arXiv subjects

Murilo S. Baptista

Publications and source records attributed to Murilo S. Baptista.

At least 19 recordsLinked to original sources

arXiv2026

Ptolemy's Equant Equates to a Universal Dynamical Clock via Machine Learning

Oscillatory dynamics arise ubiquitously in nonlinear systems, yet identifying a physically interpretable phase and phase dynamics in nonlinear, high-dimensional oscillations remains a central unresolved problem. Here we establish the principle of a universal dynamical clock, a physical perspective in which oscillations of arbitrary dimensionality and geometry are equivalently represented as uniform rotation through an equant-induced nonlinear viewing coordinate, inspired by Ptolemy's equant and formalised through an areal-uniformity principle reminiscent of Kepler's second law. Using a machine-learning framework, we demonstrate the existence of such an equant for a broad class of oscillatory dynamics and construct the associated dynamical clock and phase dynamics under additive forces, including noise, periodic perturbations, and coupling. Its value in uncovering new physical rules and phenomena is demonstrated by four findings: (i) collective oscillations in Escherichia coli populations obey a previously unexplained superlinear scaling law, resolving a long-standing open problem posed in 2004; (ii) the response mechanisms of engineered genetic circuits to changes in gene expression and environmental conditions; (iii) a classical-mechanics counterpart of the Berry geometric phase emerges naturally from the phase of the dynamical clock; and (iv) optimal equant non-uniformity provides a geometric early-warning signal for critical transitions and enables prediction of critical parameters. By providing operational and system-agnostic phase dynamics that can be constructed directly from data, the dynamical clock enables principled classification, comparison, and control of oscillatory systems, and offers a new route to understanding how specific dynamical regimes support distinct functional behaviours in networked systems.

math.DS↗

arXiv2025

All optical chaos synchronization between nonidentical optomechanical cavities

Optomechanical cavities, with nonlinear photon-phonon interactions, offer a more compact approach to chaos generation than conventional feedback-based optical systems. However, proper study on chaos synchronization of two optomechanical cavities connected by optical means is still unexplored. In this work, we theoretically investigate all-optical complete synchronization between unidirectionally coupled optomechanical cavities in the master-slave configuration. Traditionally, achieving complete synchronization in nonlinear coupled oscillators and in optical systems necessitates identical systems. Our findings, which arise naturally from the fundamental mathematical properties of optomechanical cavities, demonstrate that parameter heterogeneity can, in fact, not only enable complete synchronization but make it stable.

physics.optics↗

arXiv2024

Chaotic dynamics under the influence of synthetic magnetic field in optomechanical system

The optomechanical systems produce chaotic behaviour due to nonlinear interaction between photons and phonons, and the same systems are used to understand the synthetic fields as well. Here, we report on the study of chaotic behaviour in the presence of a phononic synthetic magnetic field in a closed loop configuration consisting of a single optical mode and two mechanical modes. The modulation phase of the mechanical coupling between the two mechanical modes plays a critical role in determining the mechanical and optical intensity dynamics in the nonlinear regime. Our study shows the dark mode breaking effect in the presence of a synthetic magnetic field, which brings about a complex way of mechanical energy exchange that causes the cavity field to alternate between chaotic and regular behaviour periodically in temporal domain. However in the stronger nonlinear regime the temporal dynamics demonstrate predominantly chaotic behaviour. Besides, with the advent of advanced fabrication technologies, this study holds promises in developing phase tunable integrated low-power chaotic light sources to support efficient optical secure communication systems.

physics.optics↗

arXiv2022

Analytical Solutions for the Inverse Problem within Gradual Semantics

Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived. While some semantics operate over standard argumentation frameworks, many utilise a weighted framework, where a numeric initial weight is associated with each argument. Recent work has examined the inverse problem within gradual semantics. Rather than determining a preference ordering given an argumentation framework and a semantics, the inverse problem takes an argumentation framework, a gradual semantics, and a preference ordering as inputs, and identifies what weights are needed to over arguments in the framework to obtain the desired preference ordering. Existing work has attacked the inverse problem numerically, using a root finding algorithm (the bisection method) to identify appropriate initial weights. In this paper we demonstrate that for a class of gradual semantics, an analytical approach can be used to solve the inverse problem. Unlike the current state-of-the-art, such an analytic approach can rapidly find a solution, and is guaranteed to do so. In obtaining this result, we are able to prove several important properties which previous work had posed as conjectures.

cs.AI↗

arXiv2020

Wonders of chaos for communication

This work shows that chaotic signals with different power spectrum are robust to linear superposition, meaning that the superposition preserves Ergodic quantities (Lyapunov exponents) and the information content of the source signals, even after being transmitted over non-ideal physical medium. This wonderful property that chaotic signals have allows me to propose a novel communication system based on chaos, where information composed from and to multiple users each operating with different base frequencies and that is carried by chaotic wavesignals can be fully preserved after transmission in the open air wireless physical medium, and it can be trivially decoded with low probability of errors. This work tackles with great detail how chaotic signals and their information content are affected when travelling through medium that presents the non-ideal properties of multipath propagation, noise and chaotic interference (linear superposition), and how this impacts on the proposed communication system. Physical media with other non-ideal properties (dispersion and interference with periodic signals) are also discussed.

eess.SP↗

arXiv2020

Zooming into chaos for a fast, light and reliable cryptosystem

In previous work, the $k$-logistic map [Machicao and Bruno, Chaos, vol. 27, 053116 (2017)] was introduced as a transformation operating in the $k$ less significant digits of the Logistic map. It exploited the map's pseudo-randomness character that is present in its less significant digits. In this work, we comprehensively analyze the dynamical and ergodic aspects of this transformation, show its applicability to generic chaotic maps or sets, and its potential impact on enabling the creation of a cryptosystem that is fast, light and reliable.

nlin.CD↗

arXiv2018

Evaluating performance of neural codes in model neural communication networks

Information needs to be appropriately encoded to be reliably transmitted over physical media. Similarly, neurons have their own codes to convey information in the brain. Even though it is well-known that neurons exchange information using a pool of several protocols of spatio-temporal encodings, the suitability of each code and their performance as a function of network parameters and external stimuli is still one of the great mysteries in neuroscience. This paper sheds light on this by modeling small-size networks of chemically and electrically coupled Hindmarsh-Rose spiking neurons. We focus on a class of temporal and firing-rate codes that result from neurons' membrane-potentials and phases, and quantify numerically their performance estimating the Mutual Information Rate, aka the rate of information exchange. Our results suggest that the firing-rate and interspike-intervals codes are more robust to additive Gaussian white noise. In a network of four interconnected neurons and in the absence of such noise, pairs of neurons that have the largest rate of information exchange using the interspike-intervals and firing-rate codes are not adjacent in the network, whereas spike-timings and phase codes (temporal) promote large rate of information exchange for adjacent neurons. If that result would have been possible to extend to larger neural networks, it would suggest that small microcircuits would preferably exchange information using temporal codes (spike-timings and phase codes), whereas on the macroscopic scale, where there would be typically pairs of neurons not directly connected due to the brain's sparsity, firing-rate and interspike-intervals codes would be the most efficient codes.

q-bio.NC↗

arXiv2018

Exploiting ergodicity of the logistic map using deep-zoom to improve security of chaos-based cryptosystems

This paper explores the deep-zoom properties of the chaotic k-logistic map, in order to propose an improved chaos-based cryptosystem. This map was shown to enhance the random features of the Logistic map, while at the same time reducing the predictability about its orbits. We incorporate its strengths to security into a previously published cryptosystem to provide an optimal pseudo-random number generator (PRNG) as its core operation. The result is a reliable method that does not have the weaknesses previously reported about the original cryptosystem.

cs.CR↗

arXiv2018

Space-time nature of causality

In a causal world the direction of the time arrow dictates how past causal events in a variable $X$ produce future effects in $Y$. $X$ is said to cause an effect in $Y$, if the predictability (uncertainty) about the future states of $Y$ increases (decreases) as its own past and the past of $X$ are taken into consideration. Causality is thus intrinsic dependent on the observation of the past events of both variables involved, to the prediction (or uncertainty reduction) of future event of the other variable. We will show that this {temporal} notion of causality leads to another natural spatio-temporal definition for it, and that can be exploited to detect the arrow of influence from $X$ to $Y$, either by considering shorter time-series of $X$ and longer time-series of $Y$ (an approach that explores the time nature of causality) or lower precision measured time-series in $X$ and higher precision measured time-series in $Y$ (an approach that explores the spatial nature of causality). Causality has thus space and time signatures, causing a break of symmetry in the topology of the probabilistic space, or causing a break of symmetry in the length of the measured time-series, a consequence of the fact that information flows from $X$ to $Y$.

nlin.CD↗

arXiv2018

Delegating via Quitting Games

Delegation allows an agent to request that another agent completes a task. In many situations the task may be delegated onwards, and this process can repeat until it is eventually, successfully or unsuccessfully, performed. We consider policies to guide an agent in choosing who to delegate to when such recursive interactions are possible. These policies, based on quitting games and multi-armed bandits, were empirically tested for effectiveness. Our results indicate that the quitting game based policies outperform those which do not explicitly account for the recursive nature of delegation.

cs.AI↗

arXiv2017

Entropy-based Generating Markov Partitions for Complex Systems

Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found when a Generating Markov Partition (GMP) is obtained, which is only defined once the unstable and stable manifolds are known with infinite precision and for all times. However, these manifolds usually form highly convoluted Euclidean sets, are \emph{a priori} unknown, and, as it happens in any real-world experiment, measurements are made with finite resolution and over a finite time-span. The task gets even more complicated if the system is a network composed of interacting dynamical units, namely, a high-dimensional complex system. Here, we tackle this task and solve it by defining a method to approximately construct GMPs for any complex system's finite-resolution and finite-time trajectory. We critically test our method on networks of coupled maps, encoding their trajectories into symbolic sequences. We show that these sequences are optimal because they minimise the information loss and also any spurious information added. Consequently, our method allows us to approximately calculate the invariant probability measures of complex systems from observed data. Thus, we can efficiently define complexity measures that are applicable to a wide range of complex phenomena, such as the characterisation of brain activity from EEG signals measured at different brain regions or the characterisation of climate variability from temperature anomalies measured at different Earth regions.

nlin.CD↗

arXiv2017

Methods for removal of unwanted signals from gravity time-series: comparison using linear techniques complemented with analysis of system dynamics

The presence of undesirable dominating signals in geophysical experimental data is a challenge in many subfields. One remarkable example is surface gravimetry, where frequencies from Earth tides correspond to time-series fluctuations up to a thousand times larger than the phenomena of major interest, such as hydrological gravity effects or co-seismic gravity changes. This work discusses general methods for removal of unwanted dominating signals by applying them to 8 long-period gravity time-series of the International Geodynamics and Earth Tides Service, equivalent to the acquisition from 8 instruments in 5 locations representative of the network. We compare three different conceptual approaches for tide removal: frequency filtering, physical modelling and data-based modelling. Each approach reveals a different limitation to be considered depending on the intended application. Vestiges of tides remain in the residues for the modelling procedures, whereas the signal was distorted in different ways by the filtering and data-based procedures. The linear techniques employed were power spectral density, spectrogram, cross-correlation and classical harmonics decomposition, while the system dynamics was analysed by state-space reconstruction and estimation of the largest Lyapunov exponent. Although the tides could not be completely eliminated, they were sufficiently reduced to allow observation of geophysical events of interest above the $10 \text{ nm s}^{-2}$ level, exemplified by a hydrology-related event of $60 \text{ nm s}^{-2}$. The implementations adopted for each conceptual approach are general, so that their principles could be applied to other kinds of data affected by undesired signals composed mainly by periodic or quasi-periodic components.

physics.geo-ph↗

arXiv2017

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of the brain. The presence of noise enhances the strength of both types of synapses, but if the initial network has synapses of both natures with similar strengths. Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.

q-bio.NC↗

arXiv2017

Uncovering hidden flows in physical networks

Understanding the interactions among nodes in a complex network is of great importance, since they disclose how these nodes are cooperatively supporting the functioning of the network. Scientists have developed numerous methods to uncover the underlying adjacent physical connectivity based on measurements of functional quantities of the nodes states. Often, the physical connectivity, the adjacency matrix, is available. Yet, little is known about how this adjacent connectivity impacts on the "hidden" flows being exchanged between any two arbitrary nodes, after travelling longer non-adjacent paths. In this Letter, we show that hidden physical flows in conservative flow networks, a quantity that is usually inaccessible to measurements, can be determined by the interchange of physical flows between any pair of adjacent nodes. Our approach applies to steady or dynamic state of either linear or non-linear complex networks that can be modelled by conservative flow networks, such as gas supply networks, water supply networks and power grids.

physics.soc-ph↗

arXiv2017

Understanding Information Transmission in Complex Networks

Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused on the source-channel-receiver problem and on the asymptotic limits of accuracy and communication rates, which are the classical problems studied by Shannon. However, the impact of Information Theory on networks (acting as the channel) is just starting. Here, we present an approach to understand how information flows in any connected complex network. Our approach is based on defining linear conservative flows that travel through the network from source to receiver. This framework allows us to have an analytical description of the problem and also linking the topological invariants of the network, such as the node degree, with the information flow. In particular, our approach is able to deal with information transmission in modular networks (networks containing community structures) or multiplex networks (networks with multiple layers), which are nowadays of paramount importance.

nlin.AO↗

arXiv2017

Maintaining extensivity in evolutionary multiplex networks

In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e. networks of subnetworks (layers), by means of the sum of the positive Lyapunov exponents, $H_{KS}$, a quantity related to entropy. We show that extensivity relies not only on the interplay between the coupling strengths of the dynamics associated to the intra (short-range) and inter (long-range) interactions, but also on the sum of the intra-degrees of the nodes of the layers. For the analytically treated networks of size $N$, among several other results, we show that if the sum of the intra-degrees (and the sum of inter-degrees) scales as $N^{θ+1},\;θ>0$, extensivity can be maintained if the intra-coupling (and the inter-coupling) strength scales as $N^{-θ}$, when evolution is driven by the maximisation of $H_{KS}$. We then verify our analytical results by performing numerical simulations in multiplex networks formed by electrically and chemically coupled neurons.

nlin.CD↗

arXiv2017

Spike timing-dependent plasticity induces non-trivial topology in the brain

We study the capacity of Hodgkin-Huxley neuron in a network to change temporarily or permanently their connections and behavior, the so called spike timing-dependent plasticity (STDP), as a function of their synchronous behavior. We consider STDP of excitatory and inhibitory synapses driven by Hebbian rules. We show that the final state of networks evolved by a STDP depend on the initial network configuration. Specifically, an initial all-to-all topology envolves to a complex topology. Moreover, external perturbations can induce co-existence of clusters, those whose neurons are synchronous and those whose neurons are desynchronous. This work reveals that STDP based on Hebbian rules leads to a change in the direction of the synapses between high and low frequency neurons, and therefore, Hebbian learning can be explained in terms of preferential attachment between these two diverse communities of neurons, those with low-frequency spiking neurons, and those with higher-frequency spiking neurons.

q-bio.NC↗

arXiv2017

Optimization of synchronizability in multiplex networks by rewiring one layer

The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modelling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks by evolving only one layer while keeping other layers fixed. Our main finding is to show the conditions under which the efficiency of convergence to the most optimal structure is almost as good as the case where both layers are rewired during an optimization process. In particular, inter-layer coupling strength responsible for the integration between the layers turns out to be crucial factor governing the efficiency of optimization even for the cases when the layer going through the evolution has nodes interacting much weakly than those in the fixed layer. Additionally, we investigate the dependency of synchronizability on the rewiring probability which governs the network structure from a regular lattice to the random networks. The efficiency of the optimization process preceding evolution driven by the optimization process is maximum when the fixed layer has regular architecture, whereas the optimized network is more synchronizable for the fixed layer having the rewiring probability lying between the small-world transition and the random structure.

nlin.AO↗