Time-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications including the spreading of diseases. Past contributions have investigated random processes on timevarying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness based complex networks literature, but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed form solutions for the quantities of interest using a factorisable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection, but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks are very different from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment.

We study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions.

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In the last years, concepts have been developed to use etched ion tracks in insulators, such as polymer foils or silicon oxide layers as hosts for nano- and microelectronic structures. Depending on their etching procedure and the thickness of the insulating layer in which they are embedded, such tracks have typical diameters between some 10 nm and a few μm and lengths between some 100 nm and some 10 μm. Due to their extremely high aspect ratios, and due to the possibility to cover very large sample areas, they exceed the potential of nanolithography. In this paper, the strategies of etched ion track manipulation are briefly outlined, that lead to the formation of nanotubules, nanowires, or tubular arrangements of nanoclusters. Examples where nanoelectronic structures are based on single ion tracks, are nanocondensors or sensors for temperature, light, pressure, humidity and/or alcohol vapor. By combination of ion track metallization and conducting track-to-track connections on the foil surface, micromagnets, microtransformers and microcondensors could be formed within polymer foils. Finally, we present our new "TEMPOS" (Tunable Electronic Material with Pores in Oxide on Silicon) concept where nanometric pores, produced by etching of tracks in silicon oxide on silicon wafers, are used as charge extraction (or injection) channels. In comparison with the metal oxide semiconductor field effect transistors (MOS-FETs), the TEMPOS structures have a number of additional parameters (such as the track diameter, density, and shape, and the material embedded therein and its spatial distribution) which makes these novel structures much more complex. This eventually leads to higher compactation of the TEMPOS circuits and to unexpected electronic properties. TEMPOS structures can overtake the function of tunable resistors, condensors, photocells, hygrocells, diodes, sensors, and other elements. As an example, some corresponding current/voltage relations and TEMPOS circuits are presented. In this work we concentrate on TEMPOS structures with fullerene and phthalocyanine. Though not yet verified, TEMPOS structures could, in principle, be scaled down to nanometer sizes.

The ability to understand the impact of adversarial processes on networks is crucial to various disciplines. The objects of study in this article are fitness-driven networks. Fitness-dependent networks are fully described by a probability distribution of fitness and an attachment kernel. Every node in the network is endowed with a fitness value and the attachment kernel translates the fitness of two nodes into the probability that these two nodes share an edge. This concept is also known as mutual attractiveness. In the present article, fitness does not only serve as a measure of attractiveness, but also as a measure of a node's robustness against failure. The probability that a node fails increases with the number of failures in its direct neighborhood and decreases with higher fitness. Both static and dynamic network models are considered. Analytical results for the percolation threshold and the occupied fraction are derived. One of the results is that the distinction between the dynamic and the static model has a profound impact on the way failures spread over the network. Additionally, we find that the introduction of mutual attractiveness stabilizes the network compared to a pure random attachment.

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