; it does not estimate anything beyond the positions it is given.

1. Counting positions in a gridOne CPU count grid with closed bounds and native ceil-plus-one dimensions.Counts the supplied positions in each cell of one grid over a stated bounded area, with the cell size you state. It reports raw counts; it does not smooth them or estimate positions that were not supplied.How many of these positions fall in each cell of a grid over this area?Measures: Positions counted; Largest cell count

How hot a person feels outdoors depends on more than air temperature: sunshine, heat radiated by nearby surfaces, humidity and wind all add to it. This model takes surfaces, sunlight and weather that you state for one spot and computes the radiant heat reaching a standing person and the Universal Thermal Climate Index (UTCI), refusing conditions outside the range where that index is defined.

1. Radiant heat and comfort at one spotCompute directional longwave, standing MRT and guarded UTCI from ten owned declared sources.Computes the longwave and shortwave radiation reaching a standing person from up to ten surfaces and the sunlight and weather you state, the mean radiant temperature, and the Universal Thermal Climate Index, which it refuses outside the conditions for which the index is defined. It uses only the scene you state; it does not read terrain, buildings or a weather service.At this spot, with these surfaces, this sunlight and this weather, how much radiant heat reaches a standing person, and what is the UTCI?Measures: Standing mean radiant temperature; UTCI with supplied weather

Computes solar position, shade from supplied surfaces, radiant heat and the Universal Thermal Climate Index (UTCI) at a person's position from supplied geometry, sunlight and weather. The calculation supports optional diffuse reflection between surfaces and optional canopy attenuation, which reduces direct and diffuse sunlight passing through declared foliage. The calculation excludes leaf scattering and leaf thermal emission. Results remain global screening; agreement with measurements remains unassessed. The simulation records the requested and achieved calculation classes and refuses an unsupported class unless the caller explicitly authorizes global screening.

1. Radiant heat and comfort with the sun and shade worked outDerive direct-beam and sky shortwave from the scene's geometry and the sun's position, then compute directional longwave, standing MRT and guarded UTCI from ten owned declared sources.Computes solar position, the part of the solar disc visible between supplied surfaces, radiant heat, mean radiant temperature and the Universal Thermal Climate Index. The calculation supports optional diffuse reflection between surfaces and optional canopy attenuation, which reduces direct and diffuse sunlight passing through declared foliage. A supplied ground height enables shade on the ground visible to the person; otherwise the horizontal ground is unshaded. The sky is isotropic. The calculation excludes leaf scattering and leaf thermal emission. Results remain global screening; agreement with measurements remains unassessed. The simulation refuses UTCI outside its defined conditions and an unsupported calculation class unless the caller explicitly authorizes global screening. Geometry, sunlight, materials and weather are supplied inputs rather than automatically retrieved measurements.At this spot, at this moment, with these surfaces around it, how much of the sun can a standing person see, and how much radiant heat reaches them?Measures: Standing mean radiant temperature from the scene's sunlight; UTCI with supplied weather; Share of the sun's disc in view; Sun elevation
2. Surface temperatures and heat exposure through time1.0.0: Advance opaque thermal state using scene-derived radiation, publish every forcing-boundary checkpoint and read each checkpoint for directional longwave, standing MRT and guarded UTCI.; 2.0.0: Read owned forcing, derive mixed shortwave and longwave, advance thermal and water state, publish each checkpoint and evaluate standing MRT and guarded UTCI at each boundary. Source applicability remains unassessed.Advances surface temperatures over one to four supplied weather intervals and computes radiant heat and thermal comfort at every interval boundary. It saves each accepted state for exact restart and evaluates the person's declared position and optional body orientation at each boundary. The calculation uses the surfaces, materials, sunlight and weather you supply. It refuses leaf state. Results are global screening; agreement with measurements remains unassessed.Given these surfaces and this weather, how do surface temperatures and a person's heat exposure change over the declared intervals?Measures: Final standing mean radiant temperature; Final UTCI with supplied weather; Completed thermal intervals

Walls, pavements and leaves warm and cool through the day as sunlight, air temperature and wind change. This model takes the surfaces and leaves you describe and the weather you supply, advances their temperatures through time, and saves checkpoints from which the run can be restarted exactly. Each step's arithmetic is checked independently before it is published.

1. Surface and leaf temperatures through timeAdvance the supplied surfaces, and leaves when supplied, and publish exact restart checkpoints after independent arithmetic checks.Advances the temperatures of the surfaces and leaves you describe under the weather you supply, checks each step's arithmetic independently, and saves checkpoints from which the run can restart exactly. It uses only the scene and weather you supply.With this weather, how do the temperatures of these walls, pavements and leaves change through the day?Measures: Accepted thermal half steps; Maximum final opaque surface temperature; Maximum final leaf temperature; Maximum final opaque liquid water; Maximum final available leaf water

When many drivers choose routes, each choice changes the delays the others face. Traffic assignment looks for the spread of routes at which no driver could save time by switching. This model assigns stated hourly car trips over a road graph you supply and reports how close it got to that balance.

1. Traffic assignment by the Frank-Wolfe methodPrepared native assignment with actual gap/stopping facts; MSA gap is heuristic.Assigns stated hourly light-vehicle trips over a supplied directed road graph with the Frank-Wolfe method for user equilibrium, and reports link flows, travel times, the relative gap it reached and why it stopped. Capacities and trip rates are the caller's, not observations, and the routing runs in single precision.If these car trips choose their routes on this road graph until no one can save time by switching, how are the roads loaded?Measures: Native total system travel cost; Native shortest-path travel cost; Native signed relative gap
2. Traffic assignment by successive averagesPrepared native assignment with actual gap/stopping facts; MSA gap is heuristic.Assigns stated hourly light-vehicle trips over a supplied directed road graph by the method of successive averages, with alternative routes generated by penalties, and reports link flows, travel times and why it stopped. Its gap is a heuristic measure, so the result is not certified as an equilibrium.If these car trips choose their routes on this road graph, and their choices are averaged step by step, how are the roads loaded?Measures: Native total system travel cost; Native shortest-path travel cost; Native signed relative gap