
Luis Rocha
The structure of networks has provided many insights into the organization of complex systems. The success of this approach is its ability to capture the organization of multivariate interactions, and how it changes in time (network evolution) without explicit dynamical rules for node variables. As the field matures, however, there is a need to move from understanding to controlling complex systems. This is particularly true in systems biology and medicine, where increasingly accurate models of biochemical regulation have been produced. More than understanding the organization of biochemical regulation, we need to derive control strategies that allow us, for instance, to move a mutant cell to a wildtype state, or revert a mature cell to a pluripotent state. Here I present two concepts developed in our group aimed at supporting this goal. First I will present the schema redescription methodology, used to remove redundancy from automata rules to reveal their canalization properties, thus simplifying the characterization of control in large models of natural networks, such as systems biology models of biochemical regulation [MarquesPita & Rocha, 2013]. Secondly, we introduce effective connectivity and input redundancy as a measures of canalization, and demonstrate that effective connectivity is an order parameter of Boolean Network (BN) dynamics, and a major factor in network controllability [MarquesPita et al, 2015; Gates and Rocha, 2015]. We also show that existing structural control methods do not predict the actual controllability of Boolean network models, as they can both undershoot and overshoot the number and which sets of variables actually control these models, highlighting the importance of the system dynamics in determining control. Finally, we show that controllability can both be hindered or aided by how canalization unfolds in a given network, leaving room for natural selection or human design to effectively control large complex networks

Angelia Nedich
We will consider the problem of distributed cooperative learning in a network of agents, where the agents are repeatedly gaining partial information about an unknown random variable whose distribution is to be jointly estimated. The learning is based on Bayesian update adapted to distributed information structure inherited from the network. The joint objective of the agent system is to globally agree on a hypothesis (distribution) that best describes the observed data by all agents in the network. Interactions between agents occur according to an unknown sequence of timevarying graphs. We highlight some interesting aspects of Bayesian learning and stochastic approximation approach for the case of a single agent, which has not been observed before and it allows for a new connection between optimization and statistical learning. Then, we discuss and analyze the general case where subsets of agents have conflicting hypothesis models, in the sense that the optimal solutions are different if the subset of agents were isolated. Additionally, we provide a new nonBayesian learning protocol that converges an order of magnitude faster than the learning protocols currently available in the literature for arbitrary fixed undirected graphs. Our results establish consistency and a nonasymptotic, explicit, geometric convergence rate for the learning dynamics.

Domitilla Del Vecchio
The behavior of gene circuits is contextdependent, that is, the input/output functionality of a circuit depends on its context. Context includes other systems to which the circuit directly connects, which apply a load (retroactivity), and systems that are simply present in the cellular environment. The latter ones, in particular, also affect the functionality of the circuit due to sharing a common pool of limited resources. Because of these contexteffects, a set of new â€œhiddenâ€? interactions appear in gene networks, which dramatically change the expected networkâ€™s behavior. These hidden interactions confound both the design of de novo systems in synthetic biology and the analysis of existing natural systems. In this talk, I will present a systematic modeling framework that captures hidden interactions in a networkâ€™s description and provides simple graphical rules to draw them. I will then present recent experimental results performed in our lab that validate these predictions. Finally, I will illustrate that a distributed control scheme, in which the local negative feedback at each node is realized through mRNA interference, can mitigate the effects of those hidden interactions due to scarcity of resources needed for gene expression.

Stefano Allesina
Biological systems are large: to understand the development of D. melanogaster, we need to account for a generegulation network with more than 15,000 nodes; the spread of influenza in Chicago is mediated by a contact network composed of several million nodes; ecosystems can harbor thousands of different species interacting with each other in different ways.
Modeling this staggering diversity is difficult using traditional methods, and a possible alternative is represented by the application of random matrix theory to biological dynamics. I present a series of studies on the stability of large ecological systems which use and extend the theory of random matrices, to gain insight on the principal quantities determining the response to perturbations. I show how these methods can be applied to a diversity of problems in biology, and conclude with a list of challenges that need to be overcome to make this theory more applicable and complete.

Pablo Iglesias
Chemotaxis, the directed motion of cells in response to chemical gradients, requires the coordinated action of three different and separable processes: motility, gradient sensing and polarization. Much effort has been expended understanding each of these processes, and numerous mathematical models have been proposed that explain each one. In this talk I will present a comprehensive model that explains all three aspects of chemotaxis. The central element is the presence of a biased excitable system. This model takes into account reports that the actin cytoskeleton and other signaling elements in motile cells have many of the hallmarks of an excitable medium, including the presence of propagating waves. This excitable behavior can account for the spontaneous migration of cells. We suggest that the chemoattractantmediated signaling can bias excitability, thus providing a means by which cell motility can be directed. We also provide a mechanism for cell polarity that can be incorporated into the existing framework. Finally, we show that the model predicts a number of other possible dynamic behaviors, and demonstrate how these behaviors can be induced in live cells.

Daniel Gauthier
Autonomous Boolean networks (ABNs) are commonly used to model the dynamics of gene regulatory networks. Often, however, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on the repressilator, we develop an experimental testbed that explicitly includes both internode time delays and stochastic noise using digital logic elements on fieldprogrammable gate arrays. We observe transients that last billions of characteristic time scales and scale exponentially with the amount of time delays between nodes, a phenomenon known as supertransient scaling. To counteract these long transients, we show that small, occasional perturbations applied to the time delays can force the transient trajectories to rapidly approach the asymptotic attractors.
This work is in collaboration with Otti Dâ€™Huys, Johannes Lohmann, Nicholas D. Haynes, and Eckehard SchÃ¶ll, and is supported financially by the US Army Research Office Grant # W911NF1210099.

Colin Campbell
The topology of a network provides a substrate upon which dynamical processes may occur; understanding the manner in which topology constrains dynamics is therefore central to our ability to predict and influence the behavior of complex systems. Recent work has considered canonical linear dynamics, where the state variable associated with a node varies according to the summative influence of the node's regulators. Under these dynamics, the controlrelated properties of networks are differentiated only by their topological structure. As such, analyzing the relationships between network topology and controlrelated properties offers a rich avenue for characterizing networks in a way that complements traditional measures such as the degree distribution.
For instance, it has been shown that under these dynamics it is possible to drive a network to any state in finite time by directly controlling a (typically small) subset of its nodes. In a given network, how many nodes must be directly controlled to achieve complete control over the network? Are these nodes uniquely defined, or can multiple sets of nodes be used to populate the socalled minimal driver set? Where are these nodes located in the network? What about a network's topological structure determines the answers to these questions? This presentation will address these and related questions, with an emphasis on the unique controlrelated characteristics of different classes of synthetic and empirical networks.

Nina Fefferman
Network analyses have revolutionized the study of social behavior in animal populations, but have been predominantly focused on describing the social actions/decisions/behaviors in currently existing populations. In this talk, I will discuss a series of simulation studies that show how efficient group organizational structure can emerge from individual selfish choices, even when the desired metric of global efficiency is something beyond the capability of any one individual to evaluate. Iâ€™ll show how these results complement standard game theoretic discussions of the evolution of cooperation (including â€˜defectingâ€™) to allow us to study evolutionary selection on group task efficiency in alreadysocial species. These results have direct implications for the evolution of social systems and (hopefully) provide some intriguing potential mechanisms for general feedback control on global network outcomes.

Jorge CortÃ©s
Recent work on linear control models for complex systems has examined their controllability and specifically explored the characterization of the ease (in terms of required energy) with which they can be controlled by means of a finite number of actuators, each affecting an individual node. In the study of effective connectivity in the brain, external inputs not only have direct effect on the state of the brain in a particular area but can also activate the connections among different brain areas. Motivated by this, in the first part of the talk we study controllability metrics for bilinear control models of complex systems, where inputs might not only affect the state of a node, but also their interconnection. In the second part of the talk, motivated by the identification procedures used in neuroscience to determine effective connectivity in the brain while performing cognitive tasks, we study the problem of identifying linear control networks from inputoutput data when there are latent nodes whose presence and number is unknown. We examine to what extent the transfer function of the manifest subnetwork can be reconstructed and explore the design of procedures to determine whether interactions between manifest nodes are direct or mediated by latent nodes.

Mason Porter
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earthâ€™s surface. However, in modern contagions, longrange edges  for example, due to airline transportation or communication media  allow clusters of a contagion to appear in distant locations. We study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach also highlights contagion maps as a viable tool for inferring lowdimensional structure in networks.

Adilson Motter
The study of unintended consequences is particularly significant when combined with the twin problem of optimization. Fuelled by the prospect that it will help us understand the workings of evolution and the principles of efficient design, optimization has been at the center of many recent studies on the network modeling of systems. In network optimization, surprising effectsâ€”some desirable, others undesirableâ€”can be exacerbated due to interconnectivity and high dimensionality. In this talk, I will discuss implications of optimization for the metabolic network activity of living cells and its role in giving rise to the recently discovered phenomenon of synthetic rescues. Then I will discuss a fundamental but often overlooked question in the study of unintended consequences, namely, whether the intended actions themselves (not to say their consequences) are possible. For the latter, I will focus on control actions in the context of network controllability and show that theoretical results on optimizing the number of driver nodes often lead to control actions that are too complex to be implemented in practice.

Ira Schwartz
Disease control is of paramount importance in public health, with total eradication as the ultimate goal. Mathematical models of disease spread in populations are an important component in implementing effective vaccination and treatment campaigns. However, human behavior in response to an outbreak of disease has only recently been included in the modeling of epidemics on networks. In this talk, I will review some of the mathematical models and machinery used to describe the underlying dynamics of rare events in finite population disease models, which include human reactions on what are called adaptive networks. I will show how to derive a new model that includes a dynamical systems description of the force of the noise that drives the disease to extinction. Coupling the effective force of noise with vaccination as well as human behavior reveals how to best utilize stochastic disease controlling resources such as vaccination and treatment programs. Finally, I will also present a general theory to derive the most probable paths to extinction for heterogeneous networks.
This research has been supported by the Office of Naval Research, Air Force of Scienti?c Research and the National Institutes of Health.=

Natasa MiskovZivanov

Sonia Martinez
Selforganization is a pervasive phenomenon in nature, observed in largescale biological and natural systems, and which has inspired the development of robotic swarms with applications to monitoring, manipulation, and construction. The deployment of largescale swarms not only requires overcoming important technological barriers but also introduces new theoretical challenges for analysis and control. In particular, large groups of agents have some essential characteristics that distinguish them from smallerscale multiagent systems. In a large swarm, agents have no individual significance and only the macroscopic objectives are of importance. A swarm largely remains unaffected by the removal of a large, but discrete, number of agents. It may also be infeasible to localize all individual agents in a swarm via a global positioning system. Moreover, it is difficult (and needlessly complicated) to specify the global configuration of the swarm using the states of individual agents; instead, it is more appropriate to employ macroscopic quantities such as a swarm spatial density distribution. In this talk, we present a type of algorithms for the density control of swarms to achieve general 1D and 2D density profiles. In our approach, we view a swarm as a discrete approximation of a (continuous) manifold with density. Under the assumption that agents are able to measure spatial functions of the local density and swarm boundary and motion control is noiseless, the control laws are defined in terms of artificial coordinates that define a diffeomorphism between the spatial domain and a disk. These artificial coordinates are computed in a distributed way through consensus techniques.

Peter Csermely
The network description of complex systems resulted in a surprisingly large number of properties, which characterize the topology of realworld networks fairly generally (e.g. the existence of hubs, hierarchy, modules, network core/periphery, etc.). In the lecture I will describe a few properties of the adaptation of complex systems to changes in their environment, which seem to be similarly general behavioral patterns ranging from macromolecules, through cells, neuronal systems and social networks. From macromolecules to social networks dominanceshifts often occur between more rigid and more plastic states (and their network descriptions; http://arxiv.org/abs/1511.01239). Here rigidity and plasticity are understood as functional terms meaning a few versus a high number of possible/reachable system responses/attractors (http://arxiv.org/abs/1204.6389). Similarly, from macromolecules to social networks often a dominanceshift can be observed in the participation of core to periphery nodes in the 'decisionmaking processes' in case of repeated/familiar/encoded responses versus novel, 'creative' responses to previously unknown environmental challenges (http://arxiv.org/abs/1511.01238).

Marco Tulio Angulo
Network reconstruction is the first step towards understanding, diagnosing and controlling the dynamics of complex networked systems. It allows us to infer properties of the interaction matrix, which characterizes how nodes in a system directly interact with each other. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations governing which properties of the interaction matrix (e.g., adjacency pattern, sign pattern and degree sequence) can be inferred from given temporal data of individual nodes remain unknown.
In this talk, I will discuss our recent work on deriving the necessary conditions to reconstruct any desired property of the interaction matrix. These conditions characterize how uncertain can we be about the coupling functions of the system (that characterize how nodes interact), and how informative does the measured temporal data need to be. Counterintuitively, we find that reconstructing any property of the interaction matrix is generically as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. In other words, reconstructing less information (e.g., adjacency pattern instead of edgeweights) does not make the network reconstruction problem easier. Revealing these fundamental limitations shed light on the design of better network reconstruction algorithms, which offer practical improvements over existing methods.
Joint work with YangYu Liu (Harvard), LÃ¡szlo BarabÃ¡si (Northeastern), Gabor Lippner (Northeastern) and Jaime Moreno (UNAM, Mexico).

Biswadip Dey
Mathematical analysis of synchronization in networks of neuronal oscillators provides a better understanding of neuronal ensemble behavior in the brain. Moreover, systematic means to analyze the influence of network structure and external stimulation on network synchronization have the potential to improve methods for treating synchronizationrelated neurological disorders (e.g. epileptic seizure, Parkinson's disease etc.). In this talk, we will investigate synchronization in networks of homogeneous FitzHughNagumo (FN) oscillators interconnected via electrical gap junction couplings, and derive sufficient condition (a bound on the coupling strength) for synchronization. By using nonsmooth Lyapunov functions, our approach provides an improvement over previous results. Then, by considering a FN network with heterogeneous inputs, we will demonstrate how cluster synchronization emerges out of symmetry in the interconnection graph.

Andrew GainerDewar
Signalling networks play an important role in biological systems, and many diseases are the result of dysfunctional behavior in such networks. In this talk, I will present the latest progress on the OCSANA computational approach for discovering combinatorial interventions in largescale signalling networks, first published by VeraLicona et al. in 2013. Recent advances in combinatorial algorithms have improved the time performance significantly, and we are incorporating chemo and pharmacoinformatic data about the drugability of specific nodes to help prioritize and explain the proposed interventions.

Jason Papin
The comparative analysis of metabolic networks can provide mechanistic understanding of speciesspecific differences of metabolism and associated biomarkers and drug targets for various applications. The laboratory rat has been used as a surrogate to study human biology for more than a century. We have generated the first genomescale reconstruction of Rattus norvegicus metabolism, iRno, and a significantly improved reconstruction of human metabolism, iHsa. Comparative analyses with these models captured metabolic features that distinguish rats from humans including vitamin C and bile acid synthesis pathways. After extensive manual curation and network reconciliation between iRno and iHsa, we generated biomarker predictions for rat and human hepatocytes by integrating gene expression changes in response to 76 pharmaceutical compounds and environmental toxicants. Biomarker predictions were validated with literaturebased evidence for antipyretic and antigout medicines. Comparative analyses provided mechanistic insights into the selection of metabolite biomarkers common to rats and humans. These models will serve as powerful computational platforms for contextualizing experimental data and making functional predictions consistent with rat and human biology for clinical and basic science applications.=

Kayhan Özcimder

Reka Albert
Mutations or alterations in the expression of elements of cellular signaling networks can lead to incorrect behavioral decisions that could result in tumor development or metastasis. Thus, mitigation of the cascading effects of such dysregulations is an important control objective. My group at Penn State is collaborating with wetbench biologists to develop and validate predictive models of various biological systems. Over the years we found that discrete dynamic modeling is very useful in molding qualitative interaction information into a predictive model. The attractors of these models can be directly related to the real systemâ€™s behaviors, and various interventions are straightforward to implement. We recently developed an efficient method to predict interventions that can drive the system toward a desired attractor or away from an undesired one . This method is based on an integration of the signal transduction network and the regulatory logic into an expanded network, and the identification of a specific type of strongly connected component, called stable motif, of this expanded network. Each stable motif corresponds to a point of no return in the dynamics of the system, and each attractor corresponds to a successive stabilization of a small set of stable motifs. Control of these stable motifs (by imposing a sustained state for a subset of their nodes) drives any initial condition of the system into the desired attractor. The predicted control sets were validated experimentally in two different systems.

John Baillieul
In 1983, Bosch GmbH began a feasibility study of using networked devices to control different functions in passenger cars. The study bore fruit, and in February 1986, the (at the time) innovative communications protocol of the Contgrol Area Network (CAN) was announced at the Congress of the Society of Automotive Engineers. Driven by technological developments in embedded systems, the proliferation of MEMS device arrays, the realization that life itself is supported by biomolecular networks, interest in multiagent robotics, and many other factors, the technology of realtime networked control systems has become perhaps the most important component of the rapidly emerging science of networks. This talk is an updated version of a broad overview that I gave at Boston University in 2008. I hope it will serve as a suitable introduction to this Workshop on Control and Observability of Network Dynamics.

Yannis Paschalidis
We are interested in deciphering the activity of biochemical networks, and in particular the genomescale metabolic network reconstructions. The metabolic network of a cell is often at steadystate with no drastic changes in metabolite concentrations assuming a fixed external environment. Flux Balance Analysis (FBA) is a widely used predictive model which computes a cell's steadystate chemical reaction fluxes as a solution to an optimization problem with constraints that capture stoichiometry mass balances and the composition of the growth medium. FBA, however, assumes a certain global cellular objective function which is not necessarily known. Understanding its structure can elucidate the cellular metabolic control mechanisms and infer important information regarding an organism's evolution. To that end, I will present a general framework for model estimation from observed equilibria. In metabolic networks, for instance, reaction fluxes of the cells under specific growth conditions can be measured. In other types of networks, such as transportation networks, users' congestion function are not typically known but equilibria (traffic flows) can easily be measured. Our framework allows for both parametric and nonparametric estimation and provides probabilistic guarantees on the quality of the estimated quantities. I will apply this general framework to estimating cellular objectives in metabolic networks.I will present results that show good agreement with simulated E. coli data, timedependent flux estimates inferred from gene expression data, and experimental flux measurements in longterm evolved E. coli strains. The latter data, in particular, reveal cellular objective functions that provide insight into possible metabolic adaptation trajectories.

Jie Sun
Understanding the dynamics and functioning of biological systems is one of the most challenging tasks faced in modern science. An important problem in practice regards how to accurately infer the underlying causeandeffect (i.e., causal) network from observational data, especially when the underlying system consists of a large number of interacting components and the dynamics is intrinsicaly nonlinear. Utilizing our recently developed theory of causation entropy (J. Sun, D. Taylor, and E. M. Bollt, SIAM Journal on Applied Dynamical Systems 14, 73â€“106, 2015), we devised an efficient computational approach of optimal causation entropy (oCSE) to infer causal networks from data, and demonstrate its effectiveness using both synthetic and experimental data.

Jorge G. T. Zanudo

Danielle Bassett
How do we make difficult decisions, inhibit inappropriate behaviors, or switch between different cognitive tasks? These capabilities are facilitated by socalled "cognitive control", which is driven by a few very specific regions of the human brain. While the anatomical locations of these regions are known, exactly how these regions enable cognitive control is far from understood. In this talk, I will posit that network control is a fundamental mechanism of cognitive control. I will develop, apply, and test structural controllability theory in the context of images of the brain acquired noninvasively in healthy adults. These studies demonstrate that the exact location of regions within the brain's structural wiring explain their unique roles in cognitive function. I will close by discussing the potential applications of this new knowledge in the context of clinical interventions in people with neurological disease and psychiatric disorders.

David Murrugarra
Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This talk focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This talk presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. Additionally, a formula, based on the properties of Boolean canalization, for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram will be discussed. Finally, an optimal control algorithm for the identification of the best combination of control actions in a stochastic system will be presented.

Zhaodan Kong
Networked dynamical systems are increasingly used as models for a variety of processes ranging from robotic teams to collections of genetically engineered living cells. As the complexity of these systems increases, so does the range of emergent properties that they exhibit. In this short talk, I will propose a new logic called SpatialTemporal Logic (SpaTeL) that is a unification of signal temporal logic (STL) and tree spatial superposition logic (TSSL). SpaTeL is capable of describing highlevel spatial patterns that change over time. I will present a statistical model checking procedure that evaluates the probability with which a networked system satisfies a SpaTeL formula. I will also show a synthesis procedure that determines system parameters maximizing the average degree of satisfaction, a continuous measure that quantifies how strongly a system execution satisfies a given formula. Finally I will demonstrate our algorithms on some biological system models.

Sean Cornelius
The proper functioning and reliability of many manmade and natural systems is fundamentally tied to our ability to control them. Indeed, applications as diverse as ecosystem management, emergency response and cell reprogramming all, at their heart, require us to drive a system toor keep it ina desired state. This process is complicated by the nonlinear dynamics inherent to most real systems, which has traditionally been viewed as an obstacle to their control. I will discuss two ways in which nonlinearity turns this view on its head, becoming an asset to network control. First, I will show how nonlinearity in the form of multi stability allows one to systematically design control interventions that can deliberately induce â€œreverse cascading failures", in which a network spontaneously evolves to a desirable (rather than a failed) state. Second, I will show that nonlinearity in the form of timevarying dynamics unexpectedly makes temporal networks easier to control than their static counterparts, with the former enjoying dramatic and simultaneous reductions in all costs of control. This is true despite the intuition that temporality should fragment a networkâ€™s structure, disrupting the paths that allow the directlycontrolled or â€œdriver" nodes to communicate with the rest of the network. Taken together, these parables shed new light on the crucial role of nonlinearity in network control, and provide support to the idea we can advantageously control nonlinearity, rather than letting nonlinearity control us.