Dynamics of cascades on burstiness-controlled temporal networks

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. Here we develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.

Photoinduced Mass Transport in Azo-Polymers in 2D: Monte Carlo Study of Polarization Effects

We studied the impact of light polarization on photoinduced dynamics of model azo-polymer chains in two dimensions, using bond-fluctuation Monte Carlo simulations. For two limiting models—sensitive to and independent of light polarization—their dynamics driven by photoisomerization of azo-dyes as well as by thermal effects was studied, including characterization of mass transport and chain reorientations. The corresponding schemes of light–matter interaction promote qualitatively different dynamics of photoinduced motion of azo-polymer chains. In particular, they can inhibit or trigger off a directed mass transport along a gradient of light illumination. The generic dynamics of single chains is superdiffusive and is promoted by breaking a symmetry present in the polarization independent model.

On Baire measurable colorings of group actions

The field of descriptive combinatorics investigates to what extent classical combinatorial results and techniques can be made topologically or measure-theoretically well behaved. This paper examines a class of coloring problems induced by actions of countable groups on Polish spaces, with the requirement that the desired coloring be Baire measurable. We show that the set of all such coloring problems that admit a Baire measurable solution for a particular free action $\unicode[STIX]{x1D6FC}$ is complete analytic (apart from the trivial situation when the orbit equivalence relation induced by $\unicode[STIX]{x1D6FC}$ is smooth on a comeager set); this result confirms the ‘hardness’ of finding a topologically well-behaved coloring. When $\unicode[STIX]{x1D6FC}$ is the shift action, we characterize the class of problems for which $\unicode[STIX]{x1D6FC}$ has a Baire measurable coloring in purely combinatorial terms; it turns out that closely related concepts have already been studied in graph theory with no relation to descriptive set theory. We remark that our framework permits a wholly dynamical interpretation (with colorings corresponding to equivariant maps to a given subshift), so this article can also be viewed as a contribution to generic dynamics.

Formation Control Algorithm of Multi-UAV-Based Network Infrastructure

This paper addresses the analysis and the deployment of the network infrastructure based on multiple Unmanned Air Vehicles (UAVs). Despite the unprecedented potential to the mobility of the network infrastructure, there has been no effort to establish a mathematical model of the infrastructure and formation control strategies. We model the generic dynamics of the network infrastructure and derive the network throughput of the infrastructure. Through the parametrization of the model, we extract the generic factors of the network protocols and verify our model through the Network Simulator 3 (ns-3). By exploiting our network analysis model, we propose a novel formation control algorithm that determines the location of the UAVs to maximize the efficiency of the network. To achieve the objectives of the infrastructure, we define the formation-shaping effect as forces and elaborately design them using the generic factors. The formation algorithm continuously approaches to the optimized formation of a fleet of UAVs to enhance the overall throughput of the terrestrial devices. Our evaluations show that the algorithm guarantees remarkably higher throughput than the static formations. Through the dynamic transformation of the UAV formation, we believe that the multi-UAV-based network infrastructure could expand the boundary of the existing infrastructure while reducing the network traffic.

Ontological Tools for the Process Turn in Biology

The purpose of this chapter is to introduce an outline of general process theory (GPT), a non-Whiteheadian systematic process ontology, and to provide some pointers on how this framework could be applied in philosophy of biology to clarify questions of individuality, composition, and emergence. GPT is a mono-categorial framework based on the new category of more or less generic (non-particular) dynamic individuals called ‘general processes’ or ‘dynamics’. According to GPT, the world is the interaction of (more or less generic) dynamics. The chapter sets out some elements of a non-standard mereology (with non-transitive part relations) on processes and introduces the five-dimensional classification system of GPT. It is shown how the theoretical predicates of homeomereity and automereity can be used to distinguish between developments and ‘non-developmental’ or ‘dynamically stable’ temporally unbounded activities that persist in time by literal recurrence.

Equivariant Hopf-Pitchfork Bifurcation of Symmetric Coupled Neural Network with Delay

This paper is concerned with how the symmetry and singularity of a system of differential equations affect generic dynamics and bifurcations. By computation of Hopf-pitchfork point in a two-parameter nonlinear problem satisfying a [Formula: see text]-symmetry condition, the mode interactions in two-parameter bifurcations with a single zero and two pairs of imaginary roots are considered. The codimension two normal form with equivariant Hopf-pitchfork bifurcations are given. Through analyzing the unfolding structure, local classification in the neighborhood of equivariant Hopf-pitchfork bifurcations point for the [Formula: see text]-symmetric is undertaken. A rich variety of dynamical and bifurcation behaviors is pointed out. Beyond a stable fixed point or a pair of stable fixed points, some interesting phenomena are also found, such as the coexistence of two periodic solutions which are verified both theoretically and numerically.