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• Journal article
Evans TS, Calmon L, Vasiliauskaite V,

### Longest Path in the Price Model

, Scientific Reports, ISSN: 2045-2322

The Price model, the directed version of the Barab\'{a}si-Albert model,produces a growing directed acyclic graph. We look at variants of the model inwhich directed edges are added to the new vertex in one of two ways: usingcumulative advantage (preferential attachment) choosing vertices in proportionto their degree, or with random attachment in which vertices are chosenuniformly at random. In such networks, the longest path is well defined and insome cases is known to be a better approximation to geodesics than the shortestpath. We define a reverse greedy path and show both analytically andnumerically that this scales with the logarithm of the size of the network witha coefficient given by the number of edges added using random attachment. Thisis a lower bound on the length of the longest path to any given vertex and weshow numerically that the longest path also scales with the logarithm of thesize of the network but with a larger coefficient that has some weak dependenceon the parameters of the model.

• Journal article
Falkenberg M, Lee J-H, Amano S-I, Ogawa K-I, Yano K, Miyake Y, Evans TS, Christensen Ket al., 2020,

### Identifying time dependence in network growth

, Physical Review & Research International, Vol: 2, Pages: 023352 – 1-023352 – 17, ISSN: 2231-1815

Identifying power-law scaling in real networks—indicative of preferential attachment—has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution when looking for preferential attachment. However, many of the established methods do not account for any potential time dependence in the attachment kernels of growing networks, or methods assume that node degree is the key observable determining network evolution. In this paper, we argue that these assumptions may lead to misleading conclusions about the evolution of growing networks. We illustrate this by introducing a simple adaptation of the Barabási-Albert model, the “k2 model,” where new nodes attach to nodes in the existing network in proportion to the number of nodes one or two steps from the target node. The k2 model results in time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment, and without the need to include explicit time dependence in key network parameters (such as the average out-degree). We show that similar effects are seen in several real world networks where constant network growth rules do not describe their evolution. This implies that measurements of specific degree distributions in real networks are likely to change over time.

• Journal article
Ciacci A, Falkenberg M, Manani KA, Evans TS, Peters NS, Christensen Ket al., 2020,

### Understanding the transition from paroxysmal to persistent atrial fibrillation

, Physical Review Research, Vol: 2, Pages: 023311-023311

Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterisedby the chaotic motion of electrical wavefronts in the atria. In clinicalpractice, AF is classified under two primary categories: paroxysmal AF, shortintermittent episodes separated by periods of normal electrical activity, andpersistent AF, longer uninterrupted episodes of chaotic electrical activity.However, the precise reasons why AF in a given patient is paroxysmal orpersistent is poorly understood. Recently, we have introduced the percolationbased Christensen-Manani-Peters (CMP) model of AF which naturally exhibits bothparoxysmal and persistent AF, but precisely how these differences emerge in themodel is unclear. In this paper, we dissect the CMP model to identify the causeof these different AF classifications. Starting from a mean-field model wherewe describe AF as a simple birth-death process, we add layers of complexity tothe model and show that persistent AF arises from the formation of temporallystable structural re-entrant circuits that form from the interaction ofwavefront collisions during paroxysmal AF. These results are compatible withrecent findings suggesting that the formation of re-entrant drivers in fibroticborder zones perpetuates persistent AF.

• Journal article
Evans TS, Calmon L, Vasiliauskaite V,

### The longest path in the price model

, Scientific Reports, ISSN: 2045-2322

The Price model, the directed version of the Barabasi-Albert model, produces a growing directed acyclic graph. We look at ´variants of the model in which directed edges are added to the new vertex in one of two ways: using cumulative advantage(preferential attachment) choosing vertices in proportion to their degree, or with random attachment in which vertices arechosen uniformly at random. In such networks, the longest path is well defined and in some cases is known to be a betterapproximation to geodesics than the shortest path. We define a reverse greedy path and show both analytically and numericallythat this scales with the logarithm of the size of the network with a coefficient given by the number of edges added usingrandom attachment. This is a lower bound on the length of the longest path to any given vertex and we show numerically thatthe longest path also scales with the logarithm of the size of the network but with a larger coefficient that has some weakdependence on the parameters of the model.

• Journal article
Vasiliauskaite V, Evans TS, 2020,

### Making communities show respect for order

, Applied Network Science, Vol: 5, Pages: 1-24, ISSN: 2364-8228

In this work we give a community detection algorithm in which the communities both respects the intrinsic order of a directed acyclic graph and also finds similar nodes. We take inspiration from classic similarity measures of bibliometrics, used to assess how similar two publications are, based on their relative citation patterns. We study the algorithm’s performance and antichain properties in artificial models and in real networks, such as citation graphs and food webs. We show how well this partitioning algorithm distinguishes and groups together nodes of the same origin (in a citation network, the origin is a topic or a research field). We make the comparison between our partitioning algorithm and standard hierarchical layering tools as well as community detection methods. We show that our algorithm produces different communities from standard layering algorithms.

• Journal article
Cofré R, Videla L, Rosas F, 2019,

### An introduction to the non-equilibrium steady states of maximum entropy spike trains

, Entropy, Vol: 21, Pages: 1-28, ISSN: 1099-4300

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the literature of non-equilibrium statistical mechanics. This tutorial provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics.

• Journal article
Rosas FE, Mediano PAM, Gastpar M, Jensen HJet al., 2019,

### Quantifying high-order interdependencies via multivariate extensions of the mutual information

, Physical Review E, Vol: 100, ISSN: 2470-0045

This paper introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannon's mutual information, and introduces the O-information as a metric that is capable of characterizing synergy- and redundancy-dominated systems. The O-information is a symmetric quantity, and can assess intrinsic properties of a system without dividing its parts into “predictors” and “targets.” We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we present an exploration on the relevance of statistical synergy in Baroque music scores.

• Journal article
Yao Q, Evans TS, Christensen K, Evans TS, Plato ADKet al., 2019,

### How the network properties of shareholders vary with investor type and country

, PLoS One, Vol: 14, Pages: 1-19, ISSN: 1932-6203

We construct two examples of shareholder networks in which shareholders are connected if they have shares in the same company. We do this for the shareholders in Turkish companies and we compare this against the network formed from the shareholdings in Dutch companies. We analyse the properties of these two networks in terms of the different types of shareholder. We create a suitable randomised version of these networks to enable us to find significant features in our networks. For that we find the roles played by different types of shareholder in these networks, and also show how these roles differ in the two countries we study.

• Journal article
Azari MM, Rosas F, Pollin S, 2019,

### Cellular connectivity for UAVs: Network modeling, performance analysis, and design guidelines

, IEEE Transactions on Wireless Communications, Vol: 18, Pages: 3366-3381, ISSN: 1536-1276

The growing use of aerial user equipments (UEs) in various applications requires ubiquitous and reliable connectivity for safe control and data exchange between these devices and ground stations. Key questions that need to be addressed when planning the deployment of aerial UEs are whether the cellular network is a suitable candidate for enabling such connectivity and how the inclusion of aerial UEs might impact the overall network efficiency. This paper provides an in-depth analysis of user and network-level performance of a cellular network that serves both unmanned aerial vehicles (UAVs) and ground users in the downlink. Our results show that the favorable propagation conditions that UAVs enjoy due to their height often backfire on them, as the increased load-dependent co-channel interference received from neighboring ground base stations (BSs) is not compensated by the improved signal strength. When compared with a ground user in an urban area, our analysis shows that a UAV flying at 100 m can experience a throughput decrease of a factor 10 and a coverage drop from 76% to 30%. Motivated by these findings, we develop UAV and network-based solutions to enable an adequate integration of UAVs into cellular networks. In particular, we show that an optimal tilting of the UAV antenna can increase the coverage from 23% to 89% and throughput from 3.5 to 5.8 b/s/Hz, outperforming ground UEs. Furthermore, our findings reveal that depending on the UAV altitude and its antenna configuration, the aerial user performance can scale with respect to the network density better than that of a ground user. Finally, our results show that network densification and the use of microcells limit the UAV performance. Although UAV usage has the potential to increase the area spectral efficiency (ASE) of cellular networks with a moderate number of cells, they might hamper the development of future ultradense networks.

• Journal article
Vasiliauskaite V, Evans TS, 2019,

### Social success of perfumes

, PLoS ONE, Vol: 14, ISSN: 1932-6203

We study data on perfumes and their odour descriptors-notes-to understand how note compositions, called accords, influence successful fragrance formulas. We obtain accords which tend to be present in perfumes that receive significantly more customer ratings. Our findings show that the most popular notes and the most over-represented accords are different to those that have the strongest effect to the perfume ratings. We also used network centrality to understand which notes have the highest potential to enhance note compositions. We find that large degree notes, such as musk and vanilla as well as generically-named notes, e.g. floral notes, are amongst the notes that enhance accords the most. This work presents a framework which would be a timely tool for perfumers to explore a multidimensional space of scent compositions.

• Journal article
Rosas De Andraca FE, Faggian M, Ginelli F, Levnajic Zet al.,

### Synchronization in time-varying random networks with vanishing connectivity

, Scientific Reports, ISSN: 2045-2322

A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite forthe emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phaseoscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly,an extremely low instantaneous connectivity. We show that with strong coupling and sufficiently fast rewiring the networkreaches partial synchronization even in the vanishing connectivity limit. In particular, we provide an approximate analyticalargument, based on the comparison between the different characteristic timescales of our system in the low connectivityregime, which is able to predict the transition to synchronization threshold with satisfactory precision beyond the formal fastrewiring limit. We interpret our results as a qualitative mechanism for emergence of consensus in social communities. Inparticular, our result suggest that groups of individuals are capable of aligning their opinions under extremely sparse exchangesof views, which is reminiscent of fast communications that take place in the modern social media. Our results may also berelevant to characterize the onset of collective behavior in engineered systems of mobile units with limited wireless capabilities

• Journal article
Patel VM, Panzarasa P, Ashrafian H, Evans TS, Kirresh A, Sevdalis N, Darzi A, Athanasiou Tet al., 2019,

### Collaborative patterns, authorship practices and scientific success in biomedical research: a network analysis.

, Journal of the Royal Society of Medicine, Vol: 112, Pages: 245-257, ISSN: 1758-1095

OBJECTIVE: To investigate the relationship between biomedical researchers' collaborative and authorship practices and scientific success. DESIGN: Longitudinal quantitative analysis of individual researchers' careers over a nine-year period. SETTING: A leading biomedical research institution in the United Kingdom. PARTICIPANTS: Five hundred and twenty-five biomedical researchers who were in employment on 31 December 2009. MAIN OUTCOME MEASURES: We constructed the co-authorship network in which nodes are the researchers, and links are established between any two researchers if they co-authored one or more articles. For each researcher, we recorded the position held in the co-authorship network and in the bylines of all articles published in each three-year interval and calculated the number of citations these articles accrued until January 2013. We estimated maximum likelihood negative binomial panel regression models. RESULTS: Our analysis suggests that collaboration sustained success, yet excessive co-authorship did not. Last positions in non-alphabetised bylines were beneficial for higher academic ranks but not for junior ones. A professor could witness a 20.57% increase in the expected citation count if last-listed non-alphabetically in one additional publication; yet, a lecturer suffered from a 13.04% reduction. First positions in alphabetised bylines were positively associated with performance for junior academics only. A lecturer could experience a 8.78% increase in the expected citation count if first-listed alphabetically in one additional publication. While junior researchers amplified success when brokering among otherwise disconnected collaborators, senior researchers prospered from socially cohesive networks, rich in third-party relationships. CONCLUSIONS: These results help biomedical scientists shape successful careers and research institutions develop effective assessment and recruitment policies that will ultimately sustain the quality of biomedical r

• Journal article
Duarte D, Amarteifio S, Ang H, Kong IY, Ruivo N, Pruessner G, Hawkins ED, Lo Celso Cet al., 2019,

### Defining the in vivo characteristics of acute myeloid leukemia cells behavior by intravital imaging

, Immunology and Cell Biology, Vol: 97, Pages: 229-235, ISSN: 1440-1711

The majority of acute myeloid leukemia (AML) patients have a poor response to conventional chemotherapy. The survival of chemoresistant cells is thought to depend on leukemia-bone marrow (BM) microenvironment interactions, which are not well understood. The CXCL12/CXCR4 axis has been proposed to support AML growth but was not studied at the single AML cell level. We recently showed that T-cell acute lymphoblastic leukemia (T-ALL) cells are highly motile in the BM; however, the characteristics of AML cell migration within the BM remain undefined. Here, we characterize the in vivo migratory behavior of AML cells and their response to chemotherapy and CXCR4 antagonism, using high-resolution 2-photon and confocal intravital microscopy of mouse calvarium BM and the well-established MLL-AF9-driven AML mouse model. We used the Notch1-driven T-ALL model as a benchmark comparison and AMD3100 for CXCR4 antagonism experiments. We show that AML cells are migratory, and in contrast with T-ALL, chemoresistant AML cells become less motile. Moreover, and in contrast with T-ALL, the in vivo exploratory behavior of expanding and chemoresistant AML cells is unaffected by AMD3100. These results expand our understanding of AML cells-BM microenvironment interactions, highlighting unique traits of leukemia of different lineages.

• Conference paper
Rassouli B, Rosas F, Gunduz D, 2019,

### Latent Feature Disclosure under Perfect Sample Privacy

, 10th IEEE International Workshop on Information Forensics and Security (WIFS), Publisher: IEEE, ISSN: 2157-4766
• Journal article
Garcia Millan R, Pausch J, Walter B, Pruessner Get al., 2018,

### Field-theoretic approach to the universality of branching processes

, Physical Review E, Vol: 98, ISSN: 1539-3755

Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival probability, expected avalanche duration, the so-called avalanche shape, the n-point correlation function, and the probability density function of the total avalanche size. Previous studies have shown universality in certain observables of branching processes using probabilistic arguments; however, a comprehensive description is lacking. We derive the field theory that describes the process and demonstrate how to use it to calculate the relevant observables and their scaling to leading order in time, revealing the universality of the moments of the population size. Our results explain why the first and second moment of the offspring distribution are sufficient to fully characterize the process in the vicinity of criticality, regardless of the underlying offspring distribution. This finding implies that branching processes are universal. We illustrate our analytical results with computer simulations.

• Journal article
Rosas De Andraca F, Chen K-C, Gunduz D, 2018,

### Social learning for resilient data fusion against data falsification attacks

, Computational Social Networks, Vol: 5, ISSN: 2197-4314

BackgroundInternet of Things (IoT) suffers from vulnerable sensor nodes, which are likely to endure data falsification attacks following physical or cyber capture. Moreover, centralized decision-making and data fusion turn decision points into single points of failure, which are likely to be exploited by smart attackers.MethodsTo tackle this serious security threat, we propose a novel scheme for enabling distributed decision-making and data aggregation through the whole network. Sensor nodes in our scheme act following social learning principles, resembling agents within a social network.ResultsWe analytically examine under which conditions local actions of individual agents can propagate through the network, clarifying the effect of Byzantine nodes that inject false information. Moreover, we show how our proposed algorithm can guarantee high network performance, even for cases when a significant portion of the nodes have been compromised by an adversary.ConclusionsOur results suggest that social learning principles are well suited for designing robust IoT sensor networks and enabling resilience against data falsification attacks.

• Journal article
Jensen H, Tempesta P, 2018,

### Group entropies: from phase space geometry to entropy functionals via group theory

, Entropy, Vol: 20, ISSN: 1099-4300

The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective.

• Journal article
Rosas De Andraca FE, Martinez Mediano P, Ugarte M, Jensen Het al., 2018,

### An information-theoretic approach to self-organisation: Emergence of complex interdependencies in coupled dynamical systems

, Entropy, Vol: 20, ISSN: 1099-4300

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.

• Journal article
Sahasranaman A, Jensen HJ, 2018,

### Ethnicity and wealth: the dynamics of dual segregation

, PLoS ONE, Vol: 13, ISSN: 1932-6203

Creating inclusive cities requires meaningful responses to inequality and segregation. We build an agent-based model of interactions between wealth and ethnicity of agents to investigate ‘dual’ segregations—due to ethnicity and due to wealth. As agents are initially allowed to move into neighbourhoods they cannot afford, we find a regime where there is marginal increase in both wealth segregation and ethnic segregation. However, as more agents are progressively allowed entry into unaffordable neighbourhoods, we find that both wealth and ethnic segregations undergo sharp, non-linear transformations, but in opposite directions—wealth segregation shows a dramatic decline, while ethnic segregation an equally sharp upsurge. We argue that the decrease in wealth segregation does not merely accompany, but actually drives the increase in ethnic segregation. Essentially, as agents are progressively allowed into neighbourhoods in contravention of affordability, they create wealth configurations that enable a sharp decline in wealth segregation, which at the same time allow co-ethnics to spatially congregate despite differences in wealth, resulting in the abrupt worsening of ethnic segregation.

• Journal article
Dolan D, Jensen H, Martinez Mediano P, Molina-Solana MJ, Rajpal H, Rosas De Andraca F, Sloboda JAet al., 2018,

### The improvisational state of mind: a multidisciplinary study of an improvisatory approach to classical music repertoire performance

, Frontiers in Psychology, Vol: 9, ISSN: 1664-1078

The recent re-introduction of improvisation as a professional practice within classical music, however cautious and still rare, allows direct and detailed contemporary comparison between improvised and “standard” approaches to performances of the same composition, comparisons which hitherto could only be inferred from impressionistic historical accounts. This study takes an interdisciplinary multi-method approach to discovering the contrasting nature and effects of prepared and improvised approaches during live chamber-music concert performances of a movement from Franz Schubert’s “Shepherd on the Rock”, given by a professional trio consisting of voice, flute, and piano, in the presence of an invited audience of 22 adults with varying levels of musical experience and training. The improvised performances were found to be differ systematically from prepared performances in their timing, dynamic, and timbral features as well as in the degree of risk-taking and “mind reading” between performers including during moments of added extemporised notes. Post-performance critical reflection by the performers characterised distinct mental states underlying the two modes of performance. The amount of overall body movements was reduced in the improvised performances, which showed less unco-ordinated movements between performers when compared to the prepared performance. Audience members, who were told only that the two performances would be different, but not how, rated the improvised version as more emotionally compelling and musically convincing than the prepared version. The size of this effect was not affected by whether or not the audience could see the performers, or by levels of musical training. EEG measurements from 19 scalp locations showed higher levels of Lempel-Ziv complexity (associated with awareness and alertness) in the improvised version in both performers and audience. Results are discussed in terms of their potential

• Journal article
Jensen HJ, Pazuki RH, Pruessner G, Tempesta Pet al., 2018,

### Statistical mechanics of exploding phase spaces: ontic open systems

, Journal of Physics A: Mathematical and Theoretical, Vol: 51, ISSN: 1751-8113

The volume of phase space may grow super-exponentially ('explosively') with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.

• Journal article
Palmieri L, Jensen HJ, 2018,

### The emergence of weak criticality in SOC systems

, EPL, Vol: 123, ISSN: 0295-5075

Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self-organisation and the criticality have remained controversial. Besides, SOC-like dynamics has recently been observed in many natural processes like brain activity and rain precipitations, making a better understanding of such systems more urgent. Here we focus on the Drossel-Schwabl forest-fire model (FFM) of SOC and show that despite the model is not critical, it nevertheless exhibits a behaviour that justifies the introduction of a new kind of weak criticality. We present a method that allows to quantify the degree of criticality of a system and to introduce a new class of critical systems. This method can be easily adapted to experimental settings and contribute to a better understanding of real systems.

• Journal article
Cofré R, Maldonado C, Rosas De Andraca F, 2018,

### Large deviations properties of maximum entropy Markov chains from spike trains

, Entropy, Vol: 20, ISSN: 1099-4300

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. To find the maximum entropy Markov chain, we use the thermodynamic formalism, which provides insightful connections with statistical physics and thermodynamics from which large deviations properties arise naturally. We provide an accessible introduction to the maximum entropy Markov chain inference problem and large deviations theory to the community of computational neuroscience, avoiding some technicalities while preserving the core ideas and intuitions. We review large deviations techniques useful in spike train statistics to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability, and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

• Journal article
Goto H, Viegas E, Jensen HJ, Takayasu H, Takayasu Met al., 2018,

### Smoluchowski equation for networks: merger induced intermittent giant node formation and degree gap

, Journal of Statistical Physics, Vol: 172, Pages: 1086-1100, ISSN: 1572-9613

The dynamical phase diagram of a network undergoing annihilation, creation, and coagulation of nodes is found to exhibit two regimes controlled by the combined effect of preferential attachment for initiator and target nodes during coagulation and for link assignment to new nodes. The first regime exhibits smooth dynamics and power law degree distributions. In the second regime, giant degree nodes and gaps in the degree distribution are formed intermittently. Data for the Japanese firm network in 1994 and 2014 suggests that this network is moving towards the intermittent switching region.

• Conference paper
Azari MM, Rosas De Andraca FE, Pollin S, 2018,

### Reshaping cellular networks for the sky: major factors and feasibility

, 2018 IEEE International Conference on Communications (ICC), Publisher: IEEE, ISSN: 1938-1883

This paper studies the feasibility of supporting drone operations using existent cellular infrastructure. We propose an analytical framework that includes the effects of base station (BS) height and antenna radiation pattern, drone antenna directivity and various propagation environments. With this framework, we derive an exact expression for the coverage probability of ground and drone users through a practical cell association strategy. Our results show that a carefully designed network can control the radiated interference that is received by the drones, and therefore guarantees a satisfactory quality of service. Moreover, as the network density grows the increasing level of interference can be partially managed by lowering the drone flying altitude. However, even at optimal conditions the drone coverage performance converges to zero considerably fast, suggesting that ultra-dense networks might be poor candidates for serving aerial users.

• Journal article
Garcia Millan R, Pruessner G, Pickering L, Christensen Ket al., 2018,

### Correlations and hyperuniformity in the avalanche size of the Oslo Model

, Europhysics Letters: a letters journal exploring the frontiers of physics, Vol: 122, ISSN: 1286-4854

Certain random processes display anticorrelations resulting in local Poisson-like disorder and global order, where correlations suppress fluctuations. Such processes are called hyperuniform. Using a map to an interface picture we show via analytic calculations that a sequence of avalanche sizes of the Oslo model is hyperuniform in the temporal domain with the minimal exponent $\lambda=0$ . We identify the conserved quantity in the interface picture that gives rise to the hyperuniformity in the avalanche size. We further discuss the fluctuations of the avalanche size in two variants of the Oslo model. We support our findings with numerical results.

• Journal article
Siddiqui M, Wedemann RS, Jensen HJ, 2018,

### Avalanches and generalized memory associativity in a network model for conscious and unconscious mental functioning

, Physica A: Statistical Mechanics and its Applications, Vol: 490, Pages: 127-138, ISSN: 0378-4371

We explore statistical characteristics of avalanches associated with the dynamics of a complex-network model, where two modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental processes. The model illustrates Freud’s ideas regarding the neuroses and that consciousness is related with symbolic and linguistic memory activity in the brain. It incorporates the Stariolo–Tsallis generalization of the Boltzmann Machine in order to model memory retrieval and associativity. In the present work, we define and measure avalanche size distributions during memory retrieval, in order to gain insight regarding basic aspects of the functioning of these complex networks. The avalanche sizes defined for our model should be related to the time consumed and also to the size of the neuronal region which is activated, during memory retrieval. This allows the qualitative comparison of the behaviour of the distribution of cluster sizes, obtained during fMRI measurements of the propagation of signals in the brain, with the distribution of avalanche sizes obtained in our simulation experiments. This comparison corroborates the indication that the Nonextensive Statistical Mechanics formalism may indeed be more well suited to model the complex networks which constitute brain and mental structure.

• Journal article
Nesbitt D, Pruessner G, Lee C, 2017,

### Edge instability in incompressible planar active fluids

, Physical Review E, Vol: 96, ISSN: 1539-3755

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014)], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

• Journal article
Willis G, Pruessner G, 2017,

### Spatio-temporal correlations in the Manna model in one, three and five dimensions

, International Journal of Modern Physics B, Vol: 32, ISSN: 0217-9792

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d

• Journal article
Fallesen T, Roostalu J, Duellberg C, Pruessner G, Surrey Tet al., 2017,

### Ensembles of Bidirectional Kinesin Cin8 Produce Additive Forces in Both Directions of Movement

, Biophysical Journal, Vol: 113, Pages: 2055-2067, ISSN: 0006-3495

Most kinesin motors move in only one direction along microtubules. Members of the kinesin-5 subfamily were initially described as unidirectional plus-end-directed motors and shown to produce piconewton forces. However, some fungal kinesin-5 motors are bidirectional. The force production of a bidirectional kinesin-5 has not yet been measured. Therefore, it remains unknown whether the mechanism of the unconventional minus-end-directed motility differs fundamentally from that of plus-end-directed stepping. Using force spectroscopy, we have measured here the forces that ensembles of purified budding yeast kinesin-5 Cin8 produce in microtubule gliding assays in both plus- and minus-end direction. Correlation analysis of pause forces demonstrated that individual Cin8 molecules produce additive forces in both directions of movement. In ensembles, Cin8 motors were able to produce single-motor forces up to a magnitude of ∼1.5 pN. Hence, these properties appear to be conserved within the kinesin-5 subfamily. Force production was largely independent of the directionality of movement, indicating similarities between the motility mechanisms for both directions. These results provide constraints for the development of models for the bidirectional motility mechanism of fission yeast kinesin-5 and provide insight into the function of this mitotic motor.

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## Publications

Publications of staff linked to the Centre for Complexity Science.

Note to staff: Publications will appear here automatically if you link your publications under the College's Sympletic Elements system.  This is done under "link to funding" under which you will find an option to find one or more papers which can be paired with an "organisational unit" where you should find the Centre for Complexity Science as one option. Any problems, talk to Tim Evans or the Faculty Web Team.