Abstract:
Many current works aiming to learn regulatory networks from systems biology data must balance model complexity with respect to data availability and quality. Methods that learn regulatory associations based on unit-less metrics, such as Mutual Information, are attractive in that they scale well and reduce the number of free parameters (model complexity) per interaction to a minimum. In contrast, methods for learning regulatory networks based on explicit dynamical models are more complex and scale less gracefully, but are attractive as they may allow direct prediction of transcriptional dynamics and resolve the directionality of many regulatory interactions.

Abstract:
Multipotent stem or progenitor cells undergo a sequential series of binary fate decisions, which ultimately generate the diversity of differentiated cells. Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transitions. However, existing gene network models do not explain more complex properties of cell fate dynamics such as the hierarchical branching of developmental paths. Here, we construct a generic minimal model of the genetic regulatory network controlling cell fate determination, which exhibits five elementary characteristics of cell differentiation: stability, directionality, branching, exclusivity, and promiscuous expression. We argue that a modular architecture comprising repeated network elements reproduces these features of differentiation by sequentially repressing selected modules and hence restricting the dynamics to lower dimensional subspaces of the high-dimensional state space. We implement our model both with ordinary differential equations (ODEs), to explore the role of bifurcations in producing the one-way character of differentiation, and with stochastic differential equations (SDEs), to demonstrate the effect of noise on the system. We further argue that binary cell fate decisions are prevalent in cell differentiation due to general features of the underlying dynamical system. This minimal model makes testable predictions about the structural basis for directional, discrete and diversifying cell phenotype development and thus can guide the evaluation of real gene regulatory networks that govern differentiation.

Abstract:
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology.

Abstract:
The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth System. However, these models are based on simplifications of our understanding of nature, thus are unavoidably imperfect. Conversely, observation-based data of climatic and environmental variables are becoming increasingly accessible over large scales due to the progress of space-borne sensing technologies and data-assimilation techniques. Albeit uncertain, these data enable the possibility to start unraveling complex multivariable, multiscale relationships if the appropriate statistical methods are applied. Here, we investigate the potential of the wavelet cross-correlation method as a tool for identifying multiscale interactions, feedback and regime shifts in geophysical systems. The ability of wavelet cross-correlation to resolve the fast and slow components of coupled systems is tested on synthetic data of known directionality, and then applied to observations to study one of the most critical interactions between land and atmosphere: the coupling between soil moisture and near-ground air temperature. Results show that our method is not only able to capture the dynamics of the soil moisture-temperature coupling over a wide range of temporal scales (from days to several months) and climatic regimes (from wet to dry), but also to consistently identify the magnitude and directionality of the coupling. Consequently, wavelet cross-correlations are presented as a promising tool for the study of multiscale interactions, with the potential of being extended to the analysis of causal relationships in the Earth system.

Abstract:
We derive the equations governing the dynamics of cosmic strings in a flat anisotropic universe of Bianchi type I and study the evolution of simple cosmic string loop solutions. We show that the anisotropy of the background can have a characteristic effect in the loop motion. We discuss some cosmological consequences of these findings and, by extrapolating our results to cosmic string networks, we comment on their ability to survive an inflationary epoch, and hence be a possible fossil remnant (still visible today) of an anisotropic phase in the very early universe.

Abstract:
Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.

Abstract:
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellular automata and find that the overall number of complex patterns decreases under increasing neighborhood size in regular graphs. As exemplary applications, we apply the formalism to complex networks and compare the potential of scale-free graphs and metabolic networks to generate complex dynamics.

Abstract:
We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.

Abstract:
Millimeter wave (mmW) wireless networks are capable to support multi-gigabit data rates, by using directional communications with narrow beams. However, existing mmW communications standards are hindered by two problems: deafness and single link scheduling. The deafness problem, that is, a misalignment between transmitter and receiver beams, demands a time consuming beam-searching operation, which leads to an alignment-throughput tradeoff. Moreover, the existing mmW standards schedule a single link in each time slot and hence do not fully exploit the potential of mmW communications, where directional communications allow multiple concurrent transmissions. These two problems are addressed in this paper, where a joint beamwidth selection and power allocation problem is formulated by an optimization problem for short range mmW networks with the objective of maximizing effective network throughput. This optimization problem allows establishing the fundamental alignment-throughput tradeoff, however it is computationally complex and requires exact knowledge of network topology, which may not be available in practice. Therefore, two standard-compliant approximation solution algorithms are developed, which rely on underestimation and overestimation of interference. The first one exploits directionality to maximize the reuse of available spectrum and thereby increases the network throughput, while imposing almost no computational complexity. The second one is a more conservative approach that protects all active links from harmful interference, yet enhances the network throughput by 100% compared to the existing standards. Extensive performance analysis provides useful insights on the directionality level and the number of concurrent transmissions that should be pursued. Interestingly, extremely narrow beams are in general not optimal.