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Article ; Online: Bridging functional and anatomical neural connectivity through cluster synchronization.

Baruzzi, Valentina / Lodi, Matteo / Sorrentino, Francesco / Storace, Marco

2023 Volume 13, Issue 1, Page(s) 22430

Abstract: The dynamics of the brain results from the complex interplay of several neural populations and is affected by both the individual dynamics of these areas and their connection structure. Hence, a fundamental challenge is to derive models of the brain that ...

Abstract	The dynamics of the brain results from the complex interplay of several neural populations and is affected by both the individual dynamics of these areas and their connection structure. Hence, a fundamental challenge is to derive models of the brain that reproduce both structural and functional features measured experimentally. Our work combines neuroimaging data, such as dMRI, which provides information on the structure of the anatomical connectomes, and fMRI, which detects patterns of approximate synchronous activity between brain areas. We employ cluster synchronization as a tool to integrate the imaging data of a subject into a coherent model, which reconciles structural and dynamic information. By using data-driven and model-based approaches, we refine the structural connectivity matrix in agreement with experimentally observed clusters of brain areas that display coherent activity. The proposed approach leverages the assumption of homogeneous brain areas; we show the robustness of this approach when heterogeneity between the brain areas is introduced in the form of noise, parameter mismatches, and connection delays. As a proof of concept, we apply this approach to MRI data of a healthy adult at resting state.
MeSH term(s)	Models, Neurological ; Brain/diagnostic imaging ; Magnetic Resonance Imaging/methods ; Brain Mapping/methods ; Connectome/methods ; Neural Pathways ; Nerve Net/diagnostic imaging
Language	English
Publishing date	2023-12-17
Publishing country	England
Document type	Journal Article
ZDB-ID	2615211-3
ISSN	2045-2322 ; 2045-2322
ISSN (online)	2045-2322
ISSN	2045-2322
DOI	10.1038/s41598-023-49746-2
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Article ; Online: Time-shift selection for reservoir computing using a rank-revealing QR algorithm.

Hart, Joseph D / Sorrentino, Francesco / Carroll, Thomas L

Chaos (Woodbury, N.Y.)

2023 Volume 33, Issue 4

Abstract: Reservoir computing, a recurrent neural network paradigm in which only the output layer is trained, has demonstrated remarkable performance on tasks such as prediction and control of nonlinear systems. Recently, it was demonstrated that adding time- ... ...

Abstract	Reservoir computing, a recurrent neural network paradigm in which only the output layer is trained, has demonstrated remarkable performance on tasks such as prediction and control of nonlinear systems. Recently, it was demonstrated that adding time-shifts to the signals generated by a reservoir can provide large improvements in performance accuracy. In this work, we present a technique to choose the time-shifts by maximizing the rank of the reservoir matrix using a rank-revealing QR algorithm. This technique, which is not task dependent, does not require a model of the system and, therefore, is directly applicable to analog hardware reservoir computers. We demonstrate our time-shift selection technique on two types of reservoir computer: an optoelectronic reservoir computer and the traditional recurrent network with a t a n h activation function. We find that our technique provides improved accuracy over random time-shift selection in essentially all cases.
Language	English
Publishing date	2023-04-05
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0141251
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Article: Algebraic Decomposition of Model Predictive Control Problems.

Nazerian, Amirhossein / Vides, Fredy / Sorrentino, Francesco

IEEE control systems letters

2023 Volume 7, Page(s) 1441–1446

Abstract: This paper is concerned with the application of model predictive control (MPC) to large-scale linear dynamical systems with linear inequality constraints. A decomposition is proposed of such problems into sets of independent MPCs of lower dimensions that ...

Abstract	This paper is concerned with the application of model predictive control (MPC) to large-scale linear dynamical systems with linear inequality constraints. A decomposition is proposed of such problems into sets of independent MPCs of lower dimensions that preserves all information about the system, cost function, and constraints. Different from previous work, the constraints are incorporated in the decomposition procedure, which is attained by generalizing a previously developed technique to simultaneously block diagonalize a set of matrices. This approach is applied to practical examples involving large-scale systems with inequality constraints. It is shown that the computational complexity and the CPU time required to solve the transformed MPC problems are lower than those required by the solution of the original MPC problem.
Language	English
Publishing date	2023-03-03
Publishing country	United States
Document type	Journal Article
ISSN	2475-1456
ISSN	2475-1456
DOI	10.1109/lcsys.2023.3252162
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Article ; Online: Controlling network ensembles.

Klickstein, Isaac / Sorrentino, Francesco

Nature communications

2021 Volume 12, Issue 1, Page(s) 1884

Abstract: The field of optimal control typically requires the assumption of perfect knowledge of the system one desires to control, which is an unrealistic assumption for biological systems, or networks, typically affected by high levels of uncertainty. Here, we ... ...

Abstract	The field of optimal control typically requires the assumption of perfect knowledge of the system one desires to control, which is an unrealistic assumption for biological systems, or networks, typically affected by high levels of uncertainty. Here, we investigate the minimum energy control of network ensembles, which may take one of a number of possible realizations. We ensure the controller derived can perform the desired control with a tunable amount of accuracy and we study how the control energy and the overall control cost scale with the number of possible realizations. Our focus is in characterizing the solution of the optimal control problem in the limit in which the systems are drawn from a continuous distribution, and in particular, how to properly pose the weighting terms in the objective function. We verify the theory in three examples of interest: a unidirectional chain network with uncertain edge weights and self-loop weights, a network where each edge weight is drawn from a given distribution, and the Jacobian of the dynamics corresponding to the cell signaling network of autophagy in the presence of uncertain parameters.
MeSH term(s)	Autophagy/physiology ; Computer Simulation ; Models, Theoretical ; Neural Networks, Computer ; Nonlinear Dynamics ; Systems Analysis
Language	English
Publishing date	2021-03-25
Publishing country	England
Document type	Journal Article ; Research Support, U.S. Gov't, Non-P.H.S.
ZDB-ID	2553671-0
ISSN	2041-1723 ; 2041-1723
ISSN (online)	2041-1723
ISSN	2041-1723
DOI	10.1038/s41467-021-22172-6
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Article ; Online: Group synchrony, parameter mismatches, and intragroup connections.

Panahi, Shirin / Sorrentino, Francesco

Physical review. E

2021 Volume 104, Issue 5-1, Page(s) 54314

Abstract: Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time evolution, but systems in different groups synchronizing ... ...

Abstract	Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time evolution, but systems in different groups synchronizing on distinct time evolutions. Group synchronization has been observed and characterized when the systems in each group are identical and the couplings between the systems satisfy specific conditions. By relaxing these constraints and allowing them to be satisfied in an approximate rather than exact way, we observe that stable group synchronization may still occur in the presence of small deviations of the parameters of the individual systems and of the couplings from their nominal values. We analyze this case and provide necessary and sufficient conditions for stability through a master stability function approach, which also allows us to quantify the synchronization error. We also investigate the stability of group synchronization in the presence of intragroup connections and for this case extend some of the existing results in the literature. Our analysis points out a broader class of matrices describing intragroup connections for which the stability problem can be reduced in a low-dimensional form.
Language	English
Publishing date	2021-12-27
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.104.054314
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Article ; Online: Synchronizing chaos using reservoir computing.

Nazerian, Amirhossein / Nathe, Chad / Hart, Joseph D / Sorrentino, Francesco

Chaos (Woodbury, N.Y.)

2023 Volume 33, Issue 10

Abstract: We attempt to achieve complete synchronization between a drive system unidirectionally coupled with a response system, under the assumption that limited knowledge on the states of the drive is available at the response. Machine-learning techniques have ... ...

Abstract	We attempt to achieve complete synchronization between a drive system unidirectionally coupled with a response system, under the assumption that limited knowledge on the states of the drive is available at the response. Machine-learning techniques have been previously implemented to estimate the states of a dynamical system from limited measurements. We consider situations in which knowledge of the non-measurable states of the drive system is needed in order for the response system to synchronize with the drive. We use a reservoir computer to estimate the non-measurable states of the drive system from its measured states and then employ these measured states to achieve complete synchronization of the response system with the drive.
Language	English
Publishing date	2023-10-11
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0161076
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Article ; Online: Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices.

Nazerian, Amirhossein / Bhatta, Kshitij / Sorrentino, Francesco

IEEE open journal of control systems

2022 Volume 2, Page(s) 24–35

Abstract: In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition ... ...

Abstract	In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is 'exact' in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.
Language	English
Publishing date	2022-12-22
Publishing country	United States
Document type	Journal Article
ISSN	2694-085X
ISSN (online)	2694-085X
DOI	10.1109/ojcsys.2022.3231553
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Article: Supermodal Decomposition of the Linear Swing Equation for Multilayer Networks.

Bhatta, Kshitij / Nazerian, Amirhossein / Sorrentino, Francesco

IEEE access : practical innovations, open solutions

2022 Volume 10, Page(s) 72658–72670

Abstract: We study the swing equation in the case of a multilayer network in which generators and motors are modeled differently; namely, the model for each generator is given by second order dynamics and the model for each motor is given by first order dynamics. ... ...

Abstract	We study the swing equation in the case of a multilayer network in which generators and motors are modeled differently; namely, the model for each generator is given by second order dynamics and the model for each motor is given by first order dynamics. We also remove the commonly used assumption of equal damping coefficients in the second order dynamics. Under these general conditions, we are able to obtain a decomposition of the linear swing equation into independent modes describing the propagation of small perturbations. In the process, we identify symmetries affecting the structure and dynamics of the multilayer network and derive an essential model based on a 'quotient network.' We then compare the dynamics of the full network and that of the quotient network and obtain a modal decomposition of the error dynamics. We also provide a method to quantify the steady-state error and the maximum overshoot error. Two case studies are presented to illustrate application of our method.
Language	English
Publishing date	2022-07-04
Publishing country	United States
Document type	Journal Article
ZDB-ID	2687964-5
ISSN	2169-3536
ISSN	2169-3536
DOI	10.1109/access.2022.3188392
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Article ; Online: Pinning control of networks: Dimensionality reduction through simultaneous block-diagonalization of matrices.

Panahi, Shirin / Lodi, Matteo / Storace, Marco / Sorrentino, Francesco

Chaos (Woodbury, N.Y.)

2022 Volume 32, Issue 11, Page(s) 113111

Abstract: In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the "pinned nodes." Previous work ... ...

Abstract	In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the "pinned nodes." Previous work has mainly focused on the case that (i) and (ii) are of the same type. We decouple the stability analysis of the target synchronous solution into subproblems of the lowest dimension by using the techniques of simultaneous block diagonalization of matrices. Interestingly, we obtain two different types of blocks, driven and undriven. The overall dimension of the driven blocks is equal to the dimension of an appropriately defined controllable subspace, while all the remaining undriven blocks are scalar. Our main result is a decomposition of the stability problem into four independent sets of equations, which we call quotient controllable, quotient uncontrollable, redundant controllable, and redundant uncontrollable. Our analysis shows that the number and location of the pinned nodes affect the number and the dimension of each set of equations. We also observe that in a large variety of complex networks, the stability of the target synchronous solution is de facto only determined by a single quotient controllable block.
Language	English
Publishing date	2022-11-28
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0090095
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Book ; Online: Synchronization in networked systems with large parameter heterogeneity

Nazerian, Amirhossein / Panahi, Shirin / Sorrentino, Francesco

2023

Abstract: Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the case of small ... ...

Abstract	Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the case of small parametric mismatches, we consider the general case that parameter mismatches may be large. We present a unified stability analysis that predicts why the range of stability of the synchronous solution either increases or decreases with parameter heterogeneity for a given network. We introduce a parametric approach, based on the definition of a curvature contribution function, which allows us to estimate the effect of mismatches on the stability of the synchronous solution in terms of contributions of pairs of eigenvalues of the Laplacian. For cases in which synchronization occurs in a bounded interval of a parameter, we study the effects of parameter heterogeneity on both transitions (asynchronous to synchronous and synchronous to asynchronous.) Comment: Accepted for publication in Communications Physics
Keywords	Electrical Engineering and Systems Science - Systems and Control ; Nonlinear Sciences - Chaotic Dynamics
Subject code	515
Publishing date	2023-04-16
Publishing country	us
Document type	Book ; Online
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