scholarly journals Random labelled trees and their branching networks

Author(s):  
G. R. Grimmett

AbstractA random rooted labelled tree on n vertices has asymptotically the same shape as a branching-type process, in which each generation of a branching process with Poisson family sizes, parameter one, is supplemented by a single additional member added at random to one of the families in that generation. In this note we use this probabilistic representation to deduce the asymptotic distribution of the distance from the root to the nearest endertex other than itself.

Author(s):  
Svante Janson

Abstract We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton–Watson trees and simply generated trees, for split trees and generalized split trees (as defined here), and for trees defined by a continuous-time branching process. These general results include, for example, random labelled trees, ordered trees, random recursive trees, preferential attachment trees, and binary search trees.


2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.


1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.


2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.


2020 ◽  
Vol 3 (2) ◽  
Author(s):  
HARNITA HARNITA ◽  
H. Anwar ◽  
Pendais Hak

ABSTRAK: Tujuan utama dalam penelitian ini mengetahui  latar belakang pelaksanaan kegiatan Ritual dalam Tradisi Pertanian (Galu) pada Masyarakat Desa Bone Tondo Kecamatan Bone Kabupaten Muna, mendeskripsikan ritual-ritual apa saja yang dilakukan dalam pelaksanaan kegiatan ritual dalam Tradisi Pertanian (Galu) pada Masyarakat Desa Bone Tondo Kecamatan Bone Kabupaten Muna, mendeskripsikan proses kegiatan ritual dalam Tradisi Pertanian pada Masyarakat Desa Bone Tondo Kecamatan Bone Kabupaten Muna dan mendeskripsikan perubahan yang terjadi saat ini dalam proses Ritual dalam Tradisi Pertanian (Galu) pada Masyarakat Desa Bone Tondo Kecamatan Bone Kabupaten Muna. Metode yang digunakan dalam penelitian ini adalah metode sejarah menurut Helius Sjamsuddin yang terdiri atas: (1) Heuristik (pengmpulan sumber), (2) Kritik sumber (verifikasi), (3) Historiografi (penulisan sejarah).Hasil penelitian menunjukan bahwa: (1) Latar belakang pelaksanaan ritual dalam tradisi pertanian pada masyarakat Desa Bone Tondo adalah dalam bercocok tanam (degalu) masyarakat Desa Bone Tondo memiliki keyakinan bahwa hutan di Muna banyak dihuni oleh makhluk ghaib yang berpotensi mengganggu kehidupan masyarakat. Maka secara intensif masyarakat melakukan hubungan komunikasi dengan melalui upacara yang tradisional yang dimana harus dilakukan sebelum bercocok tanam. Dengan maksud mendapatkan keselamatan dalam kegiatan perladangan terhindar dari marabahaya serta hasil panen yang melimpah. Ritual dilakukan karena adanya pantangan dan larangan yang apabila jika tidak dipatuhi akan menimbulkan dampak negatif. (2) Ritual-Ritual yang dilakukan dalam Tradisi Pertanian (Galu) pada Masyarakat Desa Bone Tondo ritual pembukaan lahan kawasan hutan baru yaitu desolo. Ritual kaago-ago yang dilakukan saat lahan sudah bersih dan siap untuk ditanamkan, ritual dilakukan untuk memindahkan makhluk ghaib, permohonan dan sebagai rasa syukur. Ritual kasambuno wite (deghoti wite) dan ritual kafematai, (3) Proses pelaksanaan Ritual dalam Tradisi Pertanian (Galu) pada Masyarakat Desa Bone Tondo yaitu semua proses ritual dilakukan pada hari baik yang dipimpin oleh dukun (parika), menyiapkan alat dan bahan (sesajian) yang dibutuhkan tiap-tiap upacara ritual yang akan dilaksanakan. (4) Perubahan yang terjadi saat ini dalam proses pelaksanaan Ritual dalam Tradisi Pertanian (Galu) pada masyarakat Desa Bone Tondo, dapat dilihat pada ritual kaago-ago, dimana saat ini sabagian ritual tersebut tidak lagi dijalankan. Perubahan-perubahan lain adalah terkait dengan konsistensi ritual yang sebagian masih ada yang melakukan secara utuh namun ada juga yang hanya menjalankan 2 atau 3 ritual saja. Kata Kunci: latarbelakang, jenis, proses dan perubahan, galu ABSTRACT: The main objective in this study is to find out the background of the implementation of Ritual activities in the Agricultural Tradition (Galu) of the Bone Tondo Village Community, Bone District of Muna District, describing the rituals performed in the implementation of ritual activities in the Agricultural Tradition (Galu) of the Village Community Bone Tondo, Bone District, Muna Regency, describes the process of ritual activities in the Agricultural Tradition of the Bone Tondo Village Community, Bone District Muna District and describes the changes that occur currently in the Ritual process in the Agricultural Tradition (Galu) of the Bone Tondo Village Community, Bone District, Muna Regency. The method used in this study is the historical method according to Helius Sjamsuddin which consists of: (1) Heuristics (collection of sources), (2) Criticism of sources (verification), (3) Historiography (history writing). The results of the study show that: (1 ) The background of ritual implementation in the agricultural tradition of the Bone Tondo Village community is in farming (degalu). Bone Tondo Village community has the belief that the forests in Muna are inhabited by unseen creatures that have the potential to disrupt people's lives. So the community intensively communicates through traditional ceremonies which must be carried out before planting. With the intention of obtaining safety in farming activities to avoid danger and abundant harvests. The ritual is carried out because of restrictions and prohibitions which if not obeyed will cause a negative impact. (2) Rituals carried out in the Agricultural Tradition (Galu) of the Bone Tondo Village Community in the ritual of opening a new forest area, namely desolo. Kaago-ago rituals are carried out when the land is clean and ready to be planted, rituals are performed to remove supernatural beings, requests and as gratitude. Kasambuno wite rituals (deghoti wite) and kafematai rituals, (3) The process of implementing Rituals in the Agricultural Tradition (Galu) of the Bone Tondo Village Community, namely all ritual processes carried out on a good day led by a shaman (parika), preparing tools and materials (offerings) ) required each ritual ceremony that will be carried out. (4) Changes that occur at this time in the process of carrying out the Ritual in the Agricultural Tradition (Galu) of the Bone Tondo Village community, can be seen in the kaago-ago ritual, where at present the ritual portion is no longer carried out. Other changes are related to the consistency of the ritual, some of which still do the whole, but there are also those who only carry out 2 or 3 rituals. Keywords: Background, type, process and change, galu


Author(s):  
Nabil I. Al-Najjar ◽  
Ramon Casadesus-Masanell ◽  
Emre Ozdenoren

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