https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Social Science sorted by active. https://community.wolfram.com/groups/-/m/t/3772898 Hello Intellectuals, Publication of Multifield Forecasting Model (MFM) paper was finally completed today with our website's renewal to Poll Plus Trend dot com...!!! Read the full paper here: https://doi.org/10.2139/ssrn.7210558 This is an updated version of the post I created 8 months ago! https://community.wolfram.com/groups/-/m/t/3584863 It offers professional introduction to the fundamentals behind how the calculation for election projections / predictions / forecasts of Globe Elections UN are being done. Here is an Unprecedented Proof on how One Model can be used across Infinitely Many Fields over 180 pages, the Longest for Professional Paper in a Reader Friendly format with 21 pictures, 87 tables based on 6 Years of 660+ Election Projections reflecting 24,854,939 Samples of 7,823 Polls. Min Geun Lee 2026-08-03T14:20:30Z https://community.wolfram.com/groups/-/m/t/3762192 ![Modularizing K-12 Instruction in Computational Thinking][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MCTFinal.png&userId=3760260 [2]: https://www.wolframcloud.com/obj/8fe7b019-a94d-42d3-bd12-8f7ef1d12956 Julian Jacklin 2026-07-16T18:06:54Z https://community.wolfram.com/groups/-/m/t/3761669 ![Time Is All You Need: A Tubular Representation of Historical Borders][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Macedonia.png&userId=3760172 [2]: https://www.wolframcloud.com/obj/e8f77bba-92e8-4fe7-9f19-f87007ff4577 Alejandro Barranco Pérez 2026-07-16T16:03:12Z https://community.wolfram.com/groups/-/m/t/3752838 ![Analyzing strategic voting in multi-issue Borda count elections][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-09at16.32.31.png&userId=3751552 [2]: https://www.wolframcloud.com/obj/ba5b55e0-8269-46e1-853e-5e00d5c69c54 Ava Lin 2026-07-09T21:35:13Z https://community.wolfram.com/groups/-/m/t/3752366 ![Evaluating the relationship between export diversification and economic development][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ProductSpace.png&userId=3751600 [2]: https://www.wolframcloud.com/obj/5098512b-fb45-4881-8060-e4cefe135005 Jacob Chung 2026-07-09T21:00:25Z https://community.wolfram.com/groups/-/m/t/3750820 ![Analyzing an extended Schelling segregation model][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-09at2.49.21%E2%80%AFPM.png&userId=3750541 [2]: https://www.wolframcloud.com/obj/61a9abb8-694f-4974-a2f3-6311e712cb1c Theo Archer 2026-07-09T19:01:02Z https://community.wolfram.com/groups/-/m/t/3017901 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/88e82c7f-61b9-4edd-a2c6-45ef12c405b9 Matteo Broso 2023-09-21T19:27:08Z https://community.wolfram.com/groups/-/m/t/3731000 ![Cities as social reactors: Bettencourt 2013 urban scaling replicated across 46 UK cities][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Video-dd159c55-c43d-4c58-9770-057ee8bc2922.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/176937c7-3644-4af8-a8b8-92b995c879ca Marco Thiel 2026-06-10T12:02:46Z https://community.wolfram.com/groups/-/m/t/3728221 ![Re-running the Prisoner's Dilemma tournament: from tit-for-tat to a stable mix under noise][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Re-runningthePrisoner%27sDilemmatournamentfromTit-for-Tattoastablemixundernoise2.png&userId=20103 [2]: https://www.wolframcloud.com/obj/93e1338d-de42-4a3e-b70e-49379bbc812a Marco Thiel 2026-06-05T17:05:44Z https://community.wolfram.com/groups/-/m/t/3726754 [![To what extent is The Phillips Curve still applicable?][1]][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=TowhatextentisThePhillipsCurvestillapplicable.png&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=TowhatextentisThePhillipsCurvestillapplicable.png&userId=20103 [3]: https://www.wolframcloud.com/obj/2363af94-d6ab-4870-a0b4-44e615b4e0d5 Damla Temur 2026-06-03T23:57:46Z https://community.wolfram.com/groups/-/m/t/3726084 [![What do Europeans care about? Exploratory data analysis on an ESS dataset][1]][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WhatdoEuropeanscareaboutExploratorydataanalysisonanESSdataset.png&userId=20103 [2]: https://www.wolframcloud.com/obj/8a12d447-e77d-4370-ac2c-ea7bfc14628a Dimitar Krastev 2026-06-03T10:15:22Z https://community.wolfram.com/groups/-/m/t/3722625 ![Analysis of the Dutch railway network using graph theory][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=netherldands.png&userId=2028758 [2]: https://www.wolframcloud.com/obj/72e97aaf-3b66-48ac-8739-920f045ba827 Alejandra Ortiz Duran 2026-05-26T13:49:51Z https://community.wolfram.com/groups/-/m/t/3696836 [![Diffusion Cartograms: implementation of the Gastner—Newman density-equalising map algorithm][1]][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=DiffusionCartogramsimplementationoftheGastner%E2%80%94Newmandensity-equalisingmapalgorithm.png&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=DiffusionCartogramsimplementationoftheGastner%E2%80%94Newmandensity-equalisingmapalgorithm.png&userId=20103 [3]: https://www.wolframcloud.com/obj/3a527987-4ff8-465d-a769-6bc59f8463bd Marco Thiel 2026-04-19T16:53:07Z https://community.wolfram.com/groups/-/m/t/3682277 ![A data adventure in Boston, 1929: historical census corpus analysis][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=AdataadventureinBoston,1929historicalcensuscorpusanalysis.png&userId=20103 [2]: https://www.wolframcloud.com/obj/94150fc6-d612-455a-ab7a-50e1b4b11214 Rory Foulger 2026-04-12T00:57:27Z https://community.wolfram.com/groups/-/m/t/3642736 ![A Graph Theory Analysis of Centrality, Resilience, and Community Structure in the London Subway Network][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8057image.png&userId=911151 [2]: https://www.wolframcloud.com/obj/5b7ef9aa-2d29-4836-b49a-0c3a4371eb87 Wolfram Education Programs 2026-02-20T15:55:58Z https://community.wolfram.com/groups/-/m/t/3641212 ![Modeling the Susceptibility of Different Voting Systems to the Occurrence of Different Paradoxes][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5063image.png&userId=911151 [2]: https://www.wolframcloud.com/obj/5fdefb94-8c5c-41ac-af15-99ea89f16cfa Wolfram Education Programs 2026-02-17T15:24:32Z https://community.wolfram.com/groups/-/m/t/932548 #Introduction I recently saw a TV show set at Four Corners USA, the point where Utah, Colorado, Arizona, and New Mexico meet: ![enter image description here][1] It made me wonder how frequent 4 or more geographical borders meet at one point. According to [Wikipedia][2], 4 borders meeting at a point is called a ***quadripoint***, 5 borders meeting is called a ***quintipoint***, and in general it's called a ***multipoint***. The entry only lists one quintipoint and goes on to say > Perhaps a dozen quintipoints of various levels of geopolitical subdivisions are scattered around the world; This piqued my interest to find all multipoints, using the Wolfram Language. -------- #Results Before I give the details on how to detect multipoints, I'd like to showcase the results. ###Summary - Since borders are not always precise (or even well defined at times), I allowed for an error up to ~100 meters when classifying points. - The polygons were obtained from the `"Country"` and `"AdministrativeDivision"` `Entity` types (about 40,000 in total). - There are a total of **724 quadripoints** in this dataset. - There are a total of **13 quintipoints** in this dataset. - There is **1 *10-point*** in this dataset! - There are **only 6 multipoints** in the dataset whose regions *don't* share the same parent region. ###Quadripoints With **724 quadripoints**, there are too many to list here, but here are a few interesting ones. - The only countries to form a quadripoint are **Namibia, Botswana, Zambia, and Zimbabwe**. ![enter image description here][3] - There are a considerable amount of **counties in Iowa and Texas** that are apart of multiple quadripoints, i.e. more than one corner is a quadripoint. This is because they are roughly arranged in a rectangular grid. ![enter image description here][4] - There were only 6 quadripoints found whose parent regions differ: ![enter image description here][5] - Here's a visual summary of all quadripoints found (note the level 3 regions were heavily thickened to become visible): ![enter image description here][6] ###Quintipoints Here are all **13 quintipoints** found: - **Saint Kitts and Nevis**: Saint George Gingerland - Saint James Windward - Saint John Figtree - Saint Paul Charlestown - Saint Thomas Lowland - **Boyaca, Colombia**: Chinavita - Garagoa - Miraflores - Ramiriquí - Zetaquirá - **Counties in Florida, USA**: Glades - Hendry - Martin - Okeechobee - Palm Beach - **Usulutan, El Salvador**: California - Ozatlán - Santa Elena - Tecapán - Usulután - **Arequipa, Arequipa, Peru**: Alto Selva Alegre - Cayma - Chiguata - Miraflores - San Juan de Tarucani - **Cuenca, Azuay, Ecuador**: Chiquintad - Cuenca - Ricaurte - Sidcay - Sinicay - **Pea Reang, Prey Vêng, Cambodia**: Kampong Popil - Mesa Prachan - Prey Sralet - Reab - Roka - **Rieti, Lazio, Italy**: Borgo Velino - Castel Sant' Angelo - Cittaducale - Micigliano - Rieti - **Cosenza, Calabria, Italy**: Marano Marchesato - Marano Principato - Rende - San Fili - San Lucido - **Napoli, Campania, Italy**: Boscotrecase - Ercolano - Ottaviano - Torre Del Greco - Trecase - **Savona, Liguria, Italy**: Bardineto - Boissano - Giustenice - Loano - Pietra Ligure - **Torino, Piemonte, Italy**: Cuceglio - Mercenasco - Montalenghe - Scarmagno - Vialfrè - **Viterbo, Lazio, Italy**: Bolsena - Capodimonte - Gradoli - Montefiascone - San Lorenzo Nuovo As you can see, Italy takes the cake with 6 quintipoints! Here's a visual of these quintipoints, along with the error allowing them to be classified as such: ![enter image description here][7] ###A Near 6-point Notice in the top right map above, it looks like there is room for one more region in Viterbo, Lazio, Italy, which would make it a 6-point. Here's the 6th region (Grotte Di Castro) in black: ![enter image description here][8] It turns out Grotte Di Castro is about 700 meters from the quintipoint, making this only a ***near* 6-point**: ![enter image description here][9] ###10-point As mentioned in the [Wikipedia entry][10], there is a 10-point in Italy at the summit of [Mount Etna][11]: - **Catania, Sicily, Italy**: Adrano - Belpasso - Biancavilla - Bronte - Castiglione Di Sicilia - Maletto - Nicolosi - Randazzo - Sant' Alfio - Zafferana Etnea ![enter image description here][12] ###Allowing for more error If we allow for more error, we can find ***near-multipoints*** - regions that almost have a multipoint, but clearly don't. For example, there is a near-quintipoint in Texas, USA: ![enter image description here][13] -------- #Code The idea to find multipoints within a collection of regions is as follows: 1. Obtain the `Polygon` for each region. 2. For each pair of regions, if there's a vertex from one of the polygons which is "close" to the other, mark these regions as touching. `RegionDistance` can be used for this. 3. The relation of touching between pairs forms an adjacency matrix. From this, form a `Graph` and use `FindClique` to find all multipoints in this collection. Here is code that does just that: discretize[Polygon[pts_?MatrixQ]] := MeshRegion[pts, Polygon[Range[Length[pts]]]] discretize[Polygon[pts_?(VectorQ[#, MatrixQ] &)]] := With[{pts2 = Select[pts, Length[#] > 2 &]}, MeshRegion[Join @@ pts2, Polygon[Range[# + 1, #2] & @@@ Partition[Prepend[Accumulate[Map[Length, pts2]], 0], 2, 1]]] ] discretize[expr_] := With[{mr = DiscretizeGraphics[Graphics[expr]]}, mr /; MeshRegionQ[mr] ] discretize[_] = $Failed; polyLookup = discretize /@ (Join[ EntityValue["Country", "Polygon", "EntityAssociation"], EntityValue["AdministrativeDivision", "Polygon", "EntityAssociation"] ] /. GeoPosition -> Identity); MultiPoints[divs_List, n_] /; Length[divs] < n = {}; MultiPoints[divs_List, n_] := Block[{polys, disj, cands}, polys = polyLookup /@ divs; ( disj = Boole[Outer[CoordinateNear, polys, polys]] - IdentityMatrix[Length[divs]]; ( cands = FindClique[AdjacencyGraph[divs, disj], {n, Infinity}, All]; resolveMultiPoints[cands, AssociationThread[divs, polys]] ) /; MatrixQ[disj, IntegerQ] ) /; VectorQ[polys, MeshRegionQ] ] MultiPoints[___] = {}; $tol = 0.001; CoordinateNear[mr1_, mr2_, tol_:$tol] := With[{d = {{-tol, tol}, {-tol, tol}}}, And[ NoneTrue[Transpose[{d+RegionBounds[mr1], d+RegionBounds[mr2]}], #1[[2,1]] > #1[[1,2]] || #1[[1,1]] > #1[[2,2]]&], Min[RegionDistance[mr1, MeshCoordinates[mr2]]] < tol ] ] resolveMultiPoints[{}, _] = {}; resolveMultiPoints[cands_List, passoc_?AssociationQ] := Select[cands, MultiPointQ[#, passoc]&] MultiPointQ[cands_, passoc_?AssociationQ, tol_:$tol] := Block[{coords, mrs}, mrs = passoc /@ cands; coords = Union @@ MeshCoordinates /@ mrs; Or @@ Thread[And @@ (Thread[RegionDistance[#, coords] < tol]& /@ mrs)] ] Now here's all multipoints formed from countries: ![enter image description here][14] Now to explore all cases, we can start off by looking for multipoints in all subdivisions of a given region, e.g. given Florida, find all multipoints within the counties of Florida. This can be achieved by building a hierarchical graph connecting countries and administrative divisions. Then for a given region, this graph can be used to find all subdivisions and the above code can be used to find the multipoints. ad = AdministrativeDivisionData[]; pr = EntityValue["AdministrativeDivision", "ParentRegion"]; $ADNetwork = Graph[Join[ Thread["NullPointer" -> EntityList["Country"]], DeleteCases[Thread[pr -> ad], Rule[_Missing, _]] ]]; ChildrenMultiPoints[reg_] := ChildrenMultiPoints[reg, 4] ChildrenMultiPoints[reg_, o___] := MultiPoints[Rest[VertexOutComponent[$ADNetwork, reg, 1]], o] ![enter image description here][15] Lastly, to cover all cases we need to consider sets of regions that have differing parent regions. To do this, for a given parent region $P$, first find all other regions $R_i$ (on the same level) that touch this region. Then simply run `MultiPoints` on all subdivisions in $P \cup R_i$. I omit this code here, as there were only 6 instances that came out of this case. [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=7535fourcorners.png&userId=46025 [2]: https://en.wikipedia.org/wiki/Quadripoint [3]: http://community.wolfram.com//c/portal/getImageAttachment?filename=countryquadripoint.png&userId=46025 [4]: http://community.wolfram.com//c/portal/getImageAttachment?filename=2008squarequadripoints.png&userId=46025 [5]: http://community.wolfram.com//c/portal/getImageAttachment?filename=crossregionquadripoints.png&userId=46025 [6]: http://community.wolfram.com//c/portal/getImageAttachment?filename=allquadripoints.png&userId=46025 [7]: http://community.wolfram.com//c/portal/getImageAttachment?filename=4697quintipoints.png&userId=46025 [8]: http://community.wolfram.com//c/portal/getImageAttachment?filename=8873almostsixpoint.png&userId=46025 [9]: http://community.wolfram.com//c/portal/getImageAttachment?filename=9086almostsixpointzoom.png&userId=46025 [10]: https://en.wikipedia.org/wiki/Quadripoint#Multipoints_of_greater_numerical_complexity [11]: https://en.wikipedia.org/wiki/Mount_Etna#Geopolitical_oddity [12]: http://community.wolfram.com//c/portal/getImageAttachment?filename=3719tenpoint.png&userId=46025 [13]: http://community.wolfram.com//c/portal/getImageAttachment?filename=4645almostquintpoint.png&userId=46025 [14]: http://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2016-10-0117.18.37.png&userId=46025 [15]: http://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2016-10-0117.27.16.png&userId=46025 Greg Hurst 2016-10-01T22:56:22Z https://community.wolfram.com/groups/-/m/t/3524606 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/d1f53528-68e8-48ce-98eb-37dd277cde79 Peter Barendse 2025-08-04T17:25:35Z https://community.wolfram.com/groups/-/m/t/3502732 ![Visualizing the problem of distributed consensus for environmental attitudes][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=coverphoto.png&userId=3500835 [2]: https://www.wolframcloud.com/obj/b2e9587d-7954-4a83-a12d-69a936092a74 Kaavya Majumder 2025-07-10T21:31:03Z https://community.wolfram.com/groups/-/m/t/3502384 ![Simulating macroeconomic shock propagation in interconnected economies][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=InitialImage.png&userId=3500076 [2]: https://www.wolframcloud.com/obj/40e10a9e-e3a3-452e-9175-12941af2b630 Leonardo Bartoccini 2025-07-10T20:56:52Z