Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature. We then examine how TVGs can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are a-temporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be published in Internation Journal of Parallel, Emergent and Distributed System

Towards an explanation of orbits in the extreme trans-Neptunian region: The effect of Milgromian dynamics

Milgromian dynamics (MD or MOND) uniquely predicts motion in a galaxy from the distribution of its stars and gas in a remarkable agreement with observations so far. In the solar system, MD predicts the existence of some possibly non-negligible dynamical effects, which can be used to constrain the freedom in MD theories. Known extreme trans-Neptunian objects (ETNOs) have their argument of perihelion, longitude of ascending node, and inclination distributed in highly non-uniform fashion; ETNOs are bodies with perihelion distances greater than the orbit of Neptune and with semimajor axes greater than 150 au and less than $\sim1500$ au. It is as if these bodies have been systematically perturbed by some external force. We investigated a hypothesis that the puzzling orbital characteristics of ETNOs are a consequence of MD. We set up a dynamical model of the solar system incorporating the external field effect (EFE), which is anticipated to be the dominant effect of MD in the ETNOs region. We used constraints available on the strength of EFE coming from radio tracking of the Cassini spacecraft. We performed several numerical experiments, concentrating on the long-term orbital evolution of primordial (randomised) ETNOs in MD. The EFE could produce distinct non-uniform distributions of the orbital elements of ETNOs that are related to the orientation of an orbit in space. If we demand that EFE is solely responsible for the detachment of Sedna and 2012 VP$_{113}$, then these distributions are at odds with the currently observed statistics on ETNOs unless the EFE quadrupole strength parameter $Q_{2}$ has values that are unlikely (with probability < 1$\%$) in light of the Cassini data.Comment: 19 pages, 19 figures, 4 tables; accepted for publication in A&A; v2 - language improve

Merging stellar-mass binary black holes

The LIGO and Virgo detectors have recently directly observed gravitational waves from several mergers of pairs of stellar-mass black holes, as well as from one merging pair of neutron stars. These observations raise the hope that compact object mergers could be used as a probe of stellar and binary evolution, and perhaps of stellar dynamics. This colloquium-style article summarizes the existing observations, describes theoretical predictions for formation channels of merging stellar-mass black-hole binaries along with their rates and observable properties, and presents some of the prospects for gravitational-wave astronomy.Comment: Colloquium-style article solicited by Reviews of Modern Physics; comments appreciate

The role of smart sensor networks for voltage monitoring in smart grids

The large-scale deployment of the Smart Grid paradigm will support the evolution of conventional electrical power systems toward active, flexible and self-healing web energy networks composed of distributed and cooperative energy resources. In a Smart Grid platform, distributed voltage monitoring is one of the main issues to address. In this field, the application of traditional hierarchical monitoring paradigms has some disadvantages that could hinder their application in Smart Grids where the constant growth of grid complexity and the need for massive pervasion of Distribution Generation Systems (DGS) require more scalable, more flexible control and regulation paradigms. To try to overcome these challenges, this paper proposes the concept of a decentralized non-hierarchal voltage monitoring architecture based on intelligent and cooperative smart entities. These devices employ traditional sensors to acquire local bus variables and mutually coupled oscillators to assess the main variables describing the global grid state

Using real options to select stable Middleware-induced software architectures

The requirements that force decisions towards building distributed system architectures are usually of a non-functional nature. Scalability, openness, heterogeneity, and fault-tolerance are examples of such non-functional requirements. The current trend is to build distributed systems with middleware, which provide the application developer with primitives for managing the complexity of distribution, system resources, and for realising many of the non-functional requirements. As non-functional requirements evolve, the `coupling' between the middleware and architecture becomes the focal point for understanding the stability of the distributed software system architecture in the face of change. It is hypothesised that the choice of a stable distributed software architecture depends on the choice of the underlying middleware and its flexibility in responding to future changes in non-functional requirements. Drawing on a case study that adequately represents a medium-size component-based distributed architecture, it is reported how a likely future change in scalability could impact the architectural structure of two versions, each induced with a distinct middleware: one with CORBA and the other with J2EE. An option-based model is derived to value the flexibility of the induced-architectures and to guide the selection. The hypothesis is verified to be true for the given change. The paper concludes with some observations that could stimulate future research in the area of relating requirements to software architectures

Evolution of drainage system morphology at a land-terminating Greenland outlet glacier

This work was funded by the UK Natural Environment Research Council (through grants to Nienow, Mair, and Wadham, and a studentship to Bartholomew), the Edinburgh University Moss Centenary Scholarship (Cowton and Bartholomew), and a Carnegie Research Grant (Nienow). We thank Ian Willis, Tim Bartholomaus and an anonymous referee for valuable comments which significantly improved the manuscript.Peer reviewedPublisher PD

Phenotypic evolution studied by layered stochastic differential equations

Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure. The data consists of size measurements of fossilized calcite platelets (coccoliths) that cover the living cell, found in deep-sea sediment cores from six sites in the world oceans and dated to irregular points in time. To accommodate biological theory of populations tracking their fitness optima, and to allow potentially interpretable correlations in time and space, the model framework allows for an upper layer of partially observed site-specific population means, a layer of site-specific theoretical fitness optima and a bottom layer representing environmental and ecological processes. While the modeled process has many components, it is Gaussian and analytically tractable. A total of 710 model specifications within this framework are compared and inference is drawn with respect to model structure, evolutionary speed and the effect of global temperature.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS559 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analysis of Dynamic Task Allocation in Multi-Robot Systems

Dynamic task allocation is an essential requirement for multi-robot systems operating in unknown dynamic environments. It allows robots to change their behavior in response to environmental changes or actions of other robots in order to improve overall system performance. Emergent coordination algorithms for task allocation that use only local sensing and no direct communication between robots are attractive because they are robust and scalable. However, a lack of formal analysis tools makes emergent coordination algorithms difficult to design. In this paper we present a mathematical model of a general dynamic task allocation mechanism. Robots using this mechanism have to choose between two types of task, and the goal is to achieve a desired task division in the absence of explicit communication and global knowledge. Robots estimate the state of the environment from repeated local observations and decide which task to choose based on these observations. We model the robots and observations as stochastic processes and study the dynamics of the collective behavior. Specifically, we analyze the effect that the number of observations and the choice of the decision function have on the performance of the system. The mathematical models are validated in a multi-robot multi-foraging scenario. The model's predictions agree very closely with experimental results from sensor-based simulations.Comment: Preprint version of the paper published in International Journal of Robotics, March 2006, Volume 25, pp. 225-24