Čech complex

In algebraic topology and topological data analysis, the Čech complex is an abstract simplicial complex constructed from a point cloud in any metric space which is meant to capture topological information about the point cloud or the distribution it is drawn from. Given a finite point cloud X and an ε > 0, we construct the Čech complex ${\check {C}}_{\varepsilon }(X)$ as follows: Take the elements of X as the vertex set of ${\check {C}}_{\varepsilon }(X)$ . Then, for each $\sigma \subset X$ , let $\sigma \in {\check {C}}_{\varepsilon }(X)$ if the set of ε-balls centered at points of σ has a nonempty intersection. In other words, the Čech complex is the nerve of the set of ε-balls centered at points of X. By the nerve lemma, the Čech complex is homotopy equivalent to the union of the balls, also known as the offset filtration.^[1]

Relation to Vietoris–Rips complex

The Čech complex is a subcomplex of the Vietoris–Rips complex. While the Čech complex is more computationally expensive than the Vietoris–Rips complex, since we must check for higher order intersections of the balls in the complex, the nerve theorem provides a guarantee that the Čech complex is homotopy equivalent to union of the balls in the complex. The Vietoris-Rips complex may not be.^[1]

References

^ ^a ^b Ghrist, Robert W. (2014). Elementary applied topology (1st ed.). [United States]. ISBN 9781502880857. OCLC 899283974.{{cite book}}: CS1 maint: location missing publisher (link)

Read other articles:

Mulia Hasudungan Ritonga

Ini adalah nama Batak Toba/Angkola, marganya adalah Ritonga. Mulia Hasudungan Ritonga Widyaiswara Kepolisian Utama Tingkat I Sespim Lemdiklat Polri Informasi pribadiLahir10 November 1968 (umur 55)IndonesiaAlma materAkademi Kepolisian (1990)Karier militerPihak IndonesiaDinas/cabang Sekolah Staf dan Pimpinan Lemdiklat PolriMasa dinas1990—sekarangPangkat Inspektur Jenderal PolisiNRP68110216SatuanLantasSunting kotak info • L • B Irjen. Pol. Drs. Mulia Hasudungan Rit...

Fotografi perang

Sebuah ladang di Antietam, Perang Saudara Amerika karya Alexander Gardner, 1862. Fotografi perang menangkap foto-foto konflik bersenjata dan wilayah-wilayah yang terkena perang. Meskipun foto dapat mewakili lebih langsung ketimbang lukisan atau gambar, foto-foto tersebut terkadang dimanipulasi sehingga membuat gambar tersebut menjadi tidak objektif secara jurnalistik. Sejarah Asal mula Dengan penemuan fotografi pada 1830-an, kemungkinan menangkap peristiwa-peristiwa perang untuk disebarkan ke...

Abubakar A. Latif

Abubakar A. Latif Informasi pribadiLahir1 Juli 1965 (umur 58)Keutapang, Aceh Utara, AcehKebangsaanIndonesiaPartai politikPartai AcehKarier militerPihak Gerakan Aceh MerdekaPertempuran/perangPemberontakan di AcehSunting kotak info • L • B Teungku Abubakar A. Latif, lebih dikenal dengan nama Abu Len (lahir 1 Juli 1965) adalah tokoh pejuang GAM. Dia pernah menjabat sebagai Panglima Operasi Gerakan Aceh Merdeka Wilayah Pase. Dia pernah menjabat sebagai Anggota DPRA Fraksi Parta...

Sungai Kunene

Sungai Kunene di dekat air terjun Epupa. Sungai Kunene adalah sungai yang mengalir dari dataran tinggi Angola selatan hingga daerah perbatasan Angola-Namibia. Sungai ini lalu mengalir ke arah barat di sepanjang perbatasan hingga mencapai Samudra Atlantik. Panjang sungai ini mencapai 1.050 km dengan luas daerah aliran sungai sebesar 106.560 km². Rata-rata debit tahunannya tercatat sebesar 174 m³/s di mulut sungainya.[1] Di aliran sungai ini terdapat air terjun Epupa yang me...

Rabindranath Tagore

Rabindranath TagoreRabindranath Tagore di Kolkata, sekitar tahun 1915 ketika ia mendapat anugrah gelar.Lahir(1861-05-07)7 Mei 1861Kolkata, IndiaMeninggal7 Agustus 1941(1941-08-07) (umur 80)Kolkata, IndiaPekerjaanPenyair, filsuf, dramawan, komposerAliran sastraModernisme Kontekstual Rabindranath Tagore (bahasa Bengali: Rabindranath Thakur; 7 Mei 1861 – 7 Agustus 1941 [γ]) juga dikenal dengan nama Gurudev,[δ] adalah seorang Brahmo Samaj, penyair, dramawan, filsuf, se...

Royal New Zealand Society for the Prevention of Cruelty to Animals

New Zealand animal welfare charity SPCA New ZealandFormation1933; 91 years ago (1933)Legal statusCharityWebsitewww.spca.nz The Royal New Zealand Society for the Prevention of Cruelty to Animals (abbreviated as RNZSPCA or SPCA) is a New Zealand charitable society who work to promote the humane treatment of animals. The society consists of 30 animal shelters and 6 vet partnerships around New Zealand, including many in regional areas. Under the Animal Welfare Act 1999, SPCA ins...

Parlemen Afrika Selatan

Parlemen Republik Afrika Selatan Inggris:Parliament of South AfricaAfrika:Parlement van Suid-AfrikaZulu:iPhalamende yaseNingizimu AfrikaXhosa:iPalamente yoMzantsi AfrikaSwazi:iPhalamende yeNingizimu AfrikaNdebele:iPalamende yeSewula AfrikaSotho:Palamente ya Afrika BorwaSotho Utara:Palamente ya Afrika-BorwaTsonga:Palamende ra Afrika DzongaTswana:Palamente ya Aforika BorwaVenda:Phaḽamennde ya Afurika TshipembeParlemen Ke 27Coat of arms or logoLogoJenisJenisBikameral MajelisDewan Provinsi Nasi...

Strada statale 690 Avezzano-Sora

Voci principali: Avezzano, Sora (Italia). Questa voce o sezione sull'argomento strade d'Italia non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Strada statale 690Avezzano-Sora Superstrada del LiriLocalizzazioneStato Italia Regioni Abruzzo Lazio Province L'Aquila Frosinone DatiClassificazioneStrada statale InizioA25 uscita Avezzano...

Liga 3 2017 Aceh

Liga 3 Aceh 2017Tanggal penyelenggaraan22 Juli 2017Tempat penyelenggaraan4 stadionJumlah peserta24 tim sepak bolaJuaraKuala Nanggroe FC[1](gelar ke-1)Tempat keduaAceh United FCKualifikasi untukLiga 3 2017 Putaran Regional Sumatera2019 → Liga 3 Aceh 2017 adalah edisi pertama dari musim Liga 3 Aceh yang diselenggarakan oleh PSSI Aceh.[2] Diikuti oleh 24 klub, Juara dan runner-up kompetisi ini akan melaju ke putaran regional Sumatera mewakili Aceh untuk menuju promosi ke Liga 2...

List of Netflix original films (2022)

For Netflix original series and related specials, see List of Netflix original programming. For Netflix original stand-up comedy specials, see List of Netflix original stand-up comedy specials. For Netflix exclusive international distribution films, see Lists of Netflix exclusive international distribution programming. Netflix is an American global on-demand Internet streaming media provider, that has distributed a number of original programs, including original series, specials, miniseries,...

Zahir Farjabi

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Desember 2022. Zahir Farjabi adalah seorang penyair terkenal yang berasal dari bangsa Iran.[1] ia hidup sekitar tahun 1156 sampai dengan tahun 1201.[1] Ia diperkirakan meninggal pada bulan november atau desember tahun 1201 di sebuah tempat bernama Ta...

Joel Beinin

American academic and historian (born 1948) This biography of a living person needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately from the article and its talk page, especially if potentially libelous.Find sources: Joel Beinin – news · newspapers · books · scholar · JSTOR (December 2018) (Learn how and when to remov...

Launceston (Australia)

Launcestoncittà Launceston – Veduta LocalizzazioneStato Australia Stato federato Tasmania Local government areaCittà di Launceston AmministrazioneAmministratore localeDanny Gibson dal 2-11-2022 TerritorioCoordinate41°26′40″S 147°08′16″E41°26′40″S, 147°08′16″E (Launceston) Altitudine0 m s.l.m. Superficie95,1 km² Abitanti71 395 (2006) Densità750,74 ab./km² Altre informazioniCod. postaleTA 7250 Fuso orarioUTC+10 CartografiaLaunces...

Digambara

One of the two major schools of Jainism Image depicting Acharya Kundakunda Part of a series onJainism Jains History Timeline Index Philosophy Anekantavada Cosmology Ahimsa Karma Dharma Mokṣa Kevala Jnana Dravya Tattva Brahmacarya Aparigraha Gunasthana Saṃsāra EthicsEthics of Jainism Mahavratas (major vows) Ahiṃsā (non-violence) Satya (truth) Asteya (non-stealing) Brahmacarya (chastity) Aparigraha (non-possession) Anuvratas (further vows) Sāmāyika Sallekhana Jain prayers Bhaktamara S...

Karin Herrera

Vice president of Guatemala since 2024 In this Spanish name, the first or paternal surname is Herrera and the second or maternal family name is Aguilar. Her ExcellencyKarin HerreraOfficial portrait, 202418th Vice President of GuatemalaIncumbentAssumed office 15 January 2024PresidentBernardo ArévaloPreceded byGuillermo Castillo Personal detailsBorn (1967-07-25) 25 July 1967 (age 56)Guatemala City, GuatemalaPolitical partySemillaSpouse Gustavo Gómez Álvarez ̴...

Metroline

London bus operator Not to be confused with Metro line, Metroliner, or Metrobus. MetrolineWright Eclipse Gemini 3 bodied Volvo B5LH on route 328 at High Street Kensington station in April 2024ParentComfortDelGroFounded1 April 1989; 35 years ago (1989-04-01)HeadquartersCricklewood, London, United KingdomService area Greater London Hertfordshire Service typeBus servicesDepots13Fleet1,429 (March 2023)Fuel typeDiesel, Hybrid, Electric and HydrogenManaging DirectorStephen HarrisW...

Field hockey stick

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Field hockey stick – news · newspapers · books · scholar · JSTOR (June 2009) (Learn how and when to remove ...

Monothelitism

Christian theological doctrine Not to be confused with Monotheism. Part of a series onChristology Concepts Christ (Messiah)Kyrios Son of GodGod the Son LogosIncarnationPre-existence Active obedience Communicatio idiomatum Consubstantiality ExaltationHumiliation God-manHomoiōma Hypostatic unionPersonProsopon ImitationIntercession KenosisSyncatabasis KnowledgeLovePerfectionWisdom Threefold office Redeemer Doctrines Christological doctrines Adoptionism Apollinarism Eutychianism Chalcedonism (Ne...

Prussian State Council

Upper house of Prussian Parliament of Prussia from 1920 to 1933 This article is about the Prussian State Council during the Weimar Republic. For Nazi Germany, see Prussian State Council (Nazi Germany). Prussian State Council Preußischer StaatsratCoat of arms of PrussiaTypeTypeUpper Chamber HistoryEstablished30 November 1920Disbanded8 July 1933Preceded byPrussian House of LordsSucceeded byPrussian State Council (Nazi Germany)LeadershipPresidentKonrad Adenauer, Centre Party ̳...

Pitié-Salpêtrière Hospital

You can help expand this article with text translated from the corresponding article in French. (April 2020) Click [show] for important translation instructions. View a machine-translated version of the French article. Machine translation, like DeepL or Google Translate, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedi...

PROFILPELAJAR.COM