Showing papers by "Mauricio Barahona published in 2012"

Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit.

Abstract: In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the ‘right’ split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted ‘field-of-view’ limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection [1], [2], in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity. We illustrate our ideas with constructive examples and through the analysis of real-world networks from imaging, protein structures and the power grid, where a multiscale structure of non clique-like communities is revealed.

Combinatorial stresses kill pathogenic Candida species.

Abstract: Pathogenic microbes exist in dynamic niches and have evolved robust adaptive responses to promote survival in their hosts. The major fungal pathogens of humans, Candida albicans and Candida glabrata , are exposed to a range of environmental stresses in their hosts including osmotic, oxidative and nitrosative stresses. Signifi cant efforts have been devoted to the characterization of the adaptive responses to each of these stresses. In the wild, cells are frequently exposed simultaneously to combinations of these stresses and yet the effects of such combinatorial stresses have not been explored. We have developed a common experimental platform to facilitate the comparison of combinatorial stress responses in C. glabrata and C. albicans . This platform is based on the growth of cells in buffered rich medium at 30 ° C, and was used to defi ne relatively low, medium and high doses of osmotic (NaCl), oxidative (H 2 O 2 ) and nitrosative stresses (e.g., dipropylenetriamine (DPTA)-NONOate). The effects of combinatorial stresses were compared with the corresponding individual stresses under these growth conditions. We show for the fi rst time that certain combinations of combinatorial stress are especially potent in terms of their ability to kill C. albicans and C. glabrata and/or inhibit their growth. This was the case for combinations of osmotic plus oxidative stress and for oxidative plus nitrosative stress. We predict that combinatorial stresses may be highly signifi cant in host defences against these pathogenic yeasts.

Encoding dynamics for multiscale community detection: Markov time sweeping for the map equation.

Abstract: The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the map equation formalism [Rosvall and Bergstrom, Proc. Natl. Acad. Sci. USA 105, 1118 (2008)] through an information-theoretic description of the process of coding inter- and intracommunity transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original map coding scheme, which is both block-averaged and one-step, neglects the internal structure of the communities and introduces an upper scale, the ``field-of-view'' limit, in the communities it can detect. As a consequence, map is well tuned to detect clique-like communities but can lead to undesirable overpartitioning when communities are far from clique-like. We show that a signature of this behavior is a large compression gap: The map description length is far from its ideal limit. To address this issue, we propose a simple dynamic approach that introduces time explicitly into the map coding through the analysis of the weighted adjacency matrix of the time-dependent multistep transition matrix of the Markov process. The resulting Markov time sweeping induces a dynamical zooming across scales that can reveal (potentially multiscale) community structure above the field-of-view limit, with the relevant partitions indicated by a small compression gap.

Engineering and ethical perspectives in synthetic biology. Rigorous, robust and predictable designs, public engagement and a modern ethical framework are vital to the continued success of synthetic biology

Abstract: The applications of synthetic biology will involve the release of artificial life forms into the environment. These organisms will present unique safety challenges that need to be addressed by researchers and regulators to win public engagement and support.

Robustness of random graphs based on graph spectra.

Abstract: It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Renyi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.

Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells

Abstract: Background Stomata are tiny pores in plant leaves that regulate gas and water exchange between the plant and its environment. Abscisic acid and ethylene are two well-known elicitors of stomatal closure when acting independently. However, when stomata are presented with a combination of both signals, they fail to close.

Quantitative measure of hysteresis for memristors through explicit dynamics

Abstract: We introduce a mathematical framework for the analysis of the inputoutput dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli d...

Device Properties of Bernoulli Memristors

Abstract: This paper explains why charge- and flux-controlled memristor dynamics comply with Bernoulli's nonlinear differential equation. These devices are termed Bernoulli memristors. Based on the fact that their identified nonlinear dynamics can always be treated in a linearized manner, a general mathematical framework suitable for the systematic study of individual or networks of Bernoulli memristors can be developed. The paper details the novel mathematical framework and showcases its usefulness: 1) by applying it to obtain a closed-form expression of the output as an explicit function of the input for an example memristor model whose dynamics are described by a power law; 2) by determining analytically the harmonic content of the output of a Bernoulli memristor driven by a sinewave; 3) by investigating systematically the dynamics of networks of Bernoulli memristors connected either in series or in parallel; and 4) by assessing qualitatively the impact of series parasitic ohmic resistance on the dynamics of an ideal memristor.

Sensory experience modifies spontaneous state dynamics in a large-scale barrel cortical model

Abstract: Experimental evidence suggests that spontaneous neuronal activity may shape and be shaped by sensory experience. However, we lack information on how sensory experience modulates the underlying synaptic dynamics and how such modulation influences the response of the network to future events. Here we study whether spike-timing-dependent plasticity (STDP) can mediate sensory-induced modifications in the spontaneous dynamics of a new large-scale model of layers II, III and IV of the rodent barrel cortex. Our model incorporates significant physiological detail, including the types of neurons present, the probabilities and delays of connections, and the STDP profiles at each excitatory synapse. We stimulated the neuronal network with a protocol of repeated sensory inputs resembling those generated by the protraction-retraction motion of whiskers when rodents explore their environment, and studied the changes in network dynamics. By applying dimensionality reduction techniques to the synaptic weight space, we show that the initial spontaneous state is modified by each repetition of the stimulus and that this reverberation of the sensory experience induces long-term, structured modifications in the synaptic weight space. The post-stimulus spontaneous state encodes a memory of the stimulus presented, since a different dynamical response is observed when the network is presented with shuffled stimuli. These results suggest that repeated exposure to the same sensory experience could induce long-term circuitry modifications via `Hebbian' STDP plasticity.

Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting

Abstract: 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 datasets. Over the years, a variety of heuristics have been proposed to solve this complex optimization problem, with good results in some cases yet with limitations in the biological setting. In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimization. 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 optimization 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.

Stochastic Oscillatory Dynamics of Generalized Repressilators

Abstract: We explore the impact of low copy number noise on the onset and quality of oscillations in the generalized repressilator model with odd-number of elements. In our previous work [Strelkowa & Barahona, 2011] we applied deterministic complexity analysis and provided analytical conditions for the emergence of stable limit cycles via Hopf Bifurcations in odd-numbered rings. Here, we extend this analysis to the stochastic description of the model and study the influence of a biochemical design 'knob' - the gene copy number - on the onset and quality of the oscillations. The gene copy number simultaneously affects two parameters that are usually considered independently in mathematical analyses of this model: namely, the system size Ω and the deterministic bifurcation parameter c1. Here we study the dynamic properties on the (Ω,c1)-plane and characterize how the oscillation characteristics depend on both parameters. The (Ω,c1)-plane can thus provide a useful perspective for the design and control of engineered s...

Device Properties of Bernoulli Memristors This paper explains why memristor dynamics comply with Bernoulli's equation; the mathematical framework and its usefulness are discussed.

Abstract: This paper explains why charge- and flux- controlled memristor dynamics comply with Bernoulli's non- linear differential equation. These devices are termed Bernoulli memristors. Based on the fact that their identified nonlinear dynamics can always be treated in a linearized manner, a general mathematical framework suitable for the systematic study of individual or networks of Bernoulli memristors can be developed. The paper details the novel mathematical frame- work and showcases its usefulness: 1) by applying it to obtain a closed-form expression of the output as an explicit function of the input for an example memristor model whose dynamics are described by a power law; 2) by determining analytically the harmonic content of the output of a Bernoulli memristor driven by a sinewave; 3) by investigating systematically the dynamics of networks of Bernoulli memristors connected either in series or in parallel; and 4) by assessing qualitatively the impact of series parasitic ohmic resistance on the dynamics of an ideal memristor.