This book brings together two of the most exciting and widely studied subjects in modern physics: namely fractals and surfaces. To the community interested in the study of surfaces and interfaces, it brings the concept of fractals. To the community interested in the exciting field of fractals and their application, it demonstrates how these concepts may be used in the study of surfaces. The authors cover, in simple terms, the various methods and theories developed over the past ten years to study surface growth. They describe how one can use fractal concepts successfully to describe and predict the morphology resulting from various growth processes. Consequently, this book will appeal to physicists working in condensed matter physics and statistical mechanics, with an interest in fractals and their application. The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html

An important goal in biology is to uncover the fundamental design principles that provide the common underlying structure and function in all cells and microorganisms [6][7][8][9][10][11][12][13] . For example, it is increasingly appreciated that the robustness of various cellular processes is rooted in the dynamic interactions among its many constituents [14][15][16] , such as proteins, DNA, RNA, and small molecules.Recent scientific developments improve our ability to identify the design principles that integrate these interactions into a complex system. Large-scale sequencing projects have not only provided complete sequence information for a number of genomes, but also allowed the development of integrated pathway-genome databases [17][18][19] that provide organism-specific connectivity maps of metabolic-and,

Understanding why some cellular components are conserved across species but others evolve rapidly is a key question of modern biology. Here we show that in Saccharomyces cerevisiae, proteins organized in cohesive patterns of interactions are conserved to a substantially higher degree than those that do not participate in such motifs. We find that the conservation of proteins in distinct topological motifs correlates with the interconnectedness and function of that motif and also depends on the structure of the overall interactome topology. These findings indicate that motifs may represent evolutionary conserved topological units of cellular networks molded in accordance with the specific biological function in which they participate.

The recognition that real networks are fundamentally different from the random models that dominated the mathematical literature in the past 40 years [1,2] leads to a surge of activity in addressing the statistical properties of these systems [3][4][5][6][7][8][9][10]. In one aspect most recently developed models, aimed to describe the large-scale topology of complex networks, are incomplete when compared with real systems: they assume that all links are equivalent. But in many fields it is well known that the interaction strengths can vary widely, such variations being essential to the network's ability to carry on its basic functions. Sociologists have repeatedly argued about the importance of assigning strengths to social links, finding that the weak links people have outside their close circle of friends play a key role in keeping the social system together [11]. Recently, Newman has showed that assigning weights to the links between scientists allows for a better characterization of the scientific collaboration web [12]. Similarly, there is an ongoing discussion about the importance of weak links between species in guaranteeing the stability of an ecosystem [13]. Finally, many transportation networks in nature, ranging from cardiovascular to respiratory networks, have well defined weights or flow rates assigned to the links, whose magnitude is intimately determined by the network's topology [14]. The issue of link strength has been extensively addressed in the neural network literature. The question posed in that context so far had a unique focus: given a network topology, how can one alter the link weights in a dynamical fashion to allow the network to perform certain desired functions, ranging from memory to pattern recognition [15]?Similarly, research on allometric scaling has also been concerned with assigning weights to links on a network with fixed, often treelike topology [14]. On the other hand, the recent advances in statistical modeling of complex networks have brought the community's attention towards large networks whose topology evolves in time. Despite the known importance of interaction strengths in the various systems these models aim to describe, in this context there have been no attempts to model networks other than binary nets, whose links have weights 0 or 1.In this paper we take a first step in the direction of a systematic study of evolving networks with nonbinary connectivities. We introduce and investigate two models that assign weights to new links as they are dynamically created, providing a prototype of a weighted evolving network. While we choose the simplest possible models, in which the weights are driven by the network connectivity only, numerical simulations indicate that the distribution of the total weight scales differently from the total connectivity. However, an analytical solution reveals that the different scaling behavior can be explained by strong logarithmic correction, and asymptotically the investigated weighted networks belong to the same universality class as t...

Recent evidence indicates that potential interactions within metabolic, protein-protein interaction, and transcriptional regulatory networks are used differentially according to the environmental conditions in which a cell exists. However, the topological units underlying such differential utilization are not understood. Here we use the transcriptional regulatory network of Escherichia coli to identify such units, called origons, representing regulatory subnetworks that originate at a distinct class of sensor transcription factors. Using microarray data, we find that specific environmental signals affect mRNA expression levels significantly only within the origons responsible for their detection and processing. We also show that small regulatory interaction patterns, called subgraphs and motifs, occupy distinct positions in and between origons, offering insights into their dynamical role in information processing. The identified features are likely to represent a general framework for environmental signal processing in prokaryotes. cellular networks ͉ regulation ͉ transcription T ranscriptional regulatory (TR) networks govern cellular life by initiating and mediating gene expression in response to environmental and intracellular cues that result in the execution of cellular programs such as metabolic adjustments, sporulation, or cell division. The nodes of this network are transcription units (genes or operons) together with their protein products, whereas the links connecting them correspond to TR interactions mediated by transcription factor (TF) proteins. The genome-scale identification of TF-binding sites, their binding specificities, and their condition-dependent utilization (1-7) results in increasingly comprehensive data sets amenable for analysis of TR-network topology and function.Previous studies analyzing the TR-network topology of the prokaryote Escherichia coli and the eukaryote Saccharomyces cerevisiae have demonstrated that their TR networks share several characteristics such as the exponential distribution of in-degree connectivity, the scale-free distribution of out-degree connectivity, and the very low number of feedback circuits except for selfregulation (8-11). In addition, the same small-scale connectivity patterns [e.g., the feed-forward loop (FFL) and bifan motif] are overrepresented in both TR networks (12-15), suggesting that their topology has evolved to accomplish similar tasks in various organisms (14). Recent studies of motif dynamics (16-17) generated the first insights into their information-processing capabilities, although the position of motifs within TR networks and their aggregation into larger topological structures (10) may modify their dynamic behavior.Despite these advances, there is a clear need to decipher the system-level organization of dynamic TR-network utilization (5) triggered by a various environmental and intracellular cues. Here, based on the inherent directionality of TR interactions in E. coli (11,12), we identify topological units of environmental signal proc...