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Fabio Pasqualetti

Publications and source records attributed to Fabio Pasqualetti.

At least 91 records · Page 5Linked to original sources

Learning in brain-computer interface control evidenced by joint decomposition of brain and behavior

Motor imagery-based brain-computer interfaces (BCIs) use an individuals ability to volitionally modulate localized brain activity as a therapy for motor dysfunction or to probe causal relations between brain activity and behavior. However, many individuals cannot learn to successfully modulate their brain activity, greatly limiting the efficacy of BCI for therapy and for basic scientific inquiry. Previous research suggests that coherent activity across diverse cognitive systems is a hallmark of individuals who can successfully learn to control the BCI. However, little is known about how these distributed networks interact through time to support learning. Here, we address this gap in knowledge by constructing and applying a multimodal network approach to decipher brain-behavior relations in motor imagery-based brain-computer interface learning using MEG. Specifically, we employ a minimally constrained matrix decomposition method (non-negative matrix factorization) to simultaneously identify regularized, covarying subgraphs of functional connectivity, to assess their similarity to task performance, and to detect their time-varying expression. Individuals also displayed marked variation in the spatial properties of subgraphs such as the connectivity between the frontal lobe and the rest of the brain, and in the temporal properties of subgraphs such as the stage of learning at which they reached maximum expression. From these observations, we posit a conceptual model in which certain subgraphs support learning by modulating brain activity in regions important for sustaining attention. To test this model, we use tools that stipulate regional dynamics on a networked system (network control theory), and find that good learners display a single subgraph whose temporal expression tracked performance and whose architecture supports easy modulation of brain regions important for attention.

q-bio.NC↗

Brain state stability during working memory is explained by network control theory, modulated by dopamine D1/D2 receptor function, and diminished in schizophrenia

Dynamical brain state transitions are critical for flexible working memory but the network mechanisms are incompletely understood. Here, we show that working memory entails brainwide switching between activity states. The stability of states relates to dopamine D1 receptor gene expression while state transitions are influenced by D2 receptor expression and pharmacological modulation. Schizophrenia patients show altered network control properties, including a more diverse energy landscape and decreased stability of working memory representations.

q-bio.NC↗

Data-Driven Minimum-Energy Controls for Linear Systems

In this paper we study the problem of computing minimum-energy controls for linear systems from experimental data. The design of open-loop minimum-energy control inputs to steer a linear system between two different states in finite time is a classic problem in control theory, whose solution can be computed in closed form using the system matrices and its controllability Gramian. Yet, the computation of these inputs is known to be ill-conditioned, especially when the system is large, the control horizon long, and the system model uncertain. Due to these limitations, open-loop minimum-energy controls and the associated state trajectories have remained primarily of theoretical value. Surprisingly, in this paper we show that open-loop minimum-energy controls can be learned exactly from experimental data, with a finite number of control experiments over the same time horizon, without knowledge or estimation of the system model, and with an algorithm that is significantly more reliable than the direct model-based computation. These findings promote a new philosophy of controlling large, uncertain, linear systems where data is abundantly available.

math.OC↗

Resilience of Traffic Networks with Partially Controlled Routing

This paper investigates the use of Infrastructure-To-Vehicle (I2V) communication to generate routing suggestions for drivers in transportation systems, with the goal of optimizing a measure of overall network congestion. We define link-wise levels of trust to tolerate the non-cooperative behavior of part of the driver population, and we propose a real-time optimization mechanism that adapts to the instantaneous network conditions and to sudden changes in the levels of trust. Our framework allows us to quantify the improvement in travel time in relation to the degree at which drivers follow the routing suggestions. We then study the resilience of the system, measured as the smallest change in routing choices that results in roads reaching their maximum capacity. Interestingly, our findings suggest that fluctuations in the extent to which drivers follow the provided routing suggestions can cause failures of certain links. These results imply that the benefits of using Infrastructure-To-Vehicle communication come at the cost of new fragilities, that should be appropriately addressed in order to guarantee the reliable operation of the infrastructure.

math.OC↗

Centralized Versus Decentralized Detection of Attacks in Stochastic Interconnected Systems

We consider a security problem for interconnected systems governed by linear, discrete, time-invariant, stochastic dynamics, where the objective is to detect exogenous attacks by processing the measurements at different locations. We consider two classes of detectors, namely centralized and decentralized detectors, which differ primarily in their knowledge of the system model. In particular, a decentralized detector has a model of the dynamics of the isolated subsystems, but is unaware of the interconnection signals that are exchanged among subsystems. Instead, a centralized detector has a model of the entire dynamical system. We characterize the performance of the two detectors and show that, depending on the system and attack parameters, each of the detectors can outperform the other. In particular, it may be possible for the decentralized detector to outperform its centralized counterpart, despite having less information about the system dynamics, and this surprising property is due to the nature of the considered attack detection problem. To complement our results on the detection of attacks, we propose and solve an optimization problem to design attacks that maximally degrade the system performance while maintaining a pre-specified degree of detectability. Finally, we validate our findings via numerical studies on an electric power system.

math.OC↗

A Fundamental Performance Limitation for Adversarial Classification

Despite the widespread use of machine learning algorithms to solve problems of technological, economic, and social relevance, provable guarantees on the performance of these data-driven algorithms are critically lacking, especially when the data originates from unreliable sources and is transmitted over unprotected and easily accessible channels. In this paper we take an important step to bridge this gap and formally show that, in a quest to optimize their accuracy, binary classification algorithms -- including those based on machine-learning techniques -- inevitably become more sensitive to adversarial manipulation of the data. Further, for a given class of algorithms with the same complexity (i.e., number of classification boundaries), the fundamental tradeoff curve between accuracy and sensitivity depends solely on the statistics of the data, and cannot be improved by tuning the algorithm.

cs.LG↗

Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators

In this paper we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the basis of several biological and technological processes; yet the underlying mechanisms to enable cluster synchronization of Kuramoto oscillators have remained elusive. In this paper we derive quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure asymptotic stability of the cluster synchronization manifold; that is, the ability to recover the desired cluster synchronization configuration following a perturbation of the oscillators' states. Qualitatively, our results show that cluster synchronization is stable when the intra-cluster coupling is sufficiently stronger than the inter-cluster coupling, the natural frequencies of the oscillators in distinct clusters are sufficiently different, or, in the case of two clusters, when the intra-cluster dynamics is homogeneous. We illustrate and validate the effectiveness of our theoretical results via numerical studies.

math.OC↗

Heterogeneity of Central Nodes Explains the Benefits of Time-Varying Control in Complex Dynamical Networks

Despite extensive research and remarkable advancements in the control of complex dynamical networks, most studies and practical control methods limit their focus to time-invariant control schedules (TICS). This is both due to their simplicity and the fact that the benefits of time-varying control schedules (TVCS) have remained largely uncharacterized. In this paper we study networks with linear and discrete-time dynamics and analyze the role of network structure in TVCS. First, we show that TVCS can significantly enhance network controllability over TICS, especially when applied to large networks. Through the analysis of a scale-dependent notion of nodal centrality, we then show that optimal TVCS involves the actuation of the most central nodes at appropriate spatial scales at all times. Consequently, it is the scale-heterogeneity of the central-nodes in a network that determine whether, and to what extent, TVCS outperforms conventional policies based on TICS. Here, scale-heterogeneity of a network refers to how diverse the central nodes of the network are at different spatial (local vs. global) scales. Several analytical results and case studies support and illustrate this relationship.

math.OC↗

On Structural Controllability of Symmetric (Brain) Networks

The question of controllability of natural and man-made network systems has recently received considerable attention. In the context of the human brain, the study of controllability may not only shed light into the organization and function of different neural circuits, but also inform the design and implementation of minimally invasive yet effective intervention protocols to treat neurological disorders. While the characterization of brain controllability is still in its infancy, some results have recently appeared and given rise to scientific debate. Among these, [1] has numerically shown that a class of brain networks constructed from DSI/DTI imaging data are controllable from one brain region. That is, a single brain region is theoretically capable of moving the whole brain network towards any desired target state. In this note we provide evidence supporting controllability of brain networks from a single region as discussed in [1], thus contradicting the main conclusion and methods developed in [2].

math.OC↗

Gramian-Based Optimization for the Analysis and Control of Traffic Networks

This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional approaches to control traffic signaling, a simplified framework allows for a more tractable analysis of the network overall dynamics, and enables the design of critical parameters while considering network-wide measures of efficiency. Motivated by the increasing availability of real-time high-resolution traffic data, we cast an optimization problem that formalizes the goal of minimizing the overall network congestion by optimally controlling the durations of green lights at intersections. Our formulation allows us to relate congestion objectives with the problem of optimizing a metric of controllability of an associated dynamical network. We then provide a technique to efficiently solve the optimization by parallelizing the computation among a group of distributed agents. Lastly, we assess the benefits of the proposed modeling and optimization framework through microscopic simulations on typical traffic commute scenarios for the area of Manhattan. The optimization framework proposed in this study is made available online on a Sumo microscopic simulator based interface [1].

math.OC↗

On the Real Stability Radius of Sparse Systems

In this paper, we study robust stability of sparse LTI systems using the stability radius (SR) as a robustness measure. We consider real perturbations with an arbitrary and pre-specified sparsity pattern of the system matrix and measure their size using the Frobenius norm. We formulate the SR problem as an equality-constrained minimization problem. Using the Lagrangian method for optimization, we characterize the optimality conditions of the SR problem, thereby revealing the relation between an optimal perturbation and the eigenvectors of an optimally perturbed system. Further, we use the Sylvester equation based parametrization to develop a penalty based gradient/Newton descent algorithm which converges to the local minima of the optimization problem. Finally, we illustrate how our framework provides structural insights into the robust stability of sparse networks.

eess.SY↗

White Matter Network Architecture Guides Direct Electrical Stimulation Through Optimal State Transitions

Electrical brain stimulation is currently being investigated as a therapy for neurological disease. However, opportunities to optimize such therapies are challenged by the fact that the beneficial impact of focal stimulation on both neighboring and distant regions is not well understood. Here, we use network control theory to build a model of brain network function that makes predictions about how stimulation spreads through the brain's white matter network and influences large-scale dynamics. We test these predictions using combined electrocorticography (ECoG) and diffusion weighted imaging (DWI) data who volunteered to participate in an extensive stimulation regimen. We posit a specific model-based manner in which white matter tracts constrain stimulation, defining its capacity to drive the brain to new states, including states associated with successful memory encoding. In a first validation of our model, we find that the true pattern of white matter tracts can be used to more accurately predict the state transitions induced by direct electrical stimulation than the artificial patterns of null models. We then use a targeted optimal control framework to solve for the optimal energy required to drive the brain to a given state. We show that, intuitively, our model predicts larger energy requirements when starting from states that are farther away from a target memory state. We then suggest testable hypotheses about which structural properties will lead to efficient stimulation for improving memory based on energy requirements. Our work demonstrates that individual white matter architecture plays a vital role in guiding the dynamics of direct electrical stimulation, more generally offering empirical support for the utility of network control theoretic models of brain response to stimulation.

q-bio.NC↗

Sex differences in network controllability as a predictor of executive function in youth

Executive function emerges late in development and displays different developmental trends in males and females. Sex differences in executive function in youth have been linked to vulnerability to psychopathology as well as to behaviors that impinge on health. Yet, the neurobiological basis of these differences is not well understood. Here we test the hypothesis that sex differences in executive function in youth stem from sex differences in the controllability of structural brain networks as they rewire over development. Combining methods from network neuroscience and network control theory, we characterize the network control properties of structural brain networks estimated from diffusion imaging data acquired in males and females in a sample of 882 youth aged 8-22 years. We summarize the control properties of these networks by estimating average and modal controllability, two statistics that probe the ease with which brain areas can drive the network towards easy- versus difficult-to-reach states. We find that females have higher modal controllability in frontal, parietal, and subcortical regions while males have higher average controllability in frontal and subcortical regions. Furthermore, average controllability values in the medial frontal cortex and subcortex, both higher in males, are negatively related to executive function. Finally, we find that average controllability predicts sex-dependent individual differences in activation during an n-back working memory task. Taken together, our findings support the notion that sex differences in the controllability of structural brain networks can partially explain sex differences in executive function. Controllability of structural brain networks also predicts features of task-relevant activation, suggesting the potential for controllability to represent context-specific constraints on network state more generally.

q-bio.NC↗

Synchronization Patterns in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control

Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators' natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples.

math.OC↗

Benchmarking measures of network controllability on canonical graph models

Many real-world systems are composed of many individual components that interact with one another in a complex pattern to produce diverse behaviors. Understanding how to intervene in these systems to guide behaviors is critically important to facilitate new discoveries and therapies in systems biology and neuroscience. A promising approach to optimizing interventions in complex systems is network control theory, an emerging conceptual framework and associated mathematics to understand how targeted input to nodes in a network system can predictably alter system dynamics. While network control theory is currently being applied to real-world data, the practical performance of these measures on simple networks with pre-specified structure is not well understood. In this study, we benchmark measures of network controllability on canonical graph models, providing an intuition for how control strategy, graph topology, and edge weight distribution mutually depend on one another. Our numerical studies motivate future analytical efforts to gain a mechanistic understanding of the relationship between graph topology and control, as well as efforts to design networks with specific control profiles.

physics.soc-ph↗

Data-Injection Attacks in Stochastic Control Systems: Detectability and Performance Tradeoffs

Consider a stochastic process being controlled across a communication channel. The control signal that is transmitted across the control channel can be replaced by a malicious attacker. The controller is allowed to implement any arbitrary detection algorithm to detect if an attacker is present. This work characterizes some fundamental limitations of when such an attack can be detected, and quantifies the performance degradation that an attacker that seeks to be undetected or stealthy can introduce.

math.OC↗

Topological Principles of Control in Dynamical Network Systems

Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology, supporting a variety of system-wide dynamical behaviors such as synchronization. While descriptions of these behaviors are important, they are only a first step towards understanding the relationship between network topology and system behavior, and harnessing that relationship to optimally control the system's function. Here, we use linear network control theory to analytically relate the topology of a subset of structural connections (those linking driver nodes to non-driver nodes) to the minimum energy required to control networked systems. As opposed to the numerical computations of control energy, our accurate closed-form expressions yield general structural features in networks that require significantly more or less energy to control, providing topological principles for the design and modification of network behavior. To illustrate the utility of the mathematics, we apply this approach to high-resolution connectomes recently reconstructed from drosophila, mouse, and human brains. We use these principles to show that connectomes of increasingly complex species are wired to reduce control energy. We then use the analytical expressions we derive to perform targeted manipulation of the brain's control profile by removing single edges in the network, a manipulation that is accessible to current clinical techniques in patients with neurological disorders. Cross-species comparisons suggest an advantage of the human brain in supporting diverse network dynamics with small energetic costs, while remaining unexpectedly robust to perturbations. Our results ground the expectation of a system's dynamical behavior in its network architecture.

q-bio.NC↗

Brain and Cognitive Reserve: Translation via Network Control Theory

Traditional approaches to understanding the brain's resilience to neuropathology have identified neurophysiological variables, often described as brain or cognitive 'reserve,' associated with better outcomes. However, mechanisms of function and resilience in large-scale brain networks remain poorly understood. Dynamic network theory may provide a basis for substantive advances in understanding functional resilience in the human brain. In this perspective, we describe recent theoretical approaches from network control theory as a framework for investigating network level mechanisms underlying cognitive function and the dynamics of neuroplasticity in the human brain. We describe the theoretical opportunities offered by the application of network control theory at the level of the human connectome to understand cognitive resilience and inform translational intervention.

q-bio.NC↗