Katharina Anna Lehmann

Chronological aging leads to apoptosis in yeast

During the past years, yeast has been successfully established as a model to study mechanisms of apoptotic regulation. However, the beneficial effects of such a cell suicide program for a unicellular organism remained obscure. Here, we demonstrate that chronologically aged yeast cultures die exhibiting typical markers of apoptosis, accumulate oxygen radicals, and show caspase activation. Age-induced cell death is strongly delayed by overexpressing YAP1, a key transcriptional regulator in oxygen stress response. Disruption of apoptosis through deletion of yeast caspase YCA1 initially results in better survival of aged cultures. However, surviving cells lose the ability of regrowth, indicating that predamaged cells accumulate in the absence of apoptotic cell removal. Moreover, wild-type cells outlast yca1 disruptants in direct competition assays during long-term aging. We suggest that apoptosis in yeast confers a selective advantage for this unicellular organism, and demonstrate that old yeast cells release substances into the medium that stimulate survival of the clone.

Algorithms for Centrality Indices

The usefulness of centrality indices stands or falls with the ability to compute them quickly. This is a problem at the heart of computer science, and much research is devoted to the design and analysis of efficient algorithms. For example, shortest-path computations are well understood, and these insights are easily applicable to all distance based centrality measures. This chapter is concerned with algorithms that efficiently compute the centrality indices of the previous chapters.

Max-tolerance graphs as intersection graphs: cliques, cycles, and recognition

Max-tolerance graphs can be regarded as generalized interval graphs, where two intervals <i>I</i><inf><i>i</i></inf> and <i>I</i><inf><i>j</i></inf> only induce an edge in the corresponding graph iff they overlap for an amount of at least <i>max</i>{<i>t</i><inf><i>i</i></inf>, <i>t</i><inf><i>j</i></inf>} where <i>t</i><inf><i>i</i></inf> is an individual tolerance parameter associated to each interval <i>I</i><inf><i>i</i></inf>. A new geometric characterization of max-tolerance graphs as intersection graphs of isosceles right triangles, shortly called semi-squares, leverages the solution of various graph-theoretic problems in connection with max-tolerance graphs. First, we solve the maximal and maximum cliques problem. It arises naturally in DNA sequence analysis where the maximal cliques might be interpreted as functional domains carrying biologically meaningful information. We prove an upper bound of <i>O</i>(<i>n</i>³) for the number of maximal cliques in max-tolerance graphs and give an efficient <i>O</i>(<i>n</i>³) algorithm for their computation. In the same vein, the semi-square representation yields a simple proof for the fact that this bound is asymptotically tight, i.e., a class of max-tolerance graphs is presented where the instances have Ω(<i>n</i>³) maximal cliques. Additionally, we answer an open question posed in [8] by showing that max-tolerance graphs do not contain complements of cycles <i>C</i><inf><i>n</i></inf> for <i>n</i> > 9. By exploiting the new representation more deeply, we can go even further and prove that the recognition problem for max-tolerance graphs is NP-hard.

T-DHT: topology-based distributed hash tables

In this paper, the authors introduced topology-based distributed hash tables (T-DHT) as an infrastructure for data-centric storage, information processing, and routing in ad hoc and sensor networks. T-DHTs do not rely on location information and work even in the presence of voids in the network. Using a virtual coordinate system, a distributed hash table which is strongly oriented to the underlying network topology was constructed. Thus, adjacent areas in the hash table commonly have a direct link in the network. Routing in the T-DHT guarantees reachability and introduces low hop-overhead compared with the shortest path.

Advanced Centrality Concepts

The sheer number of different centrality indices introduced in the literature, or even only the ones in Chapter 3, is daunting. Frequently, a new definition is motivated by the previous ones failing to capture the notion of centrality of a vertex in a new application. In this chapter we will discuss the connections, similarities and differences of centralities. The goal of this chapter is to present an overview of such connections, thus providing some kind of map of the existing centrality indices. For that we focus on formal descriptions that hold for all networks. However, this approach has its limits.

Evolutionary algorithms for the self-organized evolution of networks

While the evolution of biological networks can be modeled sensefully as a series of mutation and selection, evolution of other networks such as the social network in a city or the network of streets in a country is not determined by selection since there is no alternative network with which these singular networks have to compete. Nonetheless, these singular networks do evolve due to dynamic changes of vertices and edges. In this article we present a formal, analyzable framework for the evolution of singular networks. We show that the careful design of adaptation rules can lead to the emergence of network topologies with satisfying performance in polynomial time while other adaptation rules yield exponential runtime. We further show by example how the framework could be applied to some ad-hoc communication scenarios.

On the maximal cliques in c-max-tolerance graphs and their application in clustering molecular sequences

Given a set S of n locally aligned sequences, it is a needed prerequisite to partition it into groups of very similar sequences to facilitate subsequent computations, such as the generation of a phylogenetic tree. This article introduces a new method of clustering which partitions S into subsets such that the overlap of each pair of sequences within a subset is at least a given percentage c of the lengths of the two sequences. We show that this problem can be reduced to finding all maximal cliques in a special kind of max-tolerance graph which we call a c-max-tolerance graph. Previously we have shown that finding all maximal cliques in general max-tolerance graphs can be done efficiently in O(n3 + out). Here, using a new kind of sweep-line algorithm, we show that the restriction to c-max-tolerance graphs yields a better runtime of O(n2 log n + out). Furthermore, we present another algorithm which is much easier to implement, and though theoretically slower than the first one, is still running in polynomial time. We then experimentally analyze the number and structure of all maximal cliques in a c-max-tolerance graph, depending on the chosen c-value. We apply our simple algorithm to artificial and biological data and we show that this implementation is much faster than the well-known application Cliquer. By introducing a new heuristic that uses the set of all maximal cliques to partition S, we finally show that the computed partition gives a reasonable clustering for biological data sets.

Visualizing large and clustered networks

The need to visualize large and complex networks has strongly increased in the last decade. Although networks with more than 1000 vertices seem to be prohibitive for a comprehensive layout, real-world networks exhibit a very inhomogenous edge density that can be harnessed to derive an aesthetic and structured layout. Here, we will present a heuristic that finds a spanning tree with a very low average spanner property for the non-tree edges, the so-called backbone of a network. This backbone can then be used to apply a modified tree-layout algorithm to draw the whole graph in a way that highlights dense parts of the graph, so-called clusters, and their inter-connections.

6. Random Graphs, Small-Worlds and Scale-Free Networks

In this chapter we will introduce two famous network models that arose much interest in recent years: The small-world model of Duncan Watts and Steven Strogatz [615] and scale-free or power-law networks, first presented by the Faloutsos brethren [201] and filled with life by a model of Albert- Laszlo Barabasi and Reka Alberts [60]. These models describe some structural aspects of most real-world networks. The most prevalent network structure of small-world networks is a local mesh-like part combined with some random edges that make the network small.

On the topologies of local minimum spanning trees

This paper is devoted to study the combinatorial properties of Local Minimum Spanning Trees (LMSTs), a geometric structure that is attracting increasing research interest in the wireless sensor networks community. Namely, we study which topologies are allowed for a sensor network that uses, for supporting connectivity, a local minimum spanning tree approach. First, we refine the current definition of LMST realizability, focusing on the role of the power of transmission (i.e., of the radius of the covered area). Second, we show simple planar, connected, and triangle-free graphs with maximum degree 3 that cannot be represented as an LMST. Third, we present several families of graphs that can be represented as LMSTs. Then, we show a relationship between planar graphs and their representability as LMSTs based on homeomorphism. Finally, we show that the general problem of determining whether a graph is LMST representable is NP-hard.