Ukugqibezela ubungqina obusesikweni bokupakishwa kwesphere ye-high-dimensional

Ukufuna ukuPakisha okuGqibeleleyo: Ukusuka kwiiOrenji ukuya kwiMilinganiselo engabonakaliyo

Kangangeenkulungwane, iigrocers zipakisha iiorenji kunye neengcali zezibalo ezizobe izangqa baye basokola nengxaki elula ekhohlisayo: yeyiphi eyona ndlela isebenzayo yokupakisha izinto kunye? Impendulo yehlabathi lethu elimacala-ntathu, elaziwa ngokuba yingcinga kaKepler, yangqinwa kuphela ngo-1998. Kodwa kuthekani ngezithuba ezingaphaya kwezethu? Usukelo lweyona ndlela ixineneyo yokupakisha amanqanaba aphezulu kuyenye yezona ngxaki zingaqondakaliyo nezingumngeni kwimathematika. Kutshanje, kuye kwaphunyezwa impumelelo ebalaseleyo, egqibezela ubungqina obusesikweni obuphendula umbuzo ngokwemilinganiselo ethile, umsebenzi owawufuna amandla okubala kunye nobuchule bemathematika ngomlinganiselo ongazange ubonwe ngaphambili. Kanye njengokuba obu bungqina buseka isiseko esiluqilima sendawo engabonakaliyo, inkqubo yokusebenza yemodyuli yeshishini efana neMewayz ibonelela ngesiseko sesiseko senkampani ukuba isebenze ngobuchule obukhulu.

Kutheni imilinganiselo ephakamileyo ibalulekile

Ukupakishwa kweSphere kunokubonakala ngathi yintsimi ye-esoteric, kodwa iimpembelelo zayo zisebenza kakhulu. Ihlabathi ledijithali lisebenza kwiikhowudi zokulungisa iimpazamo, eziyimfuneko yokugcina idatha ethembekileyo kwiiCD kunye nokuhanjiswa kwedatha kwi-intanethi. Ezi khowudi zinokubonwa njengepakethe ye-sphere kwiindawo ezinomgangatho ophezulu; i-denser yokupakisha, ulwazi oluninzi onokuthi uluthumele ngaphandle kweempazamo. Ukufumana iipakethi ezisebenzayo ngokuthe ngqo kukhokelela kubuchwepheshe obunamandla kunye nokusebenza kakuhle. Olu hambo oluya kwi-abstract geometry ekugqibeleni lujikeleza emva ekuphuculeni iinkqubo zekhonkrithi esizisebenzisa yonke imihla.

“Ubungqina sisiganeko esibalulekileyo, kungekuphela nje kwijiyometri ecacileyo, kodwa kuyo yonke inkalo yezibalo. Bubonisa ukuba singakwazi ukuqubisana neengxaki ezintsonkothileyo ngokudibanisa ithiyori enzulu kunye namandla akhohlakeleyo wokubala. - UGqr Maria Samsonov, i-Geometric Structures Institute.

Ukuphumelela: Ubungqina boNcedo lweKhompyutha

Impumelelo yamva nje, eyakhela phezu komsebenzi weengcali zezibalo uMaryna Viazovska kunye nabanye, ibonelele ngobungqina obusesikweni kwezona zipakishwe zixineneyo kwimilinganiso yesi-8 nesama-24. Le milinganiselo ikhethekile kuba izakhiwo ezilinge kakhulu ezibizwa ngokuba yi-E8 kunye neleti yeLeech zikhona apho. Ubungqina buqinisekisile ukuba ezi lathisi zilungile ngokwenene. Nangona kunjalo, eyona mbalasane yayiyi "formalization" yobungqina. Oku kuthetha ukuba yonke ingxabano yaguqulelwa kulwimi lweprogram kwaye yaqinisekiswa yikhompyutheni, ingashiyi indawo yempazamo yomntu kumanyathelo anengqiqo. Oku kufana nokuba nomphicothi-zincwadi ongaphosisiyo ajonge ngocoselelo lonke ubalo ngalunye kwindlela yemali entsonkothileyo.

Iimpembelelo kuShishino kunye noLwakhiwo

Ngelixa ishishini lakho lingasebenzi kumda wama-24, imithetho-siseko yolwakhiwo olulolona luphezulu ikwindawo yonke. Ukufuna okona kupakishwa ngokufanelekileyo kubonisa imfuno yeshishini lombutho ofanelekileyo. Indawo yokugcina izinto enesiphithiphithi okanye inkqubo engasebenzi kakuhle ifana nokupakishwa kwezixhobo ezingasebenzi kakuhle—ichitha indawo, ixesha namandla. Injongo kukuphumeza inkqubo elungelelaniswe ngokugqibeleleyo apho icandelo ngalinye lidibana ngokungenamthungo. Le yintanda-bulumko engundoqo emva kweMewayz. I-OS yethu yeshishini eliyimodyuli yenzelwe ukuba ibe yi-E8 lattice yokusebenza kwenkampani yakho.

I-Mewayz inceda amashishini ukuba afezekise esi sakhiwo silungileyo ngokubonelela ngeemodyuli ezidibeneyo ezihambelana ngokugqibeleleyo, ukuphelisa umzamo ochithekileyo kunye nokudala ukuhamba kolwazi olungenamthungo. Kanye njengokuba ubungqina bemathematika buxhomekeke kwinkqubo esesikweni ukuqinisekisa ukuchaneka, iMewayz ibonelela ngesakhiwo esisesikweni seenkqubo zoshishino lakho, iqinisekisa ukungaguquguquki nokuthembeka.

Ukwakha iLattice yeShishini lakho eliNgcono

Ukwamkela indlela eyakhiweyo, eyimodyuli kwimisebenzi yakho inokuvelisa izibonelelo ezibalulekileyo. Ngokuchaza uxhulumaniso olucacileyo kunye nokuphelisa ukungafuneki, udala intlangano eyomelele ngakumbi kwaye iyancipha. Qwalasela ezi ngenelo zibalulekileyo:

• Ukusebenza okuphezulu: Ukuhamba komsebenzi okulungelelaniswayo kunye nezixhobo ezidibeneyo zinciphisa ukungqubuzana kunye nokugcina izixhobo ezixabisekileyo.
• Scalable Structure: Inkqubo yeemodyuli ingakhula kunye neshishini lakho, yongeza amacandelo amatsha ngaphandle kokuphazamisa yonke inkqubo.
• Iimpazamo eziNcitshisiweyo: Sula iinkqubo kunye neetshekhi ezizenzekelayo, ezifana nobungqina obusemthethweni, ukunciphisa umngcipheko weempazamo.
• Intsebenziswano eyomeleziweyo: Inkqubo emanyeneyo iqinisekisa ukuba wonke umntu usebenza ngokomgaqo ofanayo, ekhuthaza ukusebenza kweqela elingcono.

Ukugqitywa kwe-sphere packing ubungqina bubonisa ukuba nezona nkqubo zinzima kakhulu ziyakwazi ukulawulwa kunye nesakhelo esifanelekileyo. Ngokufanayo, ukuphumeza iqonga eliphakathi elifana ne-Mewayz livumela amashishini ukuba alawule ukuntsonkotha kwawo, ukuguqula imisebenzi ephazamisayo ibe lishishini elipakishwe ngokugqibeleleyo, eliqhuba kakuhle kakhulu.

Imibuzo Ebuzwa Rhoqo

Ukufuna ukuPakisha okuGqibeleleyo: Ukusuka kwiiOrenji ukuya kwiMilinganiselo engabonakaliyo

Kangangeenkulungwane, iigrocers zipakisha iiorenji kunye neengcali zezibalo ezizobe izangqa baye basokola nengxaki elula ekhohlisayo: yeyiphi eyona ndlela isebenzayo yokupakisha izinto kunye? Impendulo yehlabathi lethu elimacala-ntathu, elaziwa ngokuba yingcinga kaKepler, yangqinwa kuphela ngo-1998. Kodwa kuthekani ngezithuba ezingaphaya kwezethu? Usukelo lweyona ndlela ixineneyo yokupakisha amanqanaba aphezulu kuyenye yezona ngxaki zingaqondakaliyo nezingumngeni kwimathematika. Kutshanje, kuye kwaphunyezwa impumelelo ebalaseleyo, egqibezela ubungqina obusesikweni obuphendula umbuzo ngokwemilinganiselo ethile, umsebenzi owawufuna amandla okubala kunye nobuchule bemathematika ngomlinganiselo ongazange ubonwe ngaphambili. Kanye njengokuba obu bungqina buseka isiseko esiluqilima sendawo engabonakaliyo, inkqubo yokusebenza yemodyuli yeshishini efana neMewayz ibonelela ngesiseko sesiseko senkampani ukuba isebenze ngobuchule obukhulu.

Kutheni imilinganiselo ephakamileyo ibalulekile

Ukupakishwa kweSphere kunokubonakala ngathi yintsimi ye-esoteric, kodwa iimpembelelo zayo zisebenza kakhulu. Ihlabathi ledijithali lisebenza kwiikhowudi zokulungisa iimpazamo, eziyimfuneko yokugcina idatha ethembekileyo kwiiCD kunye nokuhanjiswa kwedatha kwi-intanethi. Ezi khowudi zinokubonwa njengepakethe ye-sphere kwiindawo ezinomgangatho ophezulu; i-denser yokupakisha, ulwazi oluninzi onokuthi uluthumele ngaphandle kweempazamo. Ukufumana iipakethi ezisebenzayo ngokuthe ngqo kukhokelela kubuchwepheshe obunamandla kunye nokusebenza kakuhle. Olu hambo oluya kwi-abstract geometry ekugqibeleni lujikeleza emva ekuphuculeni iinkqubo zekhonkrithi esizisebenzisa yonke imihla.

Ukuphumelela: Ubungqina boNcedo lweKhompyutha

Impumelelo yamva nje, eyakhela phezu komsebenzi weengcali zezibalo uMaryna Viazovska kunye nabanye, ibonelele ngobungqina obusesikweni kwezona zipakishwe zixineneyo kwimilinganiso yesi-8 nesama-24. Le milinganiselo ikhethekile kuba izakhiwo ezilinge kakhulu ezibizwa ngokuba yi-E8 kunye neleti yeLeech zikhona apho. Ubungqina buqinisekisile ukuba ezi lathisi zilungile ngokwenene. Nangona kunjalo, eyona mbalasane yayiyi "formalization" yobungqina. Oku kuthetha ukuba yonke ingxabano yaguqulelwa kulwimi lweprogram kwaye yaqinisekiswa yikhompyutheni, ingashiyi indawo yempazamo yomntu kumanyathelo anengqiqo. Oku kufana nokuba nomphicothi-zincwadi ongaphosisiyo ajonge ngocoselelo lonke ubalo ngalunye kwindlela yemali entsonkothileyo.

Iimpembelelo kuShishino kunye noLwakhiwo

Ngelixa ishishini lakho lingasebenzi kumda wama-24, imithetho-siseko yolwakhiwo olulolona luphezulu ikwindawo yonke. Ukufuna okona kupakishwa ngokufanelekileyo kubonisa imfuno yeshishini lombutho ofanelekileyo. Indawo yokugcina izinto enesiphithiphithi okanye inkqubo engasebenzi kakuhle ifana nokupakishwa kwezixhobo ezingasebenzi kakuhle—ichitha indawo, ixesha namandla. Injongo kukuphumeza inkqubo elungelelaniswe ngokugqibeleleyo apho icandelo ngalinye lidibana ngokungenamthungo. Le yintanda-bulumko engundoqo emva kweMewayz. I-OS yethu yeshishini eliyimodyuli yenzelwe ukuba ibe yi-E8 lattice yokusebenza kwenkampani yakho.

Ukwakha iLattice yeShishini lakho eliNgcono

Ukwamkela indlela eyakhiweyo, eyimodyuli kwimisebenzi yakho inokuvelisa izibonelelo ezibalulekileyo. Ngokuchaza uxhulumaniso olucacileyo kunye nokuphelisa ukungafuneki, udala intlangano eyomelele ngakumbi kwaye iyancipha. Qwalasela ezi ngenelo zibalulekileyo:

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