Hai Habr!
Sunana Asya. Na sami lacca mai sanyi sosai, ba zan iya taimakawa ba sai dai in raba ta.
Ina kawo muku taƙaitaccen lacca na bidiyo akan rikice-rikicen zamantakewa a cikin harshen masana ilimin lissafi. Ana samun cikakken karatun a wannan hanyar: (A.V. Leonidov, A.V. Savvateev, A.G. Semenov). 2016.
Alexey Vladimirovich Savvateev - Dan takarar Kimiyyar Tattalin Arziki, Doctor of Physical and Mathematical Sciences, Farfesa a MIPT, Jagoran Bincike a NES.
A cikin wannan lacca zan yi magana game da yadda masu ilimin lissafi da masu ilimin wasan kwaikwayo ke kallon al'amuran zamantakewa mai maimaitawa, wanda aka misalta ta hanyar jefa kuri'ar Ingila ta fice daga Tarayyar Turai (, wani al'amari na zurfin rarrabuwar kawuna a Rasha bayan , tare da sakamako mai ban sha'awa.
Ta yaya za ku iya kwaikwayi irin waɗannan yanayi don su sami ra'ayi na gaskiya? Don fahimtar wani sabon abu, ya zama dole a yi nazarinsa sosai, amma wannan lacca zai ba da misali.
Tsakanin zamantakewa yana nufin
Abin da waɗannan al’amura guda uku suka yi tarayya da su shi ne, mutum ya faɗa cikin sansani ɗaya ko kuma ya ƙi shiga ya tattauna abin da ya zaɓa. Wadancan. Zaɓin kowane mutum shine ternary - daga dabi'u uku:
- 0-ki shiga cikin rikici;
- 1 - shiga cikin rikici a gefe guda;
- -1 - shiga cikin rikici ta bangaren kishiyar.
Akwai sakamako kai tsaye waɗanda ke da alaƙa da halin ku game da rikici a zahiri. Akwai zato cewa kowane mutum yana da wani nau'i na fifiko ga wanda yake daidai a nan. Kuma wannan shi ne ainihin canji.
Misali, idan da gaske mutum bai fahimci wanene daidai ba, batu yana kan layin lamba a wani wuri kusa da sifili, misali a 0,1. Lokacin da mutum ya tabbata 100% cewa wani yana da gaskiya, to, yanayinsa na ciki zai riga ya kasance -3 ko +15, gwargwadon ƙarfin imaninsa. Wato akwai wani ma'auni na kayan aiki da mutum ke da shi a kansa, kuma yana bayyana halayensa game da rikici.
Yana da mahimmanci cewa idan kun zaɓi 0, to wannan baya haifar da sakamako a gare ku, babu nasara a wasan, kun watsar da rikici.
Idan ka zabi wani abu da bai dace da matsayinka ba, to ragi zai bayyana a gaban vi, misali vi = - 3. Idan matsayinka na ciki ya zo daidai da bangaren rikicin da kake magana a kai, kuma matsayinka σi = -1, sa'an nan vi = +3.
Sannan tambaya ta taso, a wasu dalilai wasu lokuta sai ka zabi bangaren da bai dace ba na abin da ke cikin ranka? Wannan na iya faruwa a ƙarƙashin matsin lamba daga yanayin zamantakewar ku. Kuma wannan shine postulate.
Matsakaicin matsayi shine cewa sakamakon da ya wuce ikon ku yana rinjayar ku. Ma'anar aji shine ainihin ma'auni na digiri da alamar tasiri akan ku daga j. Kai ne lamba i, kuma mutumin da ya rinjaye ka shine lambar mutum j. Sa'an nan kuma za a sami cikakken matrix na irin wannan aji.
Wannan mutumin j na iya ma yi tasiri a kan ku da mummunan hali. Misali, ta haka ne za ku iya siffanta maganar wani dan siyasa da ba ku so a wani bangare na rikicin. Lokacin da kuka kalli wasan kwaikwayo kuma kuyi tunani: "Wannan wawa, kuma ku kalli abin da yake faɗa, na gaya muku shi ɗan wawa ne."
Duk da haka, idan muka yi la'akari da tasirin mutumin kusa ko girmama ku, to ya zama dan wasa daya j a kan duk 'yan wasa i. Kuma wannan tasirin yana ƙaruwa ta hanyar daidaituwa ko rashin daidaituwa na matsayi da aka ɗauka.
Wadancan. idan σi, σj suna da alama mai kyau, kuma a lokaci guda aji kuma yana da alama mai kyau, to wannan ƙari ne ga aikin nasara. Idan kai ko mutumin da ke da mahimmanci a gare ku ya ɗauki matsayin sifili, to wannan kalmar ba ta wanzu.
Don haka, mun yi ƙoƙarin yin la'akari da duk tasirin tasirin zamantakewa.
Na gaba shine batu na gaba. Akwai nau'ikan nau'ikan hulɗar zamantakewa da yawa, waɗanda aka bayyana daga bangarori daban-daban (samfurin yanke shawara na kofa, samfuran ƙasashen waje da yawa). Suna kallon ma'auni na ra'ayi a cikin ka'idar wasan da ake kira Nash equilibrium. Akwai rashin gamsuwa da wannan ra'ayi don wasanni tare da adadi mai yawa na mahalarta, kamar misalan Birtaniya da Amurka da aka ambata a sama, watau miliyoyin mutane.
A wannan yanayin, daidaitaccen maganin matsalar yana wucewa ta hanyar ƙima ta amfani da ci gaba. Yawan 'yan wasa wani nau'i ne na ci gaba, "girgije" wasa, tare da wani wuri na mahimman sigogi. Akwai ka'idar ci gaba da wasanni,
"Abubuwan da suka shafi wasannin da ba na atomic ba". Wannan hanya ce ta ka'idar wasan haɗin gwiwa.
Babu wata ka'idar rashin haɗin gwiwa ta wasanni tare da ci gaba da adadin mahalarta a matsayin ka'idar tukuna. Akwai ajujuwa daban-daban da ake karantawa, amma har yanzu ba a samar da wannan ilimin zuwa ka'idar gama-gari ba. Kuma daya daga cikin manyan dalilan rashin sa shi ne cewa a cikin wannan musamman ma'aunin Nash ba daidai ba ne. Ainihin ra'ayi mara kyau.
Menene ma'anar daidai? A cikin 'yan shekarun da suka gabata an sami wasu yarjejeniya cewa manufar ta samo asali a cikin ayyukan Palfrey da McKelvey mai sauti kamar"", ko"", kamar yadda ni da Zakharov suka fassara shi. Fassarar tamu ce, kuma da yake ba wanda ya fassara ta zuwa Rashanci kafin mu, mun sanya wannan fassarar a kan mutanen Rasha.
Abin da muke nufi da wannan sunan shi ne, kowane mutum ba ya wasa da dabaru iri-iri, yana taka tsantsa. Amma a cikin wannan yanki na “girgije”, inda aka zaɓi ɗaya ko wani mai tsafta, kuma a mayar da martani, na ga yadda mutum yake wasa, amma ban san inda yake cikin wannan gajimare ba, watau akwai ɓoyayyun bayanai a wurin, I. gane mutum a cikin "girgije" a matsayin yiwuwar da zai bi ta wata hanya ko wata. Wannan ra'ayi ne na ƙididdiga. Ƙwararrun fahimtar juna na masana kimiyyar kimiyyar lissafi da masu nazarin ɗan wasa, ga alama a gare ni, za su ayyana ka'idar wasan ƙarni na 21st.
Muna haɓaka ƙwarewar da ake da ita wajen yin ƙirar irin waɗannan yanayi tare da cikakkun bayanan farko na sabani kuma muna rubuta tsarin daidaitawa wanda ya dace da ma'auni na amsa mai hankali. Wannan ke nan; ci gaba, don warware ma'auni, ya zama dole a yi ƙimayar yanayi mai ma'ana. Amma duk wannan yana gaba; wannan babbar alkibla ce a kimiyya.
Ma'aunin amsawa mai hankali shine ma'auni wanda a zahiri muke wasa ba a san ko wanene ba. A wannan yanayin, ana ƙara ε zuwa ga biyan kuɗi daga dabarun tsabta. Akwai nasara uku, wasu lambobi uku waɗanda ke nufin "rutse" ga gefe ɗaya, "nutse" don ɗayan kuma ka ƙi, kuma akwai ε, wanda aka ƙara zuwa waɗannan ukun. Bugu da ƙari, haɗin waɗannan ε ba a sani ba. Haɗin haɗin za a iya ƙididdige shi kawai a priori, sanin yiwuwar rarraba don ε. A wannan yanayin, yuwuwar haɗuwa ε ya kamata a yi la'akari da zaɓin mutum na kansa, watau, ƙididdigarsa na wasu mutane da ƙididdiga na yiwuwar su. Wannan daidaiton juna shine ma'auni na amsa mai hankali. Zamu dawo kan wannan batu.
Ƙirƙirar tsari ta hanyar ma'auni mai hankali
Ga yadda cin nasara yayi kama da wannan samfurin:
Yana tattara duk tasirin da ya bayyana akan ku idan kun zaɓi kowane bangare, ko kuma za a ninka shi da sifili idan ba ku zaɓi kowane gefe ba. Hakanan zai kasance tare da alamar "+" idan σ1 = 1, kuma tare da alamar "-" idan σ1 = -1. Kuma ε an ƙara wa wannan. Wato, σi yana haɓaka ta yanayin cikin ku, da duk mutanen da suke tasiri ku.
Hakazalika, wani takamaiman mutum zai iya rinjayar miliyoyin mutane, kamar yadda ƴan jarida, ƴan wasan kwaikwayo, ko ma shugaban ƙasa ke rinjayar miliyoyin mutane. Sai dai itace cewa tasirin matrix yana da matukar asymmetrical; a tsaye yana iya ƙunsar babban adadin shigarwar da ba sifili ba, kuma a kwance, daga cikin mutane miliyan 200 a cikin ƙasar, alal misali, lambobi 100 ba sifili ba. Ga kowa da kowa, wannan ribar ita ce jimillar sharuddan kaɗan, amma aij (tasirin mutum a kan wani) yana iya zama ba sifili ba ga adadi mai yawa j, kuma tasirin aji (tasirin wani a kan mutum) ba haka ba ne. mai girma, sau da yawa iyakance zuwa ɗari. Wannan shine inda babban asymmetry ya taso.
Misalai na mahalarta cibiyar sadarwa
Mun yi ƙoƙarin fassara bayanan farko na samfurin a cikin sharuddan zamantakewa. Alal misali, wanene "mai sana'ar daidaitawa"? Wannan shi ne mutumin da ba shi da hannu a cikin rikici, amma akwai mutanen da suke yin tasiri sosai a gare shi, misali, maigidan.
Yana yiwuwa a yi hasashen yadda zaɓinsa ke da alaƙa da zaɓi na shugaba a kowane ma'auni.
Bugu da ari, "mai sha'awar" shine mutumin da ke da tabbaci na ciki mai karfi a gefen rikici.
Aij (Tasirinsa ga wani) yana da girma, sabanin sigar da ta gabata, inda aji (tasirin wani a kan mutum) ya yi yawa.
Bugu da ari, "autist" shine mutumin da ba ya shiga cikin wasanni. Imaninsa yana kusa da sifili, kuma babu wanda ke rinjayarsa.
Kuma a ƙarshe, "mai tsattsauran ra'ayi" shine mutumin da babu kowa ko kadan baya tasiri.
Kalmomi na yanzu na iya zama kuskure ta mahangar harshe, amma har yanzu akwai sauran aikin da za a yi ta wannan hanyar.
Wannan yana nuna cewa, kamar "mai sha'awar," vi ya fi sifili, amma aji = 0. Lura cewa "mai sha'awar" na iya zama "mai tsattsauran ra'ayi" a lokaci guda.
Muna ɗauka cewa a cikin irin waɗannan nodes zai zama mahimmanci abin da shawarar da "mai sha'awar / mai sha'awar" ya yi, tun da wannan shawarar za ta yadu kamar girgije. Amma wannan ba ilimi ba ne, amma kawai zato. Ya zuwa yanzu ba za mu iya magance wannan matsala ta kowace ƙima ba.
Kuma akwai kuma TV. Menene TV? Wannan canji ne a cikin yanayin ku, wani nau'in "filin maganadisu".
Bugu da ƙari, tasirin TV, ya bambanta da "filin maganadisu" na jiki a kan dukkan "kwayoyin zamantakewa," na iya bambanta duka a girma da alama.
Zan iya maye gurbin TV da Intanet?
Maimakon haka, Intanet ita ce ainihin samfurin hulɗar da ke buƙatar tattaunawa. Mu kira shi tushen waje, idan ba na bayanai ba, to wani irin hayaniya.
Bari mu bayyana dabaru uku masu yiwuwa don σi=0, σi=1, σi=-1:
Ta yaya hulɗa ke faruwa? A farkon, duk mahalarta sune "girgije", kuma kowane mutum ya san game da kowa da kowa cewa wannan "girgije" ne, kuma yana ɗaukar yiwuwar rarrabawar waɗannan "girgije". Da zarar wani takamaiman mutum ya fara hulɗa, ya koyi game da kansa duka sau uku ε, watau. wani takamaiman batu, kuma a lokacin da mutum ya yanke shawarar da zai ba shi adadi mai yawa (na waɗanda aka ƙara ε a cikin nasara, ya zaɓi wanda ya fi sauran biyun girma), sauran ba su san abin da ake nufi ba. yana nan, don haka ba za su iya tsinkaya ba.
Bayan haka, mutum ya zaɓi ( σi = 0 / σi = 1 / σi = -1 ), kuma don zaɓar, yana buƙatar sanin σj ga kowa. Mu kula da madaidaicin; a cikin sashin akwai magana [∑ j ≠ i aji σj], watau. wani abu da mutum bai sani ba. Dole ne ya yi hasashen wannan a cikin ma'auni, amma a cikin ma'auni bai gane σj a matsayin lambobi ba, yana ganin su a matsayin yiwuwar.
Wannan shine ma'anar banbance-banbance tsakanin ma'aunin amsa mai hankali da ma'aunin Nash. Dole ne mutum yayi hasashen yiwuwar yiwuwar, don haka tsarin daidaiton yuwuwar ya taso. Bari mu yi la'akari da tsarin daidaitawa ga mutane miliyan 100, ninka da wani 2. Tun da akwai yiwuwar zabar "+", yiwuwar zabar "-" (ba a la'akari da yiwuwar barin barin, tun da wannan shine. abin dogara). A sakamakon haka, akwai 200 miliyan masu canji. Kuma miliyan 200 ma'auni. Ba gaskiya ba ne don warware wannan. Kuma ba shi yiwuwa a tattara irin waɗannan bayanai daidai.
Amma masana ilimin zamantakewa sun gaya mana: "Ku dakata, abokai, za mu gaya muku yadda ake buga al'umma." Suna tambayar nau'ikan matsalolin da za mu iya magance su. Na ce, har yanzu za mu warware 50 equations, kwamfuta iya warware wani tsarin inda akwai 50 equations, ko da 100 ba kome ba. Suka ce ba matsala. Sannan suka bace, ’yan iska.
A zahiri mun shirya taro tare da masana ilimin halayyar dan adam da masana zamantakewa daga HSE, sun ce za mu iya rubuta aikin juyin juya hali na ci gaba, samfurin mu, bayanan su. Kuma ba su zo ba.
Idan kana so ka tambaye ni dalilin da ya sa duk abin da ke faruwa da muni, zan gaya maka, saboda masana ilimin halayyar dan adam da ilimin zamantakewa ba sa zuwa tarurrukanmu. Idan muka taru, za mu motsa duwatsu.
A sakamakon haka, dole ne mutum ya zaɓi daga dabaru uku masu yiwuwa, amma ba zai iya ba, domin bai san σj ba. Sa'an nan kuma mu canza σj zuwa yiwuwar.
Riba a cikin ma'aunin amsawa mai hankali
Tare da σj da ba a sani ba muna maye gurbin bambance-bambance a cikin yiwuwar cewa mutum ya ɗauki ɗaya ko ɗayan a cikin rikici. Lokacin da muka san a wane nau'in vector ε za mu kai ga wane matsayi a cikin sarari mai girma uku. A waɗannan maki (cin nasara) "girgije" sun bayyana, kuma za mu iya haɗa su kuma mu sami nauyin kowane nau'i na 3 "girgije".
A sakamakon haka, muna samun yiwuwar daga mai lura da waje cewa wani mutum zai zaɓi wannan ko wancan kafin ya san ainihin matsayinsa. Wato wannan zai zama dabarar da za ta ba da nata p a matsayin martani ga ilimin duk sauran p. Kuma ana iya rubuta irin wannan dabarar ga kowane i kuma a bar shi daga tsarin daidaitawa wanda zai saba da waɗanda suka yi aiki akan samfuran Ising da Potz. Ilimin kididdiga na kididdiga ya tabbatar da cewa aij = aji, mu'amalar ba za ta zama asymmetrical ba.
Amma akwai wasu "mu'ujizai" a nan. "Ayyukan al'ajabi" na ilimin lissafi shine cewa ma'auni kusan sun dace da ma'auni daga tsarin ƙididdiga masu dacewa, duk da cewa babu wani hulɗar wasanni, amma akwai aikin da aka inganta a kan nau'o'in nau'i daban-daban.
Tare da bayanan farko na sabani, ƙirar tana nuna kamar wani yana inganta wani abu a ciki. Irin waɗannan samfuran ana kiran su "wasanni masu yuwuwa" lokacin da muke magana game da daidaiton Nash. Lokacin da aka ƙera wasan ta hanyar da za a ƙayyade daidaitattun Nash ta haɓaka wasu ayyuka akan sararin duk zaɓuɓɓuka. Menene yuwuwar da ke cikin ma'auni na amsa mai hankali ba a riga an tsara shi ba. (Ko da yake Fyodor Sandomirsky zai iya amsa wannan tambayar. Tabbas wannan zai zama ci gaba).
Wannan shi ne yadda cikakken tsarin daidaitawa yayi kama:
Yiwuwar da kuka zaɓi wannan ko waɗanda suka yi daidai da hasashen ku. Tunanin daidai yake da daidaitattun Nash, amma ana aiwatar da shi ta hanyar yuwuwar.
Rarraba na musamman ε, wato rarraba Gumbel, wanda shine ƙayyadadden wuri don ɗaukar matsakaicin babban adadin masu canji masu zaman kansu.
Ana samun rabon al'ada ta hanyar matsakaicin adadi mai yawa na masu canji masu zaman kansu tare da saɓani tsakanin ƙimar karɓuwa. Kuma idan muka ɗauki matsakaicin daga babban adadin masu canji masu zaman kansu, muna samun irin wannan rarraba ta musamman.
Af, equation ya tsallake siga na hargitsi a cikin yanke shawara da aka yanke, λ, Na manta in rubuta shi.
Fahimtar yadda ake warware wannan ma'auni zai taimaka muku fahimtar yadda ake tara al'umma. A cikin al'amari na ka'idar, yuwuwar wasanni daga mahangar ma'aunin martani mai hankali.
Kuna buƙatar gwada ginshiƙi na ainihi na zamantakewa, wanda ke da saitin kaddarorin daban-daban:
- ƙananan diamita;
- ka'idar iko na rarraba matakan digiri;
- babban tari.
Wato, zaku iya ƙoƙarin sake rubuta kaddarorin hanyar sadarwar zamantakewa ta ainihi a cikin wannan ƙirar. Babu wanda ya gwada ta har yanzu, watakila wani abu zai iya faruwa a lokacin.
Yanzu zan iya ƙoƙarin amsa tambayoyinku. Aƙalla zan iya sauraron su.
Ta yaya wannan ke bayyana tsarin Brexit da zaɓen Amurka?
To shi ke nan. Wannan bai bayyana komai ba. Amma yana ba da alamar dalilin da yasa masu jefa ƙuri'a ke samun kuskuren hasashen su. Domin mutane suna amsawa a bainar jama'a game da abin da yanayin zamantakewar su ke buƙatar amsawa, amma a asirce suna jefa kuri'a don yanke hukunci na ciki. Kuma idan za mu iya warware wannan ma'auni, abin da zai kasance a cikin mafita shine abin da binciken zamantakewa ya ba mu, kuma vi shine abin da zai kasance a cikin kuri'a.
Kuma a cikin wannan samfurin, yana yiwuwa a yi la'akari ba mutum ba, amma tsarin zamantakewa a matsayin wani abu dabam?
Wannan shine ainihin abin da nake so in yi. Amma ba mu san tsarin tsarin zamantakewa ba. Wannan shine dalilin da ya sa muke ƙoƙari mu ci gaba da kasancewa tare da masana ilimin zamantakewa da masu ilimin halin dan Adam.
Shin za a iya amfani da samfurin ku ko ta yaya don bayyana tsarin nau'ikan rikice-rikicen zamantakewa da ake gani a Rasha? Bari mu ba da izinin bambance-bambance tsakanin tasirin cibiyoyi na yau da kullun?
A'a, ba abin da ake nufi ba kenan. Wannan shi ne daidai game da rikici tsakanin mutane. Ba na tsammanin za a iya bayyana rikicin cibiyoyi a nan ta kowace hanya. A kan wannan batu, ina da ra'ayi na cewa cibiyoyin da 'yan adam suka kirkiro suna da yawa, ba za su iya kula da irin wannan nau'i na rikitarwa ba kuma za a tilasta su su wulakanta su. Wannan ita ce fahimtara ta gaskiya.
Shin zai yiwu a ko ta yaya a yi nazarin al'amuran polarization na al'umma? Kun riga kun gina v a cikin wannan, yaya yake da kyau ga kowa...
Ba da gaske ba, muna da TV a wurin, v+h. Wannan shi ne kwatankwacin statistics.
Ee, amma polarization yana faruwa a hankali. Abin da nake nufi shi ne cewa haɗin gwiwar zamantakewa tare da matsayi mai ƙarfi shine 10% v-positive, 6% v-negative, kuma rata yana ƙara karuwa tsakanin waɗannan dabi'un.
Ban san abin da zai faru a cikin motsin rai ba kwata-kwata. A cikin ingantaccen kuzari, a fili, v zai ɗauki ƙimar σ ta baya. Amma ban sani ba ko wannan tasirin zai yi aiki. Babu panacea, babu wani samfurin duniya na al'umma. Wannan samfurin wasu hangen nesa ne wanda zai iya taimakawa. Na yi imanin cewa idan muka magance wannan matsala, za mu ga yadda kuri'un jin ra'ayin jama'a ke bambanta da gaskiyar zabe. Akwai babbar hargitsi a cikin al'umma. Ko da auna ma'auni yana ba da sakamako daban-daban.
Shin wannan yana da alaƙa da ka'idar wasan matrix na gargajiya?
Waɗannan wasannin matrix ne. Kawai cewa matrices a nan sune miliyan 200 da miliyan 200. Wannan wasa ne na kowa da kowa tare da kowa da kowa, an rubuta matrix a matsayin aiki. Wannan yana da alaƙa da wasannin matrix kamar haka: Wasannin matrix wasanni ne na mutane biyu, amma a nan miliyan 200 suna wasa. Saboda haka, wannan tensor ne wanda ke da girman miliyan 200. Ba ma matrix ba ne, amma cube mai girma. na miliyan 200. Amma suna la'akari da sabon ra'ayi na mafita.
Shin akwai ra'ayi na farashin wasa?
Farashin wasan yana yiwuwa ne kawai a cikin wasan gaba na 'yan wasa biyu, watau. tare da jimlar sifili. Wannan baantagonistic game da babbar adadin 'yan wasa. Maimakon farashin wasan, akwai ladaran ma'auni, ba a cikin ma'auni na Nash ba, amma a cikin daidaitattun amsawa.
Me game da manufar "dabarun"?
Dabarun su ne, 0, -1, 1. Wannan ya fito ne daga ma'auni na gargajiya na Nash-Bayes ma'auni, daidaito. Kuma a cikin wannan yanayin musamman, ma'aunin Bayes-Nash ya dogara ne akan bayanai daga wasa na yau da kullun. Wannan yana haifar da haɗin kai da ake kira ma'aunin amsa mai hankali. Kuma wannan yana da nisa marar iyaka daga wasannin matrix na tsakiyar karni na XNUMX.
Yana da shakka cewa za ku iya yin komai tare da 'yan wasa miliyan ...
Wannan ita ce tambayar yadda ake tara al'umma; ba shi yiwuwa a warware wasa tare da 'yan wasa da yawa, kuna da gaskiya.
Littattafai akan fannoni masu alaƙa a cikin ilimin lissafi da ilimin zamantakewa
- Dorogovtsev SN, Goltsev AV, da Mendes JFF Muhimman abubuwan mamaki a cikin hadaddun cibiyoyin sadarwa // Bita na Physics na Zamani. 2008. Vol. 80. shafi. 1275-1335.
- Lawrence E. Blume, Steven Durlauf Ma'aunin Ma'auni don Samfuran Sadarwar Jama'a // Bitar Ka'idar Wasan Duniya. 2003. Vol. 5, (3). pp. 193-209.
- Gordon MB da. al., Zaɓuɓɓuka masu hankali a ƙarƙashin Tasirin Jama'a: Halayen Jumloli // Samfuran Lissafi da hanyoyin a cikin Kimiyyar Aiwatar. 2009. Vol. 19. pp. 1441-1381.
- Bouchaud J.-P. Rikice-rikice da Abubuwan Al'amura na Zamantakewa da Tattalin Arziki: Sauƙaƙan Samfura da Kalubale // Journal of Static Physics. 2013. Vol. 51(3). pp. 567-606.
- Sornette D. Physics da tattalin arziki na kuɗi (1776-2014): wasanin gwada ilimi, lsing, da samfuri na tushen wakili // Rahotanni akan Ci gaban Physics. 2014. Vol. 77, (6). pp. 1-287
Masu amfani da rajista kawai za su iya shiga cikin binciken. don Allah.
(Misali kawai) Matsayinku dangane da Igor Sysoev:
62,1%+1 (shiga cikin rikici a gefen Igor Sysoev) 175
1,4%-1 (shiga cikin rikici ta bangaren kishiyar)4
28,7%0 (ƙi shiga cikin rikici)81
7,8%yi kokarin amfani da rikici don amfanin kai22
Masu amfani 282 sun kada kuri'a. Masu amfani 63 sun ƙi.
source: www.habr.com
