David Angulo-Garcia

Bipolar II disorder (BD-II) is characterized by recurrent hypomanic and depressive episodes interspersed with periods of euthymia. This study proposes a stochastic hybrid framework that integrates multistable nonlinear mood dynamics, Gaussian white noise, Poisson jumps, and a compartmental pharmacokinetic model of lithium maintenance treatment. Unlike approaches based on intrinsic mood oscillations, the proposed model represents affective episodes as stochastic transitions between coexisting stable states. The deterministic system exhibits saddle-node bifurcations and, within a restricted parameter regime, four stable equilibria associated with hypomanic, depressive, and two euthymic states. Numerical simulations characterize how continuous and abrupt stochastic perturbations influence episode durations and recurrence frequencies, revealing asymmetric responses to perturbations acting on the two mood variables. Coupling the mood dynamics to periodic lithium administration generates periodic orbits whose stability is assessed using Floquet multipliers. Numerical continuation shows that pharmacological coupling can shift these orbits toward the euthymic region and, for suitable parameter values, produce stable periodic dynamics confined within it. The analysis of imperfect treatment adherence further shows that randomly omitted doses can alter episode occurrence and duration, while higher adherence generally favors euthymic dynamics under the investigated conditions. These findings establish a mathematical framework for examining the interplay between multistability, stochastic mood transitions, and lithium maintenance treatment, while providing a basis for future calibration and validation using longitudinal clinical data.

Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external input currents in order to sustain finite firing rates, thus raising concerns about their biological plausibility. Here, we investigate an alternative mechanism based on short-term synaptic depression (STD) acting on excitatory-excitatory synapses, which dynamically balances the network activity without the need of strong external driving. Using accurate numerical simulations and theoretical investigations we characterize the dynamics of a densely connected recurrent network made up of N rate-neuron models encompassing STD. Depending on the synaptic strength J ₀ , the network exhibits two distinct regimes: at sufficiently small J ₀ , it converges to a homogeneous fixed point, while for sufficiently large J ₀ Rate Chaos emerges. For finite networks, we observe a transition region at intermediate J ₀ , where the system passes from the homogeneous fixed point to Rate Chaos following several different routes to chaos depending on the network realization. Furthermore, we show that the width of the transition region shrinks for increasing N and eventually vanishes in the thermodynamic limit ( N → ∞ ). The characterization of the Rate Chaos regime has been performed by means of Dynamical Mean Field (DMF) approaches. This analysis has revealed on one side that the novel balancing mechanism is able to sustain finite irregular activity even in the thermodynamic limit, and on the other side that balancing occurs via dynamic cancellation of the correlations in the synaptic input currents induced by the dense connectivity. Our findings show that STD provides an intrinsic self-regulating mechanism for balanced networks, sustaining irregular yet stable activity without the need of biologically unrealistic strong external currents. This work extends the balanced network paradigm, offering insights into how cortical circuits could maintain robust dynamics via synaptic adaptation.

Total Suspended Solids (TSS) significantly degrade water quality by reducing light penetration and oxygen availability, while facilitating the transport of toxic contaminants. Managing TSS in watersheds requires an understanding of both hydrological connectivity and pollutant dynamics; however, these efforts are significantly constrained by data scarcity, particularly in extensive or remote watersheds in developing countries. This study develops a network‐based advection‐reaction model to simulate TSS transport across the Canal del Dique watershed. The watershed is represented as a directed graph, where rivers and streams form the edges of the network, and confluence points serve as nodes. To address the challenge of data scarcity, machine learning techniques are employed to estimate missing TSS values at unmonitored locations, and an optimization framework is implemented to determine the most effective TSS mitigation strategies. Results highlight the role of hydrological connectivity in TSS transport, with the model revealing that at low mitigation levels, interventions should prioritize high‐TSS nodes. As mitigation resources increase, interventions shift toward pollutant source nodes and less connected areas, preventing downstream pollutant accumulation. This study demonstrates that highly connected nodes, although crucial for flow, are less effective targets for pollution control. The proposed methodology offers a novel, data‐driven approach for optimizing TSS mitigation strategies, providing a scientifically grounded tool for improving water quality management. By prioritizing resource allocation in critical areas, this work enhances the efficiency of watershed management and supports sustainable water resource policies, especially in data‐limited regions.

Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external inputs to sustain finite firing rates, raising concerns about their biological plausibility. Here, we investigate an alternative mechanism based on short-term synaptic depression (STD) acting on excitatory-excitatory synapses, which dynamically balances the network activity without the need of external inputs. By employing accurate numerical simulations and theoretical investigations we characterize the dynamics of a massively coupled network made up of N rate-neuron models. Depending on the synaptic strength J0, the network exhibits two distinct regimes: at sufficiently small J0, it converges to a homogeneous fixed point, while for sufficiently large J0, it exhibits Rate Chaos. For finite networks, we observe several different routes to chaos depending on the network realization. The width of the transition region separating the homogeneous stable solution from Rate Chaos appears to shrink for increasing N and eventually to vanish in the thermodynamic limit (N → ∞). The characterization of the Rate Chaos regime performed by employing Dynamical Mean Field (DMF) approaches allow us on one side to confirm that this novel balancing mechanism is able to sustain finite irregular activity even in the thermodynamic limit, and on the other side to reveal that the balancing occurs via dynamic cancellation of the input correlations generated by the massive coupling. Our findings show that STD provides an intrinsic self-regulating mechanism for balanced networks, sustaining irregular yet stable activity without the need of biologically unrealistic inputs. This work extends the balanced network paradigm, offering insights into how cortical circuits could maintain robust dynamics via synaptic adaptation.

Traffic congestion is a critical challenge in urban environments, negatively affecting quality of life and economic productivity. Mathematical models have sought to provide foundational insights, with microscopic models capturing individual behaviors and macroscopic models offering computational efficiency. Microscopic models, however, are computationally intensive, while macroscopic models lack the detail required for devising traffic solutions. This work introduces a novel, intermediate-resolution framework based on networks of dynamic systems governed by ordinary differential equations with discontinuous right-hand sides. Our approach employs graph-based advection dynamics, where nodes represent discrete road segments with capacity constraints. Through analytical derivations, we gain insights into the equilibrium states that emerge as roads experience congestion. We further exploit the mathematical tractability of our model to formulate well-posed optimization problems designed to mitigate congestion. The efficacy of our framework is validated using both representative numerical examples and a real-world dataset from Manhattan's Upper West Side in New York City, USA. Notably, our findings suggest that sparse, time-dependent interventions on critical road segments can be used to effectively alleviate congestion throughout the day.

This paper presents a robust control strategy for a synchronous Zeta converter using feedback linearization combined with a PI controller. The control design is based on a state-averaged model, but it is implemented and evaluated in a digitally switched system using PSIM simulations. To ensure consistency between the averaged and switched models, the duty cycle is computed at the beginning of each period, and a centered PWM scheme is applied. This study identifies critical factors that affect stability, including the sampling period and the PWM edge selection, both of which can destabilize the switched system even when the averaged model remains stable. This study analyzes the difference in stability ranges between the averaged and switched models under variations in load and reference voltage, revealing significant discrepancies between them. Results show that the proposed control achieves robust performance, low stabilization time, and good tracking behavior across a wide range of conditions.

The boost‐flyback converter is a type of DC‐DC power converter that allows for efficient step‐up voltage conversion. Despite its potential for achieving high voltage gains, there is a lack of comprehensive analysis and practical implementation of reliable control methods for this converter. To date, only a few control techniques have been thoroughly examined and, more importantly, validated on hardware for this specific converter. In this paper, a comprehensive evaluation of two control techniques is presented, namely, zero average surface (ZAS) and hysteresis band (HB) control, for the boost‐flyback converter. Insights into the performance of these techniques and their applicability in real‐world scenarios are provided by experimental investigation. Experimental results have shown that the ZAS controller, while promising in theory, requires the inclusion of a secondary feed‐forward control loop to achieve accurate regulation of the output and effective disturbance rejection. This finding has highlighted the sensitivity of the ZAS control to measurement noise and the importance of careful consideration when implementing it in hardware. By providing a detailed comparison and insights into the performance of these control techniques, this study contributes to the advancement of control strategies for the boost‐flyback converter and guides future research in this field.

Spontaneous synchronous activity is a hallmark of developing brain circuits and promotes their formation. Ex vivo, synchronous activity was shown to be orchestrated by a sparse population of highly connected GABAergic ‘hub’ neurons. The recent development of all-optical methods to record and manipulate neuronal activity in vivo now offers the unprecedented opportunity to probe the existence and function of hub cells in vivo. Using calcium imaging, connectivity analysis and holographic optical stimulation, we show that single GABAergic, but not glutamatergic, neurons influence population dynamics in the barrel cortex of non-anaesthetized mouse pups. Single GABAergic cells mainly exert an inhibitory influence on both spontaneous and sensory-evoked population bursts. Their network influence scales with their functional connectivity, with highly connected hub neurons displaying the strongest impact. We propose that hub neurons function in tailoring intrinsic cortical dynamics to external sensory inputs.