Màster Oficial - Física dels Sistemes Complexos i Biofísica

URI permanent per a aquesta col·leccióhttps://hdl.handle.net/2445/189184

Treballs Finals del Màster en Física dels Sistemes Complexos i Biofísica de la Facultat de Física de la Universitat de Barcelona.

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Sherrington-Kirkpatrick model analysis of fMRI-BOLD data from Alzheimer’s patients and healthy controls
(2024-07) Damiani, Giada; Ruffini, Giulio; Levis, Demian; Vohryzek, Jakub
This thesis aimed to advance the understanding of Alzheimer’s disease (AD) using computational modelling tools rooted in statistical physics. Specifically, pseudo-likelihood maximisation of a spinglass model was employed to extract coupling matrices J from fMRI-BOLD data of elderly subjects diagnosed with AD and healthy controls (HC). Data was sourced from participants in the European Project Neurotwin’s clinical trial, where AD patients undergo brain stimulation as a potential treatment, and from the AD Neurological Initiative (ADNI) database for the healthy controls. The derived coupling matrices were then compared between conditions to identify differences in brain connectivity. The research also explored the criticality of these systems using Metropolis simulations to assess phase transitions and critical temperatures. First, the focus was on extracting and analysing the J matrices. It was found that the J homotopic connectivity decreased in the AD subjects compared to the healthy ones with weak statistical significance (p = 0.0496), a finding consistent with other studies on inter-hemispheric connectivity disruption in AD. Moreover, the J matrices’ standard deviation significantly differed between the HC and AD groups (p = 0.0039). Additionally, brain areas with the highest change in J across conditions aligned with regions previously identified in functional connectivity studies of AD. Then, the spin-glass systems — defined by the condition-specific J’s — were simulated with the Metropolis algorithm. The critical temperature was found to be lower in the AD spin lattice compared to the HC spin lattice, suggesting that the AD state is closer to a disordered (paramagnetic) phase, which aligns with the hypothesis that weaker inter-parcel connections in AD may lead to a state nearer to the paramagnetic phase transition. The research highlighted the potential of the J coupling matrix to capture structural features and homotopic connections, which can serve as a synthetic brain connectome when dMRI is unavailable. Future work will include using longer data and other type of data (e.g. new healthy controls, and pre- and post-stimulation data), and the optimisation of the sparsity value in the extraction of J. Also, the criticality analysis may be improved by building a theoretical phase diagram based on J characteristics.
Dynamical mean-field theory for non-reciprocal spin-glasses
(2024-06) Garcés Ortiz, Ot; Levis, Demian
In out-of-equilibrium systems, the lack of reciprocity in interactions is more the rule than the exception. Non-reciprocal interactions arise generically in out-of-equilibrium systems, such as metamaterials, neural networks, or ecosystems. In the context of glassy systems, it is known that they are crucial in the process of learning in neural networks but their role in glassy dynamics is still widely debated. In this work, we develop a generalization of a dynamical mean-field theory of spinglass models which includes non-reciprocal interactions among spins, with full analytical detail. Furthermore, we show how the dynamics of mean-field spin-glasses are quantitatively and qualitatively modified when considering non-reciprocal interactions, focusing on the high-temperature relaxational dynamics. Our theory predicts critical slowing down of the dynamics and glass melting when considering weakly non-reciprocal interactions, although we suspect that new physics can be further explored beyond that limit
Floquet stability analysis of a wall-bounded oscillatory flow of a viscoelastic fluid
(2024-09) Codina Vilanova, Arnau; Ortín, Jordi, 1959-
Oscillatory fluid flows play an important role in fluid mechanics for their long history and numerous applications. In this work we will start off from Stokes’ second problem of the boundary layer adjacent to an oscillatory wall in order to study the wall-bounded zero-mean oscillatory flow of a viscoelastic fluid placed between two parallel plates oscillating synchronously. From related experiments on the oscillatory flow of a viscoelastic solution in a vertical tube we know that the rectilinear flow at small forcing amplitudes gives rise to a secondary flow with toroidal vortices at larger amplitudes. Our purpose is to provide a theoretical understanding of this instability in a simpler setup. We analytically solve the governing equations of the periodic base flow, and carry out a Floquet linear stability analysis of the stress and velocity fields. We apply the Galerkin spectral method to numerically solve the corresponding generalized eigenvalue problem, and provide instability thresholds in forcing amplitude for both resonant and non-resonant forcing frequencies
Self-regulation of a network of Kuramoto oscillators
(2023-05) Pirker Díaz, Paula; Díaz Guilera, Albert; Soriano i Fradera, Jordi
Persistent global synchronization of a neuronal network is considered a pathological, undesired state. Such as synchronization is often caused by the loss of neurons that regulate network dynamics, or cells that assist these neurons such as glial cells. Here we propose a self-regulation model in the framework of complex networks in which we assume that, for sake of simplicity, glial cells prevent the over synchronization of the neuronal network. We have considered a brain-like network characterized by a modular organization combined with a dynamic description of the nodes as Kuramoto oscillators. We have applied a self-regulation mechanism to keep local synchronization while avoiding global synchronization at the same time. To do so, we have added self-regulation to the system by switching off for a certain period of time a selection of edges that link nodes showing a synchronization above a certain threshold. Despite the simplicity of the approximation, our results show that it is possible to maintain a high local synchronization (module level) while keeping low the global one. In addition, characteristic dynamic patterns have been observed when analysing synchronization between modules in large modular networks. Our work could help to understand the effects of localized regulatory actions on modular systems with synchronous phenomena, such as neuroscience and other fields.
Non-reciprocal interactions in the XY Model
(2023-06) Mazzanti Tarancón, David; Levis, Demian
This work focuses on the investigation of non-reciprocal interactions in the XY Model using the Kuramoto model of synchronization in the overdamped limit. Initially, we provide partial results of the reciprocal XY Model by examining the spatial correlation function and the transition temperature. Through a comparison of simulation and theoretical results, we gain insights into the critical behavior of the model. To extend the analysis, we introduce non-reciprocal interactions using the Kuramoto model in the overdamped regime, which offers a nonlinear mathematical framework for understanding the dynamics of the system. This is particularly relevant as the reciprocal XY Model lacks a Hamiltonian description. By incorporating non-reciprocal interactions, we observe that the system does not undergo a topological phase transition. Instead, a dynamic analysis reveals, under certain initial distribution and conditions, the emergence of waves and their characteristic propagation. We explore these phenomena in both one-dimensional and two-dimensional scenarios, demonstrating that the waves propagate with a linear velocity and exhibit a linear dispersion relation
Mapping opinion landscapes: analyzing network structures in climate change debates on Twitter
(2023-08) Castillo Uviña, Javier; Prignano, Luce; Cozzo, Emanuele
Society is a complex system, and studying it is challenging. We need to develop mechanisms to obtain data for statistical analysis. Our goal is to collect a substantial amount of data on a subject while also understanding how human opinion is structured and how it evolves over time, providing us with additional insights. With the advent of online social platforms, we have the opportunity to study how users generate content (data) and how others interact with this content. This presents us with a perfect tool and opens up an entire universe of possibilities. In this project, we aim to characterize opinions on the issue of climate change using Twitter data [1]. The focus of this research lies in developing a method to study the structure of human opinions. To achieve this, we will analyze three Twitter discussions where users are expected to take positions on climate change-related policies, express their opinion about COP Meetings, and discuss the creation of the 2030 Agenda among Catalan and Spanish speakers. By capturing these data based on user opinions, we will conduct a study by analyzing the networks that shape these opinions and interactions. Through this analysis, we hope to uncover the underlying structure of a Twitter discussion within the framework of complex networks. Additionally, we will attempt to identify if distinct communities are formed and who the most influential accounts are in each case. We aim to assess the polarization of the network to determine if there are two clear sides [2]. On one hand, we anticipate users who support or oppose the climate change issue, and on the other hand, we aim to identify a ”denialist” side that opposes the concept of climate change. Expanding our study, we can also track the evolution of public opinion. Nevertheless, we must acknowledge certain limitations. Not everyone uses Twitter, resulting in incomplete representation of all communities. Furthermore, such platforms do not necessarily mirror real-world interactions, yet they do offer a robust reflection of public opinion beyond the screens. The results have been less encouraging in terms of polarization. For most of the cases studied, we observed a dominant structure that does not exhibit clear polarization for or against the idea of climate change. However, we did identify another noteworthy type of structure worth discussing. In conclusion, the hypothesis that the ”denialist” side possesses significant enough support to disrupt other types of structures has not proven accurate. Nonetheless, we discovered that these debates are often steered by highly influential hubs. Analyzing these hubs can provide us with a solid understanding of the current opinion landscape.
Statistical Mechanics of non−reciprocally interacting Ising spins
(2023-07) Garcés Ortiz, Adrià; Levis, Demian
Non−reciprocal interactions are present in a large number of out−of−equilibrium systems such as active matter, social, ecological and non−Hermitian quantum systems. They are believed to be responsible for non−equilibrium phase transitions and are, still, an open topic of major interest in recent research. In this work, we present a generalization of the Ising model that includes non−reciprocal interactions among spins and analytically characterize the mean field stationary behaviour of two proposed models that incorporate non−reciprocal interactions. We show how the models exhibit a first order phase transition and how their mean field solutions are no longer spin−inversion symmetric. Furthermore, we also study d = 1 spin chains with nearest neighbours interactions, and derive the evolution equations for the first two moments. Finally, we discuss the dynamical equations for the proposed models. The derived dynamic equations signal the presence of steady currents, e.g. traveling states, in non−reciprocally interacting spin chains.
Inverse inference of a quantum spin glass
(2023-06) Torres Hugas, Lluís; Palassini, Matteo
In statistical physics, inverse problems arise when we need to design a manybody system with particular desired properties. Rather than calculating observables based on known model parameters, inverse problems involve inferring the parameters of a model based on observations. In my final degree project, we studied the inverse problem for the Viana-Bray spin glass model with a discrete distribution of the couplings, and with simulated annealing, we tried to infer the couplings of the system with the maximum pseudolikelihood method. In this project, we studied the inverse problem for the quantum Viana-Bray spin glass model with the same coupling distribution. The goal was to extend the pseudolikelihood maximization approach to a quantum spin glass with a transverse field since most research efforts have focused on the classical version and hardly anything is known about its quantum counterpart. To achieve this, we generated equilibrium configurations from the quantum partition function using quantum Monte Carlo techniques, and then we employed simulated annealing to maximize the pseudolikelihood function and infer the couplings of the system. We derived a modified version of the pseudolikelihood function from the initial proposal after closely following the approach used in the classical case. We found that when introducing the transverse field in the system, the algorithm was still able to infer the couplings; however, because of how the quantum system is treated, certain modifications had to be made to the pseudolikelihood method. Moreover, as in the classical case, we found that the algorithm performed the best around the phase transition boundaries.
Mesoscale Building Blocks of Pedestrian Mobility: a Discrete Vector Field Approach
(2023-06) Benassai Dalmau, Robert; Borge-Holthoefer, Javier; Solé Ribalta, Albert; Perelló, Josep, 1974-
Understanding and characterising pedestrian mobility is crucial to develop sustainable cities. While classical statistical analysis and diffusion models are commonly used to analyze human trajectories either at the microscopic (e.g. sidewalk flows) or macroscopic scale (e.g. origindestination matrices), they may not be suitable for capturing the nuances and intricacies of mobility patterns at the mesoscale. To overcome these limitations, the problem is approached by leveraging on vector field theory with the aim to describe how the urban geometry and structure of sidewalk networks affect pedestrian mobility flows. Considering the particularities of pedestrian movement (e.g. limited travel range) the discrete- (DTRW) and continuous-time (CTRW) random walk dynamics have been implemented to retrieve a baseline agent-based net flow along the edges of pedestrian networks with a temporal budget of mobility. These flows are subsequently interpreted as discrete vector fields. The Helmholtz-Hodge decomposition (HHD) allows the partition of vector fields into three well-defined patterns: cyclic (solenoidal and harmonic) and divergent/convergent (gradient) components. Results show that when mobility is agnostic to edge lengths (DTRW), that is, when the time budget is spent equivalently along the edges (steps), high-density regions with larger degree nodes show attractiveness, as existing literature already describes. However, when the time budget is spent proportionally to the edge lengths (CTRWs), the same regions show a repulsive effect. Intermediate regimes arise as well in the continuum between these two processes. An analytical description of both DTRWs and CTRWs has been developed to accurately estimate the gradient components of the vector fields. However, the presented deterministic developments do not predict the presence of the cyclic components as they seem to emerge from the stochasticity of the process. To validate this idea, the variance of the cyclic component, or its mean squared flow (MSF), has been analysed. Results show that the MSF grows linearly with the temporal budget of the walkers. This behaviour is similar to the characteristic linear temporal evolution of the Mean-Squared Displacement (MSD) in random walks and Brownian motion. Ultimately, this work contributes to the existing description and understanding of the behaviour of different random walk dynamics on spatially embedded graphs, providing a baseline to understand and analyse pedestrian mobility on sidewalk networks in future works.
Viscosity of blood at the microscale infected by Plasmodium falciparum
(2023-06) Masó Castro, Nil; Hernández Machado, Aurora; Portillo Obando, Hernando A. del
The viscosity of blood infected by malaria is studied using a microfluidic-based rheometer. Malaria is an infectious disease that causes numerous infectious worldwide, being one of the most prevalent diseases. The findings provide insights into the physical properties of the parasite, with potential implications for malaria diagnostics. The microrheometer allows to perform experiments and obtain the viscosity curve as a function of the shear rate using low volumes of blood, contrary to commercial viscosimeters. The viscosity of blood is well characterized using a power-law model, which only needs two parameters to be defined. Blood samples in culture media (RPMI) and at a physiological temperature were analysed. Moreover, blood samples infected with Plasmodium falciparum with different percentage of infected red blood cells were analyzed. Results show a shift towards a Newtonian behaviour as parasitemia increased, losing the characteristic shear-thinning behaviour of blood. This study also examines the influence of mature parasite stages on blood viscosity, revealing their contribution to the observed changes. These findings have two implications. Firstly, we enhance our understanding of the rheological alterations caused by malaria infection, which can aid in developing improved diagnostic tools based on rheological markers. Secondly, the surprising results obtained contribute to the knowledge about the effects of the parasite as the sample ages at 37◦C, which ultimately could aid the development of new malaria treatment techniques.
Developing modified Lotka-Volterra models to simulate in vitro clonal dynamics
(2023-06) Jurado Rodríguez, Imanol; Ibañes Miguez, Marta; Alemany i Arias, Anna
During the last decades, novel technological approaches have allowed uniquely labelling cells by integrating random barcodes in their DNAs. Such barcodes are permanent and are inherited by the cellular offspring. Thus, DNA sequencing permits their reading in order to identify those cells with common ancestors. This process, known as lineage tracing, enables the study of complex biological processes such as embryonic development, tissue homeostasis or even cancer metastasis with clonal, and even single cell, resolution. Here we aim to reveal the foundations behind the experimental results of clonal dynamics of colon cancer organoids through in silico simulations. We formulated three modified Lotka-Volterra models that allow us to investigate the role of clonal carrying capacity, proliferation rates and inter-clonal interaction network to achieve our purpose. The results show the vital role of partial interactions among clones and the importance of implementing nonequilibrium networks, i.e. architectures of interactions that vary in time. Furthermore, our results reveal a direct relationship between the harvesting time and the average number of surviving species at the end of the experiment, suggesting that external perturbations to the system can have big effects to clonal dynamics
The community structure of the geometric soft configuration model
(2023-08) González Gea, Viktor; Serrano Moral, Ma. Ángeles (María Ángeles)
Network models serve as an approach to explain the properties of real networks. The geometric soft configuration model, also known as the S1/H2 model, can be used to generate synthetic networks that replicate many features of real complex networks —sparsity, a heterogeneous degree distribution, the small world property, a high level of clustering, and more— while randomizing others. In this work, a range of parameters of the S1/H2 model has been explored, satisfactorily manipulating the level of heterogeneity of the degree distribution with the parameter γ and the level of clustering with the parameter β, in order to probe the level of control that is possible to attain in the generation of random networks. Recent theoretical evidence supports that hyperbolic networks like this one possess topological community structure, up to being maximally modular in the thermodynamic limit, even if the model is not purposefully equipped with geometric communities. The community structure of the S1/H2 model was put under scrutiny using computational simulations, revealing that synthetic networks generated according to it could be consistently partitioned with a high modularity. The modularity of equally sized angular partitions of the generated random networks was evaluated, confirming that this model tends to maximal modularity in the limit of large network size and in a regime of high clustering. The Louvain method for community detection in the topology of complex networks using modularity maximization was employed as well, giving rise to no significantly better results in comparison with the initial approach. With the S1/H2 model, it was also explored how much of the community structure of real networks can be attributed to the effect of clustering in combination with their heterogeneous degree distribution —networks with these two features are called hierarchical—. The results suggest that the communities detected in some real networks are, in part or totally, a byproduct of their hierarchicity.
Validation and Refinement of a Laminar Neural Mass Model Using in vivo Mice Data
(2023-06) Moreno Fina, Martina; Clusella Corberó, Pau; Sánchez-Todo, Roser; Soriano i Fradera, Jordi
Gamma oscillations (30-80 Hz) play a crucial role in cognitive functions and are associated with neurological disorders, including Alzheimer’s disease. Non-invasive brain stimulation techniques, such as 40 Hz transcranial alternating current stimulation (tACS), offer potential in modulating these oscillations and impact cognitive functions. The complexity of the brain, however, necessitates the use of advanced models for effective understanding and the development of therapies. This study aims to validate a framework combining Neural Mass Models (NMMs) with volume conduction physics that takes into account the brain’s physical properties and the distribution of synapses across cortical layers. The validation involves predicting a synaptic distribution across various neuronal groups and employing a Genetic Algorithm (GA) to iteratively refine the model to match experimental data. Key findings include the ability of the NMM to achieve greater similarity with experimental results by varying stochastic noise and the dominance of gamma and alpha oscillations in experimental data aligning well with model predictions. The GA also shows robustness in fitting the model to experimental data, and the predicted synaptic distribution is evaluated against existing literature for physiological accuracy. Despite limitations, our enhanced NMM provides valuable insights into cortical layer interactions, contributing to the understanding of human brain function and the development of treatments for neurological disorders.
Dynamics and critical behaviour of neuronal cultures grown on topographical patterns with fractal structure
(2023-06) Olives Verger, Mireia; Soriano i Fradera, Jordi
Neuronal cultures are an excellent experimental tool to study the collective behaviour of neuronal ensembles, providing information on the principles of synaptic functioning and propagation. However, neurons cultured on flat surfaces present limitations in terms of their functionality, as they exhibit a synchronous dynamic behaviour that differs from the much richer repertoire of activity of the brain. In order to address this limitation and help developing better in vitro tools to model the brain, here we studied the capacity to break off synchrony by modulating the spatial arrangement of neurons in the substrate they grow. For that, we designed polydimethylsiloxane (PDMS) topographical patterns with fractal geometry and used them as the substrate to grow neurons, with the goal to break the isotropy in connectivity and enrich dynamics. Neuronal activity was recorded with calcium fluorescence imaging and data analysed in the context of criticality, which was inspired by recent findings suggesting that a rich structural connectivity in the brain is behind its functioning at the edge of criticality. We observed that, first, neurons cultured on fractal patterns exhibited richer and more complex dynamics as compared to standard cultures; and, second, that an analysis of the data using the renormalisation group approach, revealed the presence of scale invariance and typical features of systems poised at criticality. Our study is a multidisciplinary endeavour that combined experimental, theoretical and data analysis aspects to validate the hypothesis of the existence of a self-organised criticality in living neuronal networks, from cultures up to the brain.
Assembly and dynamics of propelling ferromagnetic colloids
(2023-06) Manzano González, Andrés Javier; Junot, Gaspard; Tierno, Pietro
Active colloids is a growing field of research that studies the emergent phenomena exhibited in systems of self-propelling particles as a result of the interactions between them that could not be observed if these components were isolated. These phenomena can be observed in a wide variety of systems. In this work, I show how a collection of oscillating colloidal rotors, or simply, shakers, immersed in a viscoelastic fluid, specifically, a solution of polyacrylamide (PAAM), can display this behaviour, forming complex zig-zag dynamic bands that grow linearly in time. I have investigated the dynamics of this band growth for two different PAAM concentrations, as well as the hydrodynamic flow around these shakers for both cases. This helps understanding the complex dynamics of these fluids, having implications in soft matter physics and microfluidics and in biophysics
Ancient regional transportation infrastructures as co-evolving complex systems: a multiplex network approach
(2022-07) Candelas Peñalba, Pablo; Prignano, Luce
Network theory has demonstrated to be an invaluable tool for studying complex systems, and it has been widely used in many disciplines. Archaeology is no exception. Ancient transportation infrastructures (TIs) are often represented as networks of interacting settlements. However, these various TIs are different in nature, and the network they form requires a different approach. Here we show that ancient TIs as a whole can be characterized by a multiplex. After an analysis of the dynamic performance and structural properties of the individual road and river networks of Southern Etruria and Latium Vetus in the Iron Age (950 − 580 BC), we overlap both TIs by regarding them as layers in a multiplex. We then study the multiplex with the aim to assess how good the interplay between layers is. Our work thus serves as a case study of an empirical multiplex network. We prove that the tools we use are good to characterize ancient TIs as one multiplex and could become very powerful if further studied and refined.
Entropy production of DNA-translocating molecular motors
(2022-06) Rodríguez Franco, Víctor; Mañosas Castejón, María; Ritort Farran, Fèlix
Helicases are molecular motors that convert the chemical energy of ATP hydrolysis into mechanical work to move along one strand of DNA and unzip the double helix. Using magnetic tweezers (MT) we follow the activity of a single helicase unzipping a DNA hairpin. From these experiments we can characterize the enzyme motion (e.g. velocity and diffusion) but the ATP hydrolysis reaction is not directly measured. Here we investigate whether we can infer information about the helicase chemical cycle from our helicase displacement data by using non-equilibrium relations such as the thermodynamic uncertainty relation (TUR) and the fluctuation theorem (FT) for entropy production. To address this question, we use the random walk formalism to model the helicase motion and we analytically derive expressions for the TUR and the FT. The derived theoretical results are verified with simulations of the model and compared with experiments. We find qualitatively agreement between experiments and theory. However, some important differences are observed. In particular, the distributions of the helicase displacement deviates from the Gaussian distribution predicted by the theory and the experimental test of the FT fails. We conclude that a refined model is needed to better describe the real experimental system
Noise induced phenomena in ecological models
(2022-06) Colet Díaz, Clara; Miguel López, María del Carmen
Understanding population dynamics, and in particular, population cycles is one of the central issues in ecology. In this work we study noise induced phenomena in generalized Lotka-Volterra ecological models and we show how a stochastic model for population dynamics can give rise to periodic cyclic behaviour in the presence of intrinsic noise. We will show how the intrinsic noise in a prey-predator dynamics including intra-specific, or logistic auto-regulatory, interactions gives rise to a resonant frequency in the power spectrum characterizing the system evolution, but at the same time, we show that there are other types of interactions among species where a resonant frequency does not appear. Furthermore, we analyze the effects of random transport between different ecological patches or metapopulations and see that cyclic behaviours can appear, if a prey-predator dynamics is imposed, or disappear
The odd weight of granular packings: Effect of grain geometry
(2022-07) Zamorano Vega, Iker; Planet Latorre, Ramon; Fernandez-Nieves, Alberto
Granular materials are collections of solid grains that exhibit unusual mechanical properties. In 1895, the engineer Janssen found that when filling a silo with corn grains, the pressure at the bottom of the column rather than increasing linearly with the added mass showed a saturation [5]. Recently, this experiment has been repeated using spherical grains on narrow containers, where the pressure at the bottom exhibits an overshoot region, meaning that the apparent mass is larger than the added mass before saturating [14]. In this work we revisit those experiments now using two different grain geometries, being oblate and prolate grains, with the aim of studying its behaviour on narrow containers and if the reversed Janssen effect is still observed using these grain geometries. It is found that for tubes with large diameters both, oblate and prolate particles, exhibit the saturation of mass for large added mass, the qualitative response described by Janssen. As the diameter of the tube decreases, the overshoot regions gain more importance at intermediate added masses. However, the model introduced in [14] for spheres does not describe properly the results obtained. Now, the magnitude of the overshoot decays faster with the increasing size of the container. Furthermore, it is observed that the average packing fraction of the granular columns does increase until saturating, which may be related to the saturation of the pressure on the granular column.
Motility-Induced Phase Separation of harmonic Active Ornstein-Uhlenbeck particles fulfilling Detailed Balance
(2022-07) Tetro, Lior; Levis, Demian
Active matter constitutes a class of nonequilibrium systems which has attracted a lot of attention over the past decades, and Motility-Induced Phase Separation (MIPS) lies among one of its most salient collective phenomena. Although MIPS has been studied in depth, the question of whether this active phase transition can only occur in the presence of out-of-equilibrium fluctuations remains open. In this work, we numerically show that harmonic Active Ornstein-Uhlenbeck Particles (AOUP), with an equilibrium dynamics fulfilling detailed balance, undergo MIPS. We studied analytically 2-body interactions, identifying an effective attraction increasing with activity, to show that n-body effects are needed in order to account for the nature of the transition, and in particular, of the dense phase. Finally, a recursive method to obtain a multibody expansion of the partition function for the complete system is developed

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