arXiv subjects

Rui Dilão

Publications and source records attributed to Rui Dilão.

13 recordsLinked to original sources

arXiv2025

A biophysical approach to the design of networks of communication systems

Inspired by the growth dynamics of the protist \textit{Physarum polycephalum}, we employ a formalism that describes adaptive, incompressible Hagen-Poiseuille flows on channel networks to identify graphs connecting different nodes within Euclidean space. These graphs are either suboptimal or optimal with respect to their length. Occasionally, we derive graph tree configurations that are topologically equivalent to Steiner trees. This methodology can be utilised to assist in making decisions regarding the design of communication networks, such as fibre webs, motorways, or railway networks. As a demonstration of the practicality of this approach, we explicitly apply this framework to the Portuguese railway network.

physics.soc-ph↗

arXiv2025

A minimal electrical model of the human heart

We develop a minimal whole-heart model that describes cardiac electrical conduction and simulate a basic three-lead electrocardiogram (ECG). We compare our 3-lead ECG model with clinical data from a Norwegian athlete database. The results demonstrate a strong correlation with the ECGs recorded for these athletes. We simulate various pathologies of the heart's electrical conduction system, including ventricular tachycardia, atrioventricular nodal reentrant tachycardia, accessory pathways, and ischaemia-related arrhythmias, showing that the 3-lead ECGs align with the clinical data. This minimal model serves as a computationally efficient digital twin of the heart.

q-bio.TO↗

arXiv2025

Interdependence of sodium and potassium gating variables in the Hodgkin-Huxley model

We explore the relationship between sodium (Na$^+$) and potassium (K$^+$) gating variables in the 4-dimensional (4D) Hodgkin-Huxley (HH) electrophysiology model, and reducing its complexity by deriving new 3D and 2D models that maintain the dynamic properties of the original model. The new 3D and 2D models are grounded in the relationship $h \simeq c(I) - n$ between the gating variables $h$ and $n$ of the 4D HH model, where $c(I)$ depends of the input external stimulus, indicating an interdependence between the dynamics of Na$^+$ and K$^+$ transmembrane voltage-gated channels. The presence of Na$^+$/K$^+$-ATPase pumps along the axon may explain this interdependence. We derive the corresponding cable equations for the two new HH-type models and demonstrate that the action potential propagates along the axon at a speed given by $v(R, C_m) = α/ (C_m R^β):= γD^β$, where $α> 0$, $0 < β< 1$, and $γ$ are constants independent of the local stimulus intensity, $D$ is the diffusion coefficient of the electric signal along the axon, $C_m$ is the axon transmembrane capacitance, and $R$ is the axon conducting resistivity.

physics.bio-ph↗

arXiv2024

Modelling and calibration of pair-rule protein patterns in Drosophila embryo: From Even-skipped and Fushi-tarazu to Wingless expression networks

We modelled and calibrated the distributions of the seven-stripe patterns of Even-skipped (\textit{Eve}) and Fushi-tarazu (\textit{Ftz}) pair-rule proteins along the anteroposterior axis of the \textit{Drosphila} embryo, established during early development. We have identified the putative repressive combinations for five \textit{Eve} enhancers, and we have explored the relationship between \textit{Eve} and \textit{Ftz} for complementary patterns. The regulators of \textit{Eve} and \textit{Ftz} are stripe-specific DNA enhancers with embryo position-dependent activation rates and are regulated by the gap family of proteins. We achieved remarkable data matching of the \textit{Eve} stripe pattern, and the calibrated model reproduces gap gene mutation experiments. Extended work inferring the Wingless (\textit{Wg}) fourteen stripe pattern from \textit{Eve} and \textit{Ftz} enhancers have been proposed, clarifying the hierarchical structure of \textit{Drosphila}'s genetic expression network during early development.

q-bio.QM↗

arXiv2023

Formation and Optimisation of Vein Networks in Physarum

Physarum polycephalum is an acellular slime mould that grows as a highly adaptive network of veins filled with protoplasm. As it forages, Physarum dynamically rearranges its network structure as a response to local stimuli information, optimising the connection between food sources. This high-level behaviour was already exploited to solve numerous optimisation problems. We develop a flow-based model for the adaptive network formation of Physarum, which solves some inconsistencies of previous models. We first derive a general class of equations describing the adaptation and flow dynamics of a static network comprised of elastic channels filled with an incompressible fluid undergoing a Hagen-Poiseuille flow. An explicit form of the model is obtained by minimising the total power dissipated by the network. Considering a more general functional form of the adaptive equations, a phase transition in the system is also found. The model is used for maze-solving and to build efficient and resilient networks in an arena mimicking mainland Portugal. By comparing the resulting networks with the real Portuguese railway system, we found that the model produced networks with a better overall performance when considering fluctuations in the network flows. Finally, the adaption model is extended to incorporate the network growth in the presence of multiple food sources. The coupling of both processes produces networks with similar traits to several network systems found in nature. We found that when the food sources operate alternately, the model can replicate the direct connections between the food sources observed in Physarum.

physics.flu-dyn↗

arXiv2022

A solvable walking model for a two-legged robot

We present a solvable biped walking model based on an inverted pendulum with two massless articulated legs capable of walking on uneven floors and inclined planes. The stride of the two-legged robot results from the pendular motion of a standing leg and the articulated motion of a trailing leg. Gaiting is possible due to the alternating role of the legs, the standing and the trailing leg, and the conservation of energy of the pendular motion. The motion on uneven surfaces and inclined planes is possible by imposing the same maximal opening angle between the two legs in the transition between strides and the adaptability of the time of each stride. This model is solvable in closed form and is reversible in time, modelling the different types of biped motion. Several optimisation results for the speed of gaiting as a function of the robot parameters have been derived.

cs.RO↗

arXiv2022

Action potential solitons and waves in axons

We show that the action potential signals generated inside axons are reaction-diffusion solitons or reaction-diffusion waves, refuting the Hodgkin and Huxley hypothesis that action potentials propagate along axons with an elastic wave mechanism. Reaction-diffusion action potential wavefronts and solitons annihilate at collision and boundaries of axons, in contrast with elastic waves, where amplitudes add up and reflect at boundaries. We numerically calculate the values of the speed of the action potential spikes and the dispersion relations. These findings suggest several experiments as validating and falsifying tests for the Hodgkin and Huxley model.

q-bio.NC↗

arXiv2021

Adaptive Hagen-Poiseuille flows on graphs

We derive a class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels, with several sources and sinks, and adaptive conductivities. The flow is controlled by the fluxes at sources and sinks. The network is represented by a graph and the adaptive conductivities describe the transverse channel elasticities, mirroring several network structures found in physics and biology. Minimising the dissipated energy per unit time, we have found an explicit form for the adaptation equations and, asymptotically in time, a steady state tree geometry for the graph connecting sources and sinks is reached. A phase transition tuned by an order parameter for the adapted steady sate graph has been found.

physics.flu-dyn↗

arXiv2013

Dynamic trajectory control of gliders

A new dynamic control algorithm in order to direct the trajectory of a glider to a pre-assigned target point is proposed. The algorithms runs iteratively and the approach to the target point is self-correcting. The algorithm is applicable to any non-powered lift-enabled vehicle (glider) travelling in planetary atmospheres. As a proof of concept, we have applied the new algorithm to the command and control of the trajectory of the Space Shuttle during the Terminal Area Energy Management (TAEM) phase.

astro-ph.IM↗

arXiv2010

Computing the topological entropy of unimodal maps

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by the sign analysis of the itineraries of the critical point and of the boundary points of the interval map. We apply this algorithm to the estimation of the growth number and the topological entropy of maps with direct and reverse bifurcations.

nlin.CD↗

arXiv2009

mRNA diffusion explains protein gradients in \textit{Drosophila} early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of \textit{Drosophila}. In this model, we consider that \textit{bicoid} mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11 to 14 of the developing embryo of \textit{Drosophila}. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of \textit{bicoid} mRNA is in the range 4.6\times 10^{-12}-1.5\times 10^{-11}m^2s^{-1}, in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of \textit{bicoid} mRNA in \textit{Drosophila} [Spirov et al. (2009) Development 136:605-614].

q-bio.QM↗

arXiv2009

Emergent thresholds in genetic regulatory networks: Protein patterning in Drosophila morphogenesis

We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the \emph{Mathematica} software package \emph{GeneticNetworks}. This package accepts as input the interaction graphs of the transcriptional activators and repressors and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in \emph{Drosophila} early development and we calibrate and validate the genetic transcriptional network responsible for the patterning of the gap proteins Hunchback and Knirps, along the antero-posterior axis of the \emph{Drosophila} embryo. This shows that patterning at the gap genes stage is a consequence of the relations between the transcriptional regulators and their initial conditions along the embryo.

q-bio.QM↗

arXiv2006

The Exact Value for European Options on a Stock Paying a Discrete Dividend

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.

math.PR↗