23 research outputs found
Flow-Based Network Analysis of the Caenorhabditis elegans Connectome
We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios
Unravelling the forces underlying urban industrial agglomeration
As early as the 1920's Marshall suggested that firms co-locate in cities to reduce the costs of moving goods, people, and ideas. These 'forces of agglomeration' have given rise, for example, to the high tech clusters of San Francisco and Boston, and the automobile cluster in Detroit. Yet, despite its importance for city planners and industrial policy-makers, until recently there has been little success in estimating the relative importance of each Marshallian channel to the location decisions of firms. Here we explore a burgeoning literature that aims to exploit the co-location patterns of industries in cities in order to disentangle the relationship between industry co-agglomeration and customer/supplier, labour and idea sharing. Building on previous approaches that focus on across- and between-industry estimates, we propose a network-based method to estimate the relative importance of each Marshallian channel at a meso scale. Specifically, we use a community detection technique to construct a hierarchical decomposition of the full set of industries into clusters based on co-agglomeration patterns, and show that these industry clusters exhibit distinct patterns in terms of their relative reliance on individual Marshallian channels
Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction
Cellular signal transduction usually involves activation cascades, the
sequential activation of a series of proteins following the reception of an
input signal. Here we study the classic model of weakly activated cascades and
obtain analytical solutions for a variety of inputs. We show that in the
special but important case of optimal-gain cascades (i.e., when the
deactivation rates are identical) the downstream output of the cascade can be
represented exactly as a lumped nonlinear module containing an incomplete gamma
function with real parameters that depend on the rates and length of the
cascade, as well as parameters of the input signal. The expressions obtained
can be applied to the non-identical case when the deactivation rates are random
to capture the variability in the cascade outputs. We also show that cascades
can be rearranged so that blocks with similar rates can be lumped and
represented through our nonlinear modules. Our results can be used both to
represent cascades in computational models of differential equations and to fit
data efficiently, by reducing the number of equations and parameters involved.
In particular, the length of the cascade appears as a real-valued parameter and
can thus be fitted in the same manner as Hill coefficients. Finally, we show
how the obtained nonlinear modules can be used instead of delay differential
equations to model delays in signal transduction.Comment: 18 pages, 7 figure
The topology of a discussion: the #occupy case
We analyse a large sample of the Twitter activity developed around the social
movement 'Occupy Wall Street' to study the complex interactions between the
human communication activity and the semantic content of a discussion. We use a
network approach based on the analysis of the bipartite graph @Users-#Hashtags
and of its projections: the 'semantic network', whose nodes are hashtags, and
the 'users interest network', whose nodes are users In the first instance, we
find out that discussion topics (#hashtags) present a high heterogeneity, with
the distinct role of the communication hubs where most the 'opinion traffic'
passes through. In the second case, the self-organization process of users
activity leads to the emergence of two classes of communicators: the
'professionals' and the 'amateurs'. Moreover the network presents a strong
community structure, based on the differentiation of the semantic topics, and a
high level of structural robustness when a certain set of topics are censored
and/or accounts are removed. Analysing the characteristics the @Users-#Hashtags
network we can distinguish three phases of the discussion about the movement.
Each phase corresponds to specific moment of the movement: from declaration of
intent, organisation and development and the final phase of political
reactions. Each phase is characterised by the presence of specific #hashtags in
the discussion. Keywords: Twitter, Network analysisComment: 13 pages, 9 figure
Squeeze-and-Breathe Evolutionary Monte Carlo Optimisation with Local Search Acceleration and its application to parameter fitting
Motivation: Estimating parameters from data is a key stage of the modelling
process, particularly in biological systems where many parameters need to be
estimated from sparse and noisy data sets. Over the years, a variety of
heuristics have been proposed to solve this complex optimisation problem, with
good results in some cases yet with limitations in the biological setting.
Results: In this work, we develop an algorithm for model parameter fitting
that combines ideas from evolutionary algorithms, sequential Monte Carlo and
direct search optimisation. Our method performs well even when the order of
magnitude and/or the range of the parameters is unknown. The method refines
iteratively a sequence of parameter distributions through local optimisation
combined with partial resampling from a historical prior defined over the
support of all previous iterations. We exemplify our method with biological
models using both simulated and real experimental data and estimate the
parameters efficiently even in the absence of a priori knowledge about the
parameters.Comment: 15 Pages, 3 Figures, 6 Tables; Availability: Matlab code available
from the authors upon reques
Random Walks on Stochastic Temporal Networks
In the study of dynamical processes on networks, there has been intense focus
on network structure -- i.e., the arrangement of edges and their associated
weights -- but the effects of the temporal patterns of edges remains poorly
understood. In this chapter, we develop a mathematical framework for random
walks on temporal networks using an approach that provides a compromise between
abstract but unrealistic models and data-driven but non-mathematical
approaches. To do this, we introduce a stochastic model for temporal networks
in which we summarize the temporal and structural organization of a system
using a matrix of waiting-time distributions. We show that random walks on
stochastic temporal networks can be described exactly by an
integro-differential master equation and derive an analytical expression for
its asymptotic steady state. We also discuss how our work might be useful to
help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki
editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor
corrections and modifications. This chapter is based on arXiv:1112.3324,
which contains additional calculations and numerical simulation
Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study
The last decade has seen an explosion in models that describe phenomena in
systems medicine. Such models are especially useful for studying signaling
pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to
showcase current mathematical and statistical techniques that enable modelers
to gain insight into (models of) gene regulation, and generate testable
predictions. We introduce a range of modeling frameworks, but focus on ordinary
differential equation (ODE) models since they remain the most widely used
approach in systems biology and medicine and continue to offer great potential.
We present methods for the analysis of a single model, comprising applications
of standard dynamical systems approaches such as nondimensionalization, steady
state, asymptotic and sensitivity analysis, and more recent statistical and
algebraic approaches to compare models with data. We present parameter
estimation and model comparison techniques, focusing on Bayesian analysis and
coplanarity via algebraic geometry. Our intention is that this (non exhaustive)
review may serve as a useful starting point for the analysis of models in
systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte
Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction.
Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here, we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal gain cascades (i.e. when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction
Customer mobility and congestion in supermarkets
The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intra-city scales to inter-country scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65–70% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulatedannealing algorithm to find store layouts with lower congestion than a supermarket’s original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales