Local Guarantees in Graph Cuts and Clustering

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$ or $-$ and the goal is to produce a clustering that agrees with the labels as much as possible: $+$ edges within clusters and $-$ edges across clusters. The classical approach towards Correlation Clustering (and other graph cut problems) is to optimize a global objective. We depart from this and study local objectives: minimizing the maximum number of disagreements for edges incident on a single node, and the analogous max min agreements objective. This naturally gives rise to a family of basic min-max graph cut problems. A prototypical representative is Min Max $s-t$ Cut: find an $s-t$ cut minimizing the largest number of cut edges incident on any node. We present the following results: $(1)$ an $O(\sqrt{n})$-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node (thus providing the first known approximation for the above family of min-max graph cut problems), $(2)$ a remarkably simple $7$-approximation for minimizing local disagreements in complete graphs (improving upon the previous best known approximation of $48$), and $(3)$ a $1/(2+\varepsilon)$-approximation for maximizing the minimum total weight of agreement edges incident on any node, hence improving upon the $1/(4+\varepsilon)$-approximation that follows from the study of approximate pure Nash equilibria in cut and party affiliation games

Identification and differentiation of Ficus carica L. cultivars using inter simple sequence repeat markers

Information on germplasm diversity and relationships among elite materials is fundamentally important in crop improvement. The main objectives of our study is to determine the level of genetic diversity inter fig-tree cultivars using inter simple sequence repeat (ISSR) markers. Fifty-seven local Tunisian figtree cultivars were fingerprinted with ISSR marker. A total of 33 alleles were detected. A high level of genetic diversity was identified inter cultivars. The clustering grouped the studied cultivars into four clusters with no correlation to geographical origin

Unifying Sparsest Cut, Cluster Deletion, and Modularity Clustering Objectives with Correlation Clustering

Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called LambdaCC that is based on a specially weighted version of correlation clustering. A key component in our methodology is a clustering resolution parameter, $\lambda$, which implicitly controls the size and structure of clusters formed by our framework. We show that, by increasing this parameter, our objective effectively interpolates between two different strategies in graph clustering: finding a sparse cut and forming dense subgraphs. Our methodology unifies and generalizes a number of other important clustering quality functions including modularity, sparsest cut, and cluster deletion, and places them all within the context of an optimization problem that has been well studied from the perspective of approximation algorithms. Our approach is particularly relevant in the regime of finding dense clusters, as it leads to a 2-approximation for the cluster deletion problem. We use our approach to cluster several graphs, including large collaboration networks and social networks

Without purpose and strategy?: a spatio-functional analysis of the regional allocation of public investment in Greece

We utilise a large database on public investment at the prefecture (NUTS-3) level in Greece for the period 1976-2008 to examine the spatial and functional allocation of public investment in the country. We investigate the extent to which expenditures in different types of public investment are complementary across space and over time and examine their redistributive character. We also analyse regional specialisations and the geographical concentration of public investments and complementarily use an exploratory spatial data analysis to examine the extent of clustering of public investment and identify possible patterns in the geography of clusters and hotspots. Although our analysis uses predominantly descriptive tools, our results have confirmatory power, as they reveal a surprisingly random pattern for the spatial and functional allocation of public investment in Greece, thus raising important questions about the rationale for these allocations and, by implication, about the geographical, political and economic dynamics that underlie them. These questions obtain an additional salience in light of the administrative and fiscal reforms pursued currently by the Greek government under the pressure of the country’s sovereign debt crisis

FECES STANDARD MONEY: BEYOND TRANSACTIONS

Department of Urban and Environmental Engineering (Convergence of Science and Arts)Feces Standard Money (fSM), is a complementary currency that is different from other currencies in a number of ways. It is the first currency to adopt feces as its standard. In a world where objects and people are thought of as "goods and services," reality is compressed into conceptions of "use value" or "utility???. However, in the fSM system, feces and food waste that have traditionally and culturally been classified as ???human waste??? are used to produce biogas, creating value. Feces then becomes a representation of a new conception of value - one based on abundance instead of scarcity. This study aims to explore how the use of fSM can facilitate a redefinition of sustainable wealth. It begins by exploring neoclassical and modern theories of money and their relationship to the current state of money. It argues that economics??? failure to adequately account for the role of money as a basis of social relations contributes to the current unsustainable economic system. Building on the background and philosophical underpinnings of fSM, it postulates that money based on a feces standard might be a possible solution to developing a monetary system that can serve as the basis of social relations and facilitation of exchange as a means of instigating social change in attitudes towards global challenges like inequality and climate change. Social network analysis is used to investigate the social footprint of fSM in a game simulation of the fSM system. It is found that the mechanisms of fSM has the potential to imbue the network with tight knit connections -knots- that can contribute to a more inclusive monetary system.clos