Heterogeneity in Schooling Rates of Return

This paper relaxes the assumption of homogeneous rates of return to schooling by employing nonparametric kernel regression. This approach allows us to examine the differences in rates of return to education both across and within groups. Similar to previous studies we find that on average blacks have higher returns to education than whites, natives have higher returns than immigrants and younger workers have higher returns than older workers. Contrary to previous studies we find that the average gap of the rate of return between white and black workers is larger than previously thought and the gap is smaller between immigrants and natives. We also uncover significant heterogeneity, the extent of which differs both across and within groups. The estimated densities of returns vary across groups and time periods and are often skewed. For example, during the period 1950-1990, at least 5% of whites have negative returns. Finally, we uncover the characteristics common amongst those with the smallest and largest returns to education. For example, we find that immigrants, aged 50-59, are most likely to have rates of return in the bottom 5% of the population.nonparametric, Mincer regressions, rate of return to education

Light Euclidean Spanners with Steiner Points

The FOCS'19 paper of Le and Solomon, culminating a long line of research on Euclidean spanners, proves that the lightness (normalized weight) of the greedy $(1+\epsilon)$-spanner in $\mathbb{R}^d$ is $\tilde{O}(\epsilon^{-d})$ for any $d = O(1)$ and any $\epsilon = \Omega(n^{-\frac{1}{d-1}})$ (where $\tilde{O}$ hides polylogarithmic factors of $\frac{1}{\epsilon}$), and also shows the existence of point sets in $\mathbb{R}^d$ for which any $(1+\epsilon)$-spanner must have lightness $\Omega(\epsilon^{-d})$. Given this tight bound on the lightness, a natural arising question is whether a better lightness bound can be achieved using Steiner points. Our first result is a construction of Steiner spanners in $\mathbb{R}^2$ with lightness $O(\epsilon^{-1} \log \Delta)$, where $\Delta$ is the spread of the point set. In the regime of $\Delta \ll 2^{1/\epsilon}$, this provides an improvement over the lightness bound of Le and Solomon [FOCS 2019]; this regime of parameters is of practical interest, as point sets arising in real-life applications (e.g., for various random distributions) have polynomially bounded spread, while in spanner applications $\epsilon$ often controls the precision, and it sometimes needs to be much smaller than $O(1/\log n)$. Moreover, for spread polynomially bounded in $1/\epsilon$, this upper bound provides a quadratic improvement over the non-Steiner bound of Le and Solomon [FOCS 2019], We then demonstrate that such a light spanner can be constructed in $O_{\epsilon}(n)$ time for polynomially bounded spread, where $O_{\epsilon}$ hides a factor of $\mathrm{poly}(\frac{1}{\epsilon})$. Finally, we extend the construction to higher dimensions, proving a lightness upper bound of $\tilde{O}(\epsilon^{-(d+1)/2} + \epsilon^{-2}\log \Delta)$ for any $3\leq d = O(1)$ and any $\epsilon = \Omega(n^{-\frac{1}{d-1}})$.Comment: 23 pages, 2 figures, to appear in ESA 2

A Unified and Fine-Grained Approach for Light Spanners

Seminal works on light spanners from recent years provide near-optimal tradeoffs between the stretch and lightness of spanners in general graphs, minor-free graphs, and doubling metrics. In FOCS'19 the authors provided a "truly optimal" tradeoff for Euclidean low-dimensional spaces. Some of these papers employ inherently different techniques than others. Moreover, the runtime of these constructions is rather high. In this work, we present a unified and fine-grained approach for light spanners. Besides the obvious theoretical importance of unification, we demonstrate the power of our approach in obtaining (1) stronger lightness bounds, and (2) faster construction times. Our results include: _ $K_r$-minor-free graphs: A truly optimal spanner construction and a fast construction. _ General graphs: A truly optimal spanner -- almost and a linear-time construction with near-optimal lightness. _ Low dimensional Euclidean spaces: We demonstrate that Steiner points help in reducing the lightness of Euclidean $1+\epsilon$-spanners almost quadratically for $d\geq 3$.Comment: We split this paper into two papers: arXiv:2106.15596 and arXiv:2111.1374

COMMUNITY BASED GAME RANCHING AND POLITICS IN CHIRIWO WARD OF MBIRE DISTRICT, ZIMBABWE

N° ISBN - 978-2-7380-1284-5International audienceCommunity based wildlife management in Zimbabwe is rooted in ideas of global significance whose central premise is that local communities will manage natural resources sustainably when rights and responsibilities are devolved to them; benefits of management exceed costs; they capture benefits; and they are small enough in membership to enforce group rules. Using results of research conducted in Chiriwo Ward, Mbire district, this paper revisits these core principles. Six years after CIRAD handed over Chivaraidze Game Ranch to the community, the project is revealing a schism between the aforesaid principles and actual practice. First, the ideal of devolving authority over wildlife to the community has come up against powerful local sectional interests. Second, the ideal of benefits of management exceeding costs is being contradicted by the reality of costs exceeding benefits. Third, the ideal of the community capturing benefits is being negated by the reality of elite capture of benefits. Fourth, the ideal of community cohesion is being neutralised by local leaders' divisive use of kinship and party political ties to gain access to and control the ranch and its wildlife. On the basis of comparative literature and our own findings, we argue for the necessity to investigate and analyse the politics behind project appropriation at the local level. We conclude that building community collective action in wildlife management requires scrutiny and understanding of power politics which shapes local participation and structures the outcomes of wildlife management

Peer-to-Peer and Mass Communication Effect on Revolution Dynamics

Revolution dynamics is studied through a minimal Ising model with three main influences (fields): personal conservatism (power-law distributed), inter-personal and group pressure, and a global field incorporating peer-to-peer and mass communications, which is generated bottom-up from the revolutionary faction. A rich phase diagram appears separating possible terminal stages of the revolution, characterizing failure phases by the features of the individuals who had joined the revolution. An exhaustive solution of the model is produced, allowing predictions to be made on the revolution's outcome

Dynamic Matching Algorithms Under Vertex Updates

Dynamic graph matching algorithms have been extensively studied, but mostly under edge updates. This paper concerns dynamic matching algorithms under vertex updates, where in each update step a single vertex is either inserted or deleted along with its incident edges. A basic setting arising in online algorithms and studied by Bosek et al. [FOCS\u2714] and Bernstein et al. [SODA\u2718] is that of dynamic approximate maximum cardinality matching (MCM) in bipartite graphs in which one side is fixed and vertices on the other side either arrive or depart via vertex updates. In the BASIC-incremental setting, vertices only arrive, while in the BASIC-decremental setting vertices only depart. When vertices can both arrive and depart, we have the BASIC-dynamic setting. In this paper we also consider the setting in which both sides of the bipartite graph are dynamic. We call this the MEDIUM-dynamic setting, and MEDIUM-decremental is the restriction when vertices can only depart. The GENERAL-dynamic setting is when the graph is not necessarily bipartite and the vertices can both depart and arrive. Denote by K the total number of edges inserted and deleted to and from the graph throughout the entire update sequence. A well-studied measure, the recourse of a dynamic matching algorithm is the number of changes made to the matching per step. We largely focus on Maximal Matching (MM) which is a 2-approximation to the MCM. Our main results are as follows. - In the BASIC-dynamic setting, there is a straightforward algorithm for maintaining a MM, with a total runtime of O(K) and constant worst-case recourse. In fact, this algorithm never removes an edge from the matching; we refer to such an algorithm as irrevocable. - For the MEDIUM-dynamic setting we give a strong conditional lower bound that even holds in the MEDIUM-decremental setting: if for any fixed ? > 0, there is an irrevocable decremental MM algorithm with a total runtime of O(K ? n^{1-?}), this would refute the OMv conjecture; a similar (but weaker) hardness result can be achieved via a reduction from the Triangle Detection conjecture. - Next, we consider the GENERAL-dynamic setting, and design an MM algorithm with a total runtime of O(K) and constant worst-case recourse. We achieve this result via a 1-revocable algorithm, which may remove just one edge per update step. As argued above, an irrevocable algorithm with such a runtime is not likely to exist. - Finally, back to the BASIC-dynamic setting, we present an algorithm with a total runtime of O(K), which provides an (e/(e-1))-approximation to the MCM. To this end, we build on the classic "ranking" online algorithm by Karp et al. [STOC\u2790]. Beyond the results, our work draws connections between the areas of dynamic graph algorithms and online algorithms, and it proposes several open questions that seem to be overlooked thus far