A century of contested ownership: Land tenure in Alexandra, South Africa 1912 - 2011

Purpose of the paper: Alexandra was proclaimed in 1912 as the first formal township in South Africa where blacks could obtain ownership. Over the past century, a number of watershed changes in layout and ownership have taken place, most notably the promulgation of the 1913 Land Act that prohibited the proclamation of land for black ownership and a series of expropriations, resulting from apartheid policies that took place from 1950 onwards, culminating in a consolidation in 1985 that led to further expropriations. In 2011, former land owners established land claims.  These claims were complicated by the fact that a number of residents had received legal right of ownership.Investigation of the validity of the claims required a comprehensive study of the change of ownership from the original proclamation (1912) to the situation in 2011. Methodology. An analysis of current and historical development and management of Alexandra is provided, supplemented by a visual overview of the changing patterns of ownership and densification. The present status of land claims and their legal implications is summarized and a reliable estimate of the present population of Alexandra is provided.Findings: The total population as determined by this study is more than 60 per cent more than the formal 2011 census estimate, resulting in a density of more than 44 400 persons per hectare. It was also found that Occupiers on one stand can have different kind of rights.  However, adequate documentation has been assembled to drive the process of land tenure upgrading.Practical implications: The higher than previously estimated population density has severe implications - physical as well as political - for future planning of this vibrant area. The importance of a reliable estimate of the ownership of property in Alexandra becomes even more apparent when the implications of the Restitution Act are considered.

The M/M/c with critical jobs

We consider the M/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach

Geochronological database and classification system for age uncertainties in Neotropical pollen records.

The newly updated inventory of palaeoecological research in Latin America offers an important overview of sites available for multi-proxy and multi-site purposes. From the collected literature supporting this inventory, we collected all available age model metadata to create a chronological database of 5116 control points (e.g. 14C, tephra, fission track, OSL, 210Pb) from 1097 pollen records. Based on this literature review, we present a summary of chronological dating and reporting in the Neotropics. Difficulties and recommendations for chronology reporting are discussed. Furthermore, for 234 pollen records in northwest South America, a classification system for age uncertainties is implemented based on chronologies generated with updated calibration curves. With these outcomes age models are produced for those sites without an existing chronology, alternative age models are provided for researchers interested in comparing the effects of different calibration curves and age-depth modelling software, and the importance of uncertainty assessments of chronologies is highlighted. Sample resolution and temporal uncertainty of ages are discussed for different time windows, focusing on events relevant for research on centennial- to millennial-scale climate variability. All age models and developed R scripts are publicly available through figshare, including a manual to use the scripts

Universality for first passage percolation on sparse random graphs

We consider first passage percolation on the conguration model with n vertices, and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X2 logX-condition, we analyze the asymptotic distribution for the minimal weight path between a pair of typical vertices, as well the number of edges on this path namely the hopcount. The hopcount satisfies a central limit theorem (CLT). Furthermore, writing Ln for the weight of this optimal path, then we shown that Ln(log n)= n converges to a limiting random variable, for some sequence n. This sequence n and the norming constants for the CLT are expressible in terms of the parameters of an associated continuous-time branching process that describes the growth of neighborhoods around a uniformly chosen vertex in the random graph. The limit of Ln(log n)= n equals the sum of the logarithm of the product of two independent martingale limits, and a Gumbel random variable. Till date, for sparse random graph models, such results have been shown only for the special case where the edge weights have an exponential distribution, wherein the Markov property of this distribution plays a crucial role in the technical analysis of the problem. The proofs in the paper rely on a refined coupling between shortest path trees and continuous- time branching processes, and on a Poisson point process limit for the potential closing edges of shortest-weight paths between the source and destination

Universality for first passage percolation on sparse uniform and rank-1 random graphs

In [3], we considered first passage percolation on the configuration model equipped with general independent and identically distributed edge weights, where the common distribution function admits a density. Assuming that the degree distribution satisfies a uniform X^2 log X - condition, we analyzed the asymptotic distribution for the minimal weight path between a pair of typical vertices, as well as the asymptotic distribution of the number of edges on this path. Given the interest in understanding such questions for various other random graph models, the aim of this paper is to show how these results extend to uniform random graphs with a given degree sequence and rank-one inhomogeneous random graphs

Scale-free percolation

Abstract We formulate and study a model for inhomogeneous long-range percolation on Zd. Each vertex x¿Zd is assigned a non-negative weight Wx, where (Wx)x¿Zd are i.i.d. random variables. Conditionally on the weights, and given two parameters a,¿>0, the edges are independent and the probability that there is an edge between x and y is given by pxy=1-exp{-¿WxWy/|x-y|a}. The parameter ¿ is the percolation parameter, while a describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there exists an infinite component and on graph distance between remote pairs of vertices. First, we show that the tail behavior of the degree distribution is related to the tail behavior of the weight distribution. When the tail of the distribution of Wx is regularly varying with exponent t-1, then the tail of the degree distribution is regularly varying with exponent ¿=a(t-1)/d. The parameter ¿ turns out to be crucial for the behavior of the model. Conditions on the weight distribution and ¿ are formulated for the existence of a critical value ¿c¿(0,8) such that the graph contains an infinite component when ¿>¿c and no infinite component when ¿0, les arêtes sont indépendantes et la probabilité qu’il existe un lien entre x et y est pxy=1-exp{-¿WxWy/|x-y|a}. Le paramètre ¿ est le paramètre de percolation tandis que a caractérise la portée des interactions. Nous étudierons la distribution des degrés dans le graphe résultant et l’existence éventuelle d’une composante infinie ainsi que la distance de graphe entre deux sites éloignés. Nous montrons d’abord que la queue de la distribution des degrés est liée à la queue de la distribution des poids. Quand la queue de la distribution de Wx est à variation régulière d’indice t-1, alors la queue de la distribution des degrés est à variation régulière d’indice ¿=a(t-1)/d. Le paramètre ¿ s’avère crucial pour décrire le modèle. Des conditions sur la distribution des poids et de ¿ sont formulées pour l’existence d’une valeur critique ¿c¿(0,8) telle que le graphe contienne une composante infinie quand ¿>¿c et aucune composante infinie quand

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo

Managers zijn net mensen

Managers zijn net mense