246 research outputs found
Window functions and sigmoidal behaviour of memristive systems
Summary: A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner
Great cities look small
Great cities connect people; failed cities isolate people. Despite the
fundamental importance of physical, face-to-face social-ties in the functioning
of cities, these connectivity networks are not explicitly observed in their
entirety. Attempts at estimating them often rely on unrealistic
over-simplifications such as the assumption of spatial homogeneity. Here we
propose a mathematical model of human interactions in terms of a local strategy
of maximising the number of beneficial connections attainable under the
constraint of limited individual travelling-time budgets. By incorporating
census and openly-available online multi-modal transport data, we are able to
characterise the connectivity of geometrically and topologically complex
cities. Beyond providing a candidate measure of greatness, this model allows
one to quantify and assess the impact of transport developments, population
growth, and other infrastructure and demographic changes on a city. Supported
by validations of GDP and HIV infection rates across United States metropolitan
areas, we illustrate the effect of changes in local and city-wide
connectivities by considering the economic impact of two contemporary inter-
and intra-city transport developments in the United Kingdom: High Speed Rail 2
and London Crossrail. This derivation of the model suggests that the scaling of
different urban indicators with population size has an explicitly mechanistic
origin.Comment: 19 pages, 8 figure
The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions
Copyright @ 2005 American Institute of Physics.We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.This research has been supported by GlaxoSmith-Klin
Community detection and role identification in directed networks: understanding the Twitter network of the care.data debate
With the rise of social media as an important channel for the debate and discussion of public affairs, online social networks such as Twitter have become important platforms for public information and engagement by policy makers. To communicate effectively through Twitter, policy makers need to understand how influence and interest propagate within its network of users. In this chapter we use graph-theoretic methods to analyse the Twitter debate surrounding NHS Englands controversial care.data scheme. Directionality is a crucial feature of the Twitter social graph - information flows from the followed to the followers - but is often ignored in social network analyses; our methods are based on the behaviour of dynamic processes on the network and can be applied naturally to directed networks. We uncover robust communities of users and show that these communities reflect how information flows through the Twitter network. We are also able to classify users by their differing roles in directing the flow of information through the network. Our methods and results will be useful to policy makers who would like to use Twitter effectively as a communication medium
The stability of a graph partition: A dynamics-based framework for community detection
Recent years have seen a surge of interest in the analysis of complex
networks, facilitated by the availability of relational data and the
increasingly powerful computational resources that can be employed for their
analysis. Naturally, the study of real-world systems leads to highly complex
networks and a current challenge is to extract intelligible, simplified
descriptions from the network in terms of relevant subgraphs, which can provide
insight into the structure and function of the overall system.
Sparked by seminal work by Newman and Girvan, an interesting line of research
has been devoted to investigating modular community structure in networks,
revitalising the classic problem of graph partitioning.
However, modular or community structure in networks has notoriously evaded
rigorous definition. The most accepted notion of community is perhaps that of a
group of elements which exhibit a stronger level of interaction within
themselves than with the elements outside the community. This concept has
resulted in a plethora of computational methods and heuristics for community
detection. Nevertheless a firm theoretical understanding of most of these
methods, in terms of how they operate and what they are supposed to detect, is
still lacking to date.
Here, we will develop a dynamical perspective towards community detection
enabling us to define a measure named the stability of a graph partition. It
will be shown that a number of previously ad-hoc defined heuristics for
community detection can be seen as particular cases of our method providing us
with a dynamic reinterpretation of those measures. Our dynamics-based approach
thus serves as a unifying framework to gain a deeper understanding of different
aspects and problems associated with community detection and allows us to
propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte
Stability of graph communities across time scales
The complexity of biological, social and engineering networks makes it
desirable to find natural partitions into communities that can act as
simplified descriptions and provide insight into the structure and function of
the overall system. Although community detection methods abound, there is a
lack of consensus on how to quantify and rank the quality of partitions. We
show here that the quality of a partition can be measured in terms of its
stability, defined in terms of the clustered autocovariance of a Markov process
taking place on the graph. Because the stability has an intrinsic dependence on
time scales of the graph, it allows us to compare and rank partitions at each
time and also to establish the time spans over which partitions are optimal.
Hence the Markov time acts effectively as an intrinsic resolution parameter
that establishes a hierarchy of increasingly coarser clusterings. Within our
framework we can then provide a unifying view of several standard partitioning
measures: modularity and normalized cut size can be interpreted as one-step
time measures, whereas Fiedler's spectral clustering emerges at long times. We
apply our method to characterize the relevance and persistence of partitions
over time for constructive and real networks, including hierarchical graphs and
social networks. We also obtain reduced descriptions for atomic level protein
structures over different time scales.Comment: submitted; updated bibliography from v
- …