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<title>Marco Tulio Angulo</title>
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<h2>Marco Tulio Angulo</h2>
<p><br></p>
<h3>CONACyT Research Fellow<br>
<a href="http://www.matem.unam.mx/inicio?set_language=en&cl=en">Institute of Mathematics<a/><br>
<a href="https://www.unam.mx">UNAM</a>-Juriquilla
<br><br>
mangulo[AT]im[.]unam[.]mx<br>
<div id="font-weight: bold">Office 109, <a href="http://liigh.unam.mx">LIIGH</a> </div>
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<p>
<!--
I was born in Mexico City in 1985. I got my Dr.Eng. degree in Automatic Control in 2012 from <a href="https://www.unam.mx">UNAM</a>, México, under the supervision of
<a href="http://verona.fi-p.unam.mx/~lfridman/">Leonid Fridman</a> and <a href="http://www.iingen.unam.mx/es-mx/Investigacion/Coordinacion/ElectricayComputacion/Lists/ElectricaYComputacion1/DispForm.aspx?ID=51">Jaime A. Moreno</a>.
</p>
<p>
Since 2014, I am a Postdoctoral Research Associate at the <a href="http://www.barabasilab.com/people.php">Center for Complex Network Research</a> (CCNR), Northeastern University, under the supervision of <a href="http://www.barabasi.com">Albert-László Barabási</a>.
Since 2015, I also have an appointment as Sponsored Staff Collaborator in the <a href="http://brighamandwomens.org/research/depts/medicine/channing/default.aspx">Channing Division of Network Medicine</a>, Brigham and Women's Hospital and Harvard Medical School working under the supervision of <a href="http://scholar.harvard.edu/yyl/home">Yang-Yu Liu</a>. During my stay in Boston, I have been much influenced by <a href="http://web.mit.edu/nsl/www/">Jean-Jacques Slotine</a> also.
</p>
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<br>
<br>
<p>My research sits at the intersection of <b>control theory</b>, <b>system identification</b>, <b>dynamical system theory</b> and <b>network science</b>.
Inspired by these disciplines, my <b>research program</b> aims to develop mathematically rigorous theory in order to understand, diagnose and control complex networked systems in engineering, biology and medicine.
</p>
<p> The ultimate goal is to explore the <b>implications</b> that rigourous theory can have in how we approach some of the most challenging problems of our time, from undersanding and controlling microbial communities (microbiomes) in order to improve human health, to disentangling the control principles behind the gene regulatory processes in ourselves.
</p>
<p> I collaborate with researchers at several national an international instituions, such as UNAM-CU/Juriquilla, Harvard Medical School, and the Massachussetts Institute of Technology. If you are interested, please get in touch!
</p>
<!--
<p>
<span class="label label-warning">I am applying for jobs!</span> <a href="resume-MarcoTulioAngulo.pdf">CV</a> and <a href="ResearchStatement-v1.pdf">Research Statement</a>.
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Understanding, diagnosing and controlling complex systems
by blending control theory and network science.
-->
<span class="label label-success">Open positions</span> <font size="2">January, 2017 </font><br>
<font size="2">A variety of openings are available for curious and driven students (bachelor, master, PhD and postdocs) on topics pertaining to control theory, network science, and synthetic ecology/biology. <a href="">read more</a></font>
<br>
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<li>
<br>
<span class="label label-success">Recent papers</span> <font size="2">February, 2017</font> <br>
<font size="2">Our paper "Fundamental limitations of network reconstruction from temporal data" has been published in the Journal of the Royal Society Interface.</font>
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<h4>Controlling complex microbial communities</h4>
<p><font size="2">Combining network science with control theory to control complex microbial communities, either in our gut or the environment, in order to improve our helth. </font></p>
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<p>
The microbial communities (MCs) inside and around us exert a profound influence in our well-being, playing key roles in the physiology of our body and the health of the ecosystems on Earth. An increasing collection of diseases including diabetes, obesity, food allergies, cancer and even some brain disorders such as autism have been associated with disrupted MCs —communities with an abnormal abundance profile of species. Disrupted MCs distort the metabolic and immune function of our body due to the lack of bacteria that produce the needed metabolic and physiologic signals for the brain, immune and digestive systems. In the soil and oceans, disrupted MCs reduce the resistance of plants to diseases and impact global climate by altering carbon sequestration rates in the oceans. Controlling these disrupted MCs to restore their healthy abundance profile could bring novel solutions to many challenges, including global warming, sustainable agriculture and human health
</p>
<p>
Our ability to control these microbial communities is crucial to improving the hosts’ well-being and health. But this potential has not been fully harvested due to the lack of a systematic method to control these complex microbial communities. The objective of this project is to create a rigorous theoretical framework to address this challenge.
</p>
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<h4>Mapping ecological networks of microbial communities</h4>
<p><font size="2">Creating the novel system identification methods needed to map the ecological networks underlying complex microbial communities. </font></p>
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<div class="details">
<p>
Microorganism form complex dynamic ecosystems that play key roles on the health of humans, plants and other higher organisms they associate with. Mapping the underlying ecological network of those microbial ecosystems is a necessary step towards understanding their community ecology and predicting their temporal dynamics. Yet, the success of existing methods based on the fitting of time-resolved metagenomics data has been very limited by their necessity of knowing the dynamics model and the uninformativeness of such longitudinal data.
</p>
<p>
The objective of this project is to create novel system identification methods that can circumvent the above two limitations. This would open the door to better investigate their stability, assembly rules of feasible communities, and design personalized microbe-based cocktails to treat diseases related to microbial dysbiosis.
</p>
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<h3>Fundamental limitations of network reconstruction</h3>
<p>What are the limits of the properties of a network that can be reconstructed from given temporal data of the system?</p>
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<div class="details">
<p>
Network reconstruction (NR) aims to infer some property of the interaction matrix (i.e., interconnection network) of a networked system from measuring the temporal response of its nodes. Properties of interest include its sign-pattern (i.e., if interactions are inhibitory or excitatory), its connectivity (i.e., if there is an interaction or not) or the degree-sequence (i.e., number of incoming/outgoing interactions per node). Indeed, a key observation of network science is that fundamental properties of complex systems —from stability and epidemic thresholds to observability and controllability— can be determined from these properties without knowing the interaction matrix itself. Consequently, NR is being increasingly used in fields as diverse as biology, medicine or engineering, allowing us to understand, diagnose and control complex networked systems. Yet, NR remains an outstanding challenge after a decade of extensive studies. Most existing NR algo- rithms do not perform significantly better than random guesses and can even provide contradictory results for relatively simple systems. Most of these problems originate from a simple fact: our lack of understanding of the fundamentals limitations of NR, making impossible to decide if an algorithm fails due to its design limitations or due to the limitations imposed by the available data and our uncertainty about the system dynamics.
</p>
<p>By extending the notion of distinguishability —originated in system identification theory— and its analysis to consider uncertain dynamics, my collaborators and I have recently derived necessary and suf- ficient conditions to solve the NR problem. These conditions characterize how uncertain can we be about the system dynamics, and how informative does the measured temporal data need to be. Our results allows us to find the advantages and disadvantages of NR with respect to traditional parameter identification methods. We prove that NR is useful to decrease the required knowledge about the system dynamics. But, counterintuitively, NR generically requires the same the information from the measured data regardless of the property to reconstruct (e.g., degree sequence or the interaction matrix itself). Revealing these fundamental limitations shed light on designing better network reconstruction algorithms with practical improvements over existing methods.</p>
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<h4>Interplay between network structure and dynamics in complex systems</h4>
<p><font size="2">Creating a rigirous understanding of the impact of the network structure on the dynamics of complex systems.</font> </p>
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<div class="details">
<p>Real networks such as gene regulatory networks or the World-Wide-Web have specific (macroscopic) organization properties like scale-free degree distribution and (microscopic) properties like network motifs. Do these organization properties provide functional advantages when dynamics are considered?</p>
<p>Combining contraction theory —a recent method to analyze stability of nonlinear systems— with a simple model reduction methodology, my collaborators and I have recently shown that the microscopic organization of real biological networks represented by their network motifs best favor the stability of the whole network. In addition, we have also shown that the macroscopic organization of real networks (i.e., scale-free degree distribution) provides functional advantages in terms of emergence of new behavior in the limit of an infinite number of agents (i.e., the so-called ‘thermodynamic limit’). Understanding how new behavior emerges from aggregating simple agents remains a fundamental problem in modern physics, with deep branches that extend to biology, technology and the nature of consciousness. By deriving new asymptotics for the eigenvectors of random graphs in the thermodynamic limit, we characterize conditions for the emergence of new behavior in the sense that the mean behavior of the ther- modynamic limit cannot be approximated by the dynamics of a single agent. With these conditions, we show that networks with power-law degree distribution favor the emergence of new behavior. However, new behavior does not emerge in networks with other degree distributions (such as Erdös-Renyi, small-world or lattice networks)
.</p>
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<h3>Data-driven observation, identification and model reduction of dynamic systems</h3>
<p>Combining manifold learning techniques with embeddings into infinite-dimensional dynamic system, we construct data-driven approaches to observation, identification and model reduction of dynamic systems. </p>
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<p>We are in the middle of a deluge of data (the Big Data era), but we are still starving for understanding. That is, data needs to be transformed into understanding for the increasingly complex systems we encounter in fields such as biology, finance or social sciences. Indeed, in these fields, the traditional approaches to obtain such understanding based on mathematical modelling and system identification are facing big challenges, since the dynamical models underlying these complex systems are poorly known.
</p>
<p>To circumvent these challenges, this project aims to introduce novel system theoretic tools to directly transform data into understanding, without the need of knowing the dynamical models.
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<h3>Optimization of uncertain systems</h3>
<p> Optimizing nonlinear systems with unknown dynamics and without access to all their state variables.</p>
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<p>
Traditional optimal control methodologies are not robust: they strongly rely on a model of the system, and cannot guarantee that optimality is preserved under uncertainties.
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<p>The objective of this project is to create novel optimization algorithms for uncertain systems, taking inspiration from both engineering and technology.</p>
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<h2 class="title">About me</h2>
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<p> I have broad research interesets in the intersection of <strong>control theory</strong>, <b>system identification</b>, <b>dynamical systems theory</b> and <b>network science</b>. Based on these disciplines, I aim to develop mathematically rigorous theory in order to understand, diagnose and control complex networked systems in engineering, biology and medicine. </p>
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<h3>Academic Positions</h3>
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<span>Present</span>
<span>2016</span>
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<h4>CONACyT Research Fellow</h4>
<p><em>Institute of Mathematics.</em></p> <p>Universidad Nacional Autónoma de México (UNAM).</p>
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<span>2016</span>
<span>2015</span>
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<h4>Sponsored Staff Collaborator</h4>
<p><em>Brigham and Women’s Hospital, Channing Division of Network Medicine.</em></p>
<p> Harvard Medical School Boston, MA.</p>
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<span>2016</span>
<span>2014</span>
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<h4>Postdoctoral Research Associate</h4>
<p><em>Center for Complex Network Research. </em></p>
<p>Northeastern University, Boston, MA.</p>
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<span>2013</span>
<span>2012</span>
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<h4>Full-time Professor</h4>
<p><em>Faculty of Engineering</em>, UAQ, México.</p>
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<span class="degree">Dr.Eng.</span>
<span class="year">2012</span>
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<p class="waht">Dr.Eng. in Automatic Control</p>
<p class="where">UNAM, México</p>
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<span class="degree">M.Eng.</span><span class="year">2009</span>
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<p class="waht">Master in Electrical Engineering/Automatic Control</p>
<p class="where">UNAM, México</p>
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<span class="degree">B.Sc.</span><span class="year">2007</span>
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<p class="waht">Bachelor degree in Automation and Mechatronic systems</p>
<p class="where">UAQ, México</p>
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<div class="date">2014</div>
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<div class="subject">Member of the Mexican National System of Researchers, Level 1</div>
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Sistema Nacional de Investigadores (National System of Researchers) or SNI is a governmental agency established in Mexico in 1984, to promote both the quantity and quality of research in Mexico, especially in the sciences.
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<div class="subject">Grant from the Mexican National Council of Science and Technology for postdoctoral studies</div>
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The National Council of Science and Technology (abbreviated CONACyT) is Mexico's entity in charge of the promotion of scientific and technological activities, setting government policies for these matters, and granting scholarships for postgraduate studies. It is the equivalent of USA's National Science Foundation or Argentina's CONICET. It is officially designated as a decentralized public agency of Mexico's federal government.
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<div class="date">2012</div>
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<div class="subject">Dr. Eng degree with summa cum laude</div>
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Honorific mention in the defense of my thesis.
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<div class="date">2010</div>
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<div class="subject">Alfonso Caso Medal</div>
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Given to the most distinguished graduate of the Master program.
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<h4 class="pubtitle">
Inferring a qualitative contact rate index of uncertain epidemics
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<div class="pubauthor"> <strong>Marco Tulio Angulo</strong> and Jorge X. Velasco</div>
<div class="pubcite">
<span class="label label-primary">bioRxiv Preprint</span> 107474.
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<h4>Abstract</h4>
We will inevitably face new epidemic outbreaks where the mechanisms of transmission are still uncertain, making it difficult to obtain quantitative predictions. Thus we present a novel algorithm that qualitatively predicts the start, relative magnitude and decline of uncertain epidemic outbreaks, requiring to know only a few of its "macroscopic" parameters. The algorithm is based on estimating exactly the time-varying contact rate of a canonical but time-varying Susceptible-Infected-Recovered epidemic model parametrized to the particular outbreak. The algorithm can also be extended to other canonical epidemic models. Even if dynamics of the outbreak deviates significantly from the underlying epidemic model, we show the predictions of the algorithm remain robust. We validated our algorithm using real time-series data of measles, dengue and the current zika outbreak, comparing its performance to existing algorithms that also use a few macroscopic parameters (e.g., those estimating reproductive numbers) and to those using a thorough understanding of the mechanisms of the epidemic outbreak. We show our algorithm can outperform existing algorithms using a few macroscopic parameters, providing an informative qualitative evaluation of the outbreak.
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<h4 class="pubtitle">
Fundamental limitations of network reconstruction from temporal data
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Jaime A. Moreno, Gabor Lippner, Albert-László Barabási and Yang-Yu Liu</div>
<div class="pubcite">
<span class="label label-success">Journal paper</span> Journal of the Royal Society Interface DOI: 10.1098/rsif.2016.0966, 2017.
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<h4>Abstract</h4>
Inferring properties of the interaction matrix that characterizes how nodes in a networked system directly interact with each other is a well-known network reconstruction problem. 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 or degree sequence) can be inferred from given temporal data of individual nodes remain unknown. Here, we rigorously derive the necessary conditions to reconstruct any property of the interaction matrix. 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. Revealing these fundamental limitations sheds light on the design of better network reconstruction algorithms that offer practical improvements over existing methods.
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<h4 class="pubtitle">Qualitative stability of nonlinear networked systems</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong> and Jean-Jacques Slotine</div>
<div class="pubcite"><span class="label label-success">Journal Paper</span> IEEE Transactions on Automatic Control (in press).</div>
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<div class="pubdetails">
<h4>Abstract</h4>
<p>In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70’s, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.</p>
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<h4 class="pubtitle">
Revealing complex ecological dynamics via symbolic regression
</h4>
<div class="pubauthor">Yize Chen, <strong>Marco Tulio Angulo</strong> and Yang-Yu Liu</div>
<div class="pubcite">
<span class="label label-primary">bioRxiv Preprint</span> 074617.
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<div class="pubdetails">
<!-- <img alt="image" src="img/pubs/150x200.png" align="left" style="padding:0 30px 30px 0;"> -->
<h4>Abstract</h4>
Complex ecosystems, from food webs to our gut microbiota, are essential to human life. Understanding the dynamics of those ecosystems can help us better maintain or control them. Yet, reverse-engineering complex ecosystems (i.e., extracting their dynamic models) directly from measured temporal data has not been very successful so far. Here we propose to close this gap via symbolic regression. We validate our method using both synthetic and real data. We firstly show this method allows reverse engineering two-species ecosystems, inferring both the structure and the parameters of ordinary differential equation models that reveal the mechanisms behind the system dynamics. We find that as the size of the ecosystem increases or the complexity of the inter-species interactions grow, using a dictionary of known functional responses (either previously reported or reverse-engineered from small ecosystems using symbolic regression) opens the door to correctly reverse-engineer large ecosystems.
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<h4 class="pubtitle">Network motifs emerge from interconnections that favour stability</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Yang-Yu Liu and Jean-Jacques Slotine</div>
<div class="pubcite"><span class="label label-success">Journal Paper</span> Nature Physics, Volume 11, 848–852 (2015).</div>
</div>
<div class="pubdetails">
<h4>Abstract</h4>
<p>The microscopic principles organizing dynamic units in complex networks—from proteins to power generators—can be understood in terms of network ‘motifs’: small interconnection patterns that appear much more frequently in real networks than expected in random networks. When considered as small subgraphs isolated from a large network, these motifs are more robust to parameter variations, easier to synchronize than other possible subgraphs, and can provide specific functionalities. But one can isolate these subgraphs only by assuming, for example, a significant separation of timescales, and the origin of network motifs and their functionalities when embedded in larger networks remain unclear. Here we show that most motifs emerge from interconnection patterns that best exploit the intrinsic stability characteristics at different scales of interconnection, from simple nodes to whole modules. This functionality suggests an efficient mechanism to stably build complex systems by recursively interconnecting nodes and modules as motifs. We present direct evidence of this mechanism in several biological networks.</p>
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<h4 class="pubtitle">
Fundamental limitations of network reconstruction
</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Jaime A. Moreno, Gabor Lippner, Albert-László Barabási and Yang-Yu Liu</div>
<div class="pubcite">
<span class="label label-primary">ArXiv Preprint</span> arXiv:1508.03559, 2015.
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</div>
<div class="pubdetails">
<!-- <img alt="image" src="img/pubs/150x200.png" align="left" style="padding:0 30px 30px 0;"> -->
<h4>Abstract</h4>
Network reconstruction helps us understand, diagnose and control complex networked systems by inferring properties of their interaction matrices, which characterize how nodes in the system directly interact with each other. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations on which properties of the interaction matrix can be inferred from given temporal data of individual nodes remain unknown. Here we reveal these fundamental limitations by deriving the necessary and sufficient conditions to reconstruct any property of the interaction matrix. These conditions characterize how uncertain can we be about the coupling functions between nodes in the net- work, and how informative does the measured temporal data need to be; rendering two classes of fundamental limitations of network reconstruction. The first class implies a natural trade-off: the more information we want to reconstruct the more certain we need to be about the coupling functions. Consequently, reconstructing less information —such as adjacency pattern instead of edge weights— helps us decrease the needed knowledge of the system dynamics. The second class originates from the measured temporal data only and produce a rather counterintuitive limitation: even if we know the coupling functions exactly, reconstructing any property of the interaction matrix is as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. To circumvent this limitation, we show that prior knowledge of the interaction matrix —such as bounds on the edge weights— can be very helpful. Revealing these fundamental limitations shed light on designing better network reconstruction algorithms with practical improvements over existing methods.
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