A Matter of Time - Intrinsic or Extrinsic - for Diffusion in Evolving Complex Networks

International audienceDiffusion phenomena occur in many kinds of real-world complex networks, e.g., biological, information or social networks. Because of this diversity, several types of diffusion models have been proposed in the literature: epidemiological models, threshold models, innovation adoption models, among others. Many studies aim at investigating diffusion as an evolving phenomenon but mostly occurring on static networks, and much remains to be done to understand diffusion on evolving networks. In order to study the impact of graph dynamics on diffusion, we propose in this paper an innovative approach based on a notion of intrinsic time, where the time unit corresponds to the appearance of a new link in the graph. This original notion of time allows us to isolate somehow the diffusion phenomenon from the evolution of the network. The objective is to compare the diffusion features observed with this intrinsic time concept from those obtained with traditional (extrinsic) time, based on seconds. The comparison of these time concepts is easily understandable yet completely new in the study of diffusion phenomena. We experiment our approach on synthetic graphs, as well as on a dataset extracted from the Github sofware sharing platform

Extrinsic local regression on manifold-valued data

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach

Memory effects in biochemical networks as the natural counterpart of extrinsic noise

We show that in the generic situation where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger "bulk" network, the presence of the bulk causes not just extrinsic noise but also memory effects. This means that the dynamics of the subnetwork will depend not only on its present state, but also its past. We use projection techniques to get explicit expressions for the memory functions that encode such memory effects, for generic protein interaction networks involving binary and unary reactions such as complex formation and phosphorylation, respectively. Remarkably, in the limit of low intrinsic copy-number noise such expressions can be obtained even for nonlinear dependences on the past. We illustrate the method with examples from a protein interaction network around epidermal growth factor receptor (EGFR), which is relevant to cancer signalling. These examples demonstrate that inclusion of memory terms is not only important conceptually but also leads to substantially higher quantitative accuracy in the predicted subnetwork dynamics

Structural and functional largescale brain network dynamics: Examples from mental disorders

Hjernen er organisert i ulike funksjonelle og strukturelle nettverk. Til tross for omfattende forskning, er fremdeles ikke funksjonen og dynamikken i slike nettverk godt forstått. En økt innsikt kan være avgjørende for å forstå symptomer, og mekanismene som kontrollerer disse, hos pasienter med psykiske lidelser som schizofreni. Avhandlingen omfatter tre studier som hver adresserer ulike delmål i forskningen. Den første studien undersøker endringer i strukturelle nettverk hos en gruppe pasienter med schizofreni. Studien viser på gruppenivå at det er dels utbredte strukturelle forskjeller i hvit substans hos pasienter med schizofreni som opplever hørselshallusinasjoner sammenlignet med pasienter som ikke opplever disse hallusinasjonen. For å undersøke mulig samsvarende funksjonelle endringer har det vært behov for først å utvikle en ny tilnærming for å måle forskjeller i dynamikken mellom hjernens nettverk i hvile (DMN) og i aktiv oppgaveløsing av krevende kognitive oppgaver (EMN) hos en gruppe friske frivillige deltakere. I korte trekk, ble tre ulike visuelle, kognitive oppgaver presentert for deltakerne gjennom et fMRI blokk design. Resultatene i studien viste en antikorrelasjon i tid i områder som er involvert i henholdsvis hvile (DMN) og aktiv tilstand (EMN). For å gjøre undersøkelser hos pasienter med psykiske lidelser mindre tidkrevende, beskrives i avhandlingen også en studie som undersøker om hvileområder i hjernen (DMN) som er aktivert nettopp som del av en fMRI blokk design studier overlapper med en tilleggsundersøkelse med femminutters kontinuerlig hvile («resting state»). Sammenligningen er også interessant fra et mer basalforskningsperspektiv fordi en rask endring mellom aktiv tilstand og hvile kanskje bedre reflekterer en realistisk hviletilstand enn den kontinuerlige undersøkelsen som i dag representerer «gullstandarden» i denne type forskning. Resultatene fra studien viste stor grad av overlapp mellom aktiverte områder og at den foreslåtte tilnærmingen dermed kan ha et stort potensial i videre undersøkelser. I sum beskriver forskningen i avhandlingen muligheter for å undersøke strukturelle og funksjonelle nettverk hos pasienter med psykiske lidelser. Avhandlingen viser første resultater hos pasienter med schizofreni som strukturelle forskjeller i hvit substans mellom pasientgrupper avhengig om de opplever hørselshallusinasjoner eller ikke. Slike undersøkelser kan og bør komplementeres med undersøkelser av funksjonelle nettverk slik som foreslått i de andre studiene i avhandlingen, og i sum bidra til et godt rammeverk for videre undersøkelser hos pasienter.The human brain is organized in various networks both functionally and structurally. However, despite the extensive research on brain connectivity, which was made possible due to the development of in vivo brain imaging techniques, the neuroscientific field is still far from fully comprehending networks function and dynamics. Detailed knowledge about the relationship between various brain networks is essential for understanding the function of the healthy brain. However, many studies on mental disorders such as schizophrenia suggest that it might be caused by abnormal brain network functioning and structural aberrations. Therefore, the knowledge of the brain network's dynamics and structure might be critical for revealing the underpinnings of mental disorders such as schizophrenia. The presented thesis had three main goals, resulting in three structural and functional imaging studies. Firstly, the brain's structural connectivity affected by schizophrenia has been investigated to determine the nature and extent of its changes. Hence, Diffusion Tensor Imaging (DTI) and tract-based spatial statistics (TBSS) were employed to explore white matter differences between subtypes of schizophrenia patients compared to healthy controls. This study revealed widespread FA-value reduction in the hallucinating schizophrenia subjects' white matter compared to non-hallucinating ones. Since widespread aberrations of the white matter should affect the function of the large-scale brain networks, the second goal was to explore the two main functional brain networks, Default Mode Network (DMN) and Extrinsic Mode Network (EMN). This is because dysfunction of DMN and EMN networks has been previously suggested to be significant for the generation of symptoms of schizophrenia disorder, such as Auditory Verbal Hallucinations (AVH). Since the concept of EMN is relatively new and not yet deeply explored, and additionally protocol used in that study has not been previously utilized to study EMN and DMN, it was first necessary to test the design in a group of healthy participants. This study used the novel protocol based on the classic block design fMRI experiment with three different visual tasks: mental rotation, working memory, and mental arithmetic. The results of study II proved the existence of the EMN that is anti-correlated with the DMN and is domain-general. Lastly, the neuroimaging studies of the participants suffering from mental disorders such as schizophrenia require relatively short and effective examination protocols. Therefore, the last project investigated both similarities and differences in DMN activity between two experimental designs: block design and resign state. A classic block design experiment would be a good candidate for the investigation reflecting the fluctuating activity of the brain during typical daily activity. The results of Study III showed that the activity of the DMN was generally similar in the two experiments, though with some discrepancies. These differences were in the DMN architecture itself and concerning the relations of the DMN with other brain networks. These findings, in combination with the results of study number two suggest that the block design experiment could be the most effective for studying the function of the brain in schizophrenia. The studies incorporated in that thesis add to the current findings on the white matter alterations in schizophrenia disorder and contribute to a better understanding of the function and dynamics of the large-scale brain networks: EMN and DMN. Last but not least, the performed studies give a good background for future clinical studies on schizophrenia disorder.Doktorgradsavhandlin

Synchronization of stochastic hybrid oscillators driven by a common switching environment

Many systems in biology, physics and chemistry can be modeled through ordinary differential equations, which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper we suppose that this limit ODE supports a stable limit cycle. We demonstrate that a set of such oscillators can synchronize when they are uncoupled, but they share the same switching Markov jump process. The latter is taken to represent the effect of a common randomly switching environment. We determine the leading order of the Lyapunov coefficient governing the rate of decay of the phase difference in the fast switching limit. The analysis bears some similarities to the classical analysis of synchronization of stochastic oscillators subject to common white noise. However the discrete nature of the Markov jump process raises some difficulties: in fact we find that the Lyapunov coefficient from the quasi-steady-state approximation differs from the Lyapunov coefficient one obtains from a second order perturbation expansion in the waiting time between jumps. Finally, we demonstrate synchronization numerically in the radial isochron clock model and show that the latter Lyapinov exponent is more accurate

Unravelling early endovascular skill acquisition:Using psychometric predictors and multimodal magnetic resonance imaging

The structure of the brain changes as a result of learning to perform a new medical procedure In this research project, we studied what happens in the brain when medical students acquire the skills needed to perform a procedure called endovascular intervention (EI). Endovascular interventions are used to treat vascular disease, the most well-known application area is the treatment of a narrowed coronary artery. What makes learning how to perform such a procedure quite difficult is that, as opposed to open surgery, an EI is conducted via a small skin incision under x-ray guidance. As a result, there is neither direct access to nor direct sight onto the treatment site. Although these procedures are widely used, it is not clear how to best train residents to perform EIs safely. Therefore, we investigated the development of the skills needed to conduct an EI on a behavioural and brain level and tested whether pre-existing abilities influence the learning process. We trained medical students to perform an EI on a medical simulator and conducted non-invasive magnetic resonance imaging (MRI) scans to assess their brain structure before and after training. Before training, participants completed cognitive and fine-motor ability tests. We found that participants who scored higher on a test that measured mental rotation ability improved more rapidly during endovascular training. Intriguingly, our MRI data showed that the brain of participants who trained this medical skill adapted to the new demands: the volume of grey matter in the intraparietal sulcus- a brain structure crucial for hand-eye coordination- had increased in comparison to a control group. Our results identified the brain regions involved and the crucial sub-skills that are necessary to perform EIs and thus may have important implications for training endovascular interventions

Perfect Sampling of the Master Equation for Gene Regulatory Networks

We present a Perfect Sampling algorithm that can be applied to the Master Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo methods and combines it with the Dominated Coupling From The Past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for GRNs have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system, and the repressilator, a six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa

Dynamics and the Emergence of Geometry in an Information Mesh

The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a spacetime that possesses properties that would be desirable at the continuum limit, and the question of how to model matter and its dynamics has not been directly addressed. Recent advances in network science have yielded new approaches to the mechanism by which spacetime can emerge as the ground state of a simple Hamiltonian, based upon a multi-dimensional Ising model with one dimensionless coupling constant. Extensions to this model have been proposed that improve the ground state geometry, but they require additional coupling constants. In this paper we conduct an extensive exploration of the graph properties of the ground states of these models, and a simplification requiring only one coupling constant. We demonstrate that the simplification is effective at producing an acceptable ground state. Moreover we propose a scheme for the inclusion of matter and dynamics as excitations above the ground state of the simplified Hamiltonian. Intriguingly, enforcing locality has the consequence of reproducing the free non-relativistic dynamics of a quantum particle