Adaptive exponential integrate-and-fire model with fractal extension.

The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behavior of neurons. One successful model used for this purpose is the Adaptive Exponential Integrate-and-Fire (Adex), which is composed of two ordinary differential equations. Usually, this model is considered in the standard formulation, i.e., with integer order derivatives. In this work, we propose and study the fractal extension of Adex model, which in simple terms corresponds to replacing the integer derivative by non-integer. As non-integer operators, we choose the fractal derivatives. We explore the effects of equal and different orders of fractal derivatives in the firing patterns and mean frequency of the neuron described by the Adex model. Previous results suggest that fractal derivatives can provide a more realistic representation due to the fact that the standard operators are generalized. Our findings show that the fractal order influences the inter-spike intervals and changes the mean firing frequency. In addition, the firing patterns depend not only on the neuronal parameters but also on the order of respective fractal operators. As our main conclusion, the fractal order below the unit value increases the influence of the adaptation mechanism in the spike firing patterns.

Impact of periodic vaccination in SEIRS seasonal model.

We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.

Multistability and chaos in SEIRS epidemic model with a periodic time-dependent transmission rate.

In this work, we study the dynamics of a susceptible-exposed-infectious-recovered-susceptible epidemic model with a periodic time-dependent transmission rate. Emphasizing the influence of the seasonality frequency on the system dynamics, we analyze the largest Lyapunov exponent along parameter planes finding large chaotic regions. Furthermore, in some ranges, there are shrimp-like periodic structures. We highlight the system multistability, identifying the coexistence of periodic orbits for the same parameter values, with the infections maximum distinguishing by up one order of magnitude, depending only on the initial conditions. In this case, the basins of attraction have self-similarity. Parametric configurations, for which both periodic and non-periodic orbits occur, cover 13.20% of the evaluated range. We also identified the coexistence of periodic and chaotic attractors with different maxima of infectious cases, where the periodic scenario peak reaches approximately 50% higher than the chaotic one.

Fractal and fractional SIS model for syphilis data.

This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.

The Roles of Potassium and Calcium Currents in the Bistable Firing Transition.

Healthy brains display a wide range of firing patterns, from synchronized oscillations during slow-wave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking (RS) cells with frequency adaptation and do not exhibit bursts in current-clamp experiments (in vitro). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings (gsyn) and external current inputs (I). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to the bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold (IL) and low-threshold (IT) ion channels play a role in increasing and decreasing the parameter conditions (gsyn and I) in which bistable dynamics occur, respectively. For high values of IL conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance IT increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.

The Role of Potassium and Calcium Currents in the Bistable Firing Transition.

Healthy brains display a wide range of firing patterns, from synchronized oscillations during slowwave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking cells (RS) with frequency adaptation and do not exhibit bursts in current-clamp experiments ( in vitro ). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings ( g syn ) and external current inputs ( I ). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold ( I L ) and low-threshold ( I T ) ion channels play a role in increasing and decreasing the parameter conditions ( g syn and I ) in which bistable dynamics occur, respectively. For high values of I L conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance I T increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.

Analyzing bursting synchronization in structural connectivity matrix of a human brain under external pulsed currents.

Cognitive tasks in the human brain are performed by various cortical areas located in the cerebral cortex. The cerebral cortex is separated into different areas in the right and left hemispheres. We consider one human cerebral cortex according to a network composed of coupled subnetworks with small-world properties. We study the burst synchronization and desynchronization in a human neuronal network under external periodic and random pulsed currents. With and without external perturbations, the emergence of bursting synchronization is observed. Synchronization can contribute to the processing of information, however, there are evidences that it can be related to some neurological disorders. Our results show that synchronous behavior can be suppressed by means of external pulsed currents.

Quantification of Residual Stress Relief by Heat Treatments in Austenitic Cladded Layers.

The effect of the heat treatment on the residual stresses of welded cladded steel samples is analyzed in this study. The residual stresses across the plate's square sections were determined using complementary methods; applying diffraction with neutron radiation and mechanically using the contour method. The analysis of the large coarse grain austenitic cladded layers, at the feasibility limits of diffraction methods, was only made possible by applying both methods. The samples are composed of steel plates, coated on one of the faces with stainless steel filler metals, this coating process, usually known as cladding, was carried out by submerged arc welding. After cladding, the samples were submitted to two different heat treatments with dissimilar parameters: one at a temperature of 620 °C maintained for 1 h and, the second at 540 °C, for ten hours. There was some difference in residual stresses measured by the two techniques along the surface of the coating in the as-welded state, although they are similar at the welding interface and in the heat-affected zone. The results also show that there is a residual stress relaxation for both heat-treated samples. The heat treatment carried out at a higher temperature showed sometimes more than 50% reduction in the initial residual stress values and has the advantage of being less time consuming, giving it an industrial advantage and making it more viable economically.

Suppression of chaotic bursting synchronization in clustered scale-free networks by an external feedback signal.

Oscillatory activities in the brain, detected by electroencephalograms, have identified synchronization patterns. These synchronized activities in neurons are related to cognitive processes. Additionally, experimental research studies on neuronal rhythms have shown synchronous oscillations in brain disorders. Mathematical modeling of networks has been used to mimic these neuronal synchronizations. Actually, networks with scale-free properties were identified in some regions of the cortex. In this work, to investigate these brain synchronizations, we focus on neuronal synchronization in a network with coupled scale-free networks. The networks are connected according to a topological organization in the structural cortical regions of the human brain. The neuronal dynamic is given by the Rulkov model, which is a two-dimensional iterated map. The Rulkov neuron can generate quiescence, tonic spiking, and bursting. Depending on the parameters, we identify synchronous behavior among the neurons in the clustered networks. In this work, we aim to suppress the neuronal burst synchronization by the application of an external perturbation as a function of the mean-field of membrane potential. We found that the method we used to suppress synchronization presents better results when compared to the time-delayed feedback method when applied to the same model of the neuronal network.

Prediction of short-term prognosis in elderly patients with spontaneous intracerebral hemorrhage.

AIM: The incidence of spontaneous intracerebral hemorrhage (SICH) increases with age. Data on SICH mortality in the very old are sparse. We aimed to describe the predictors of 30-day SICH mortality in the very elderly in southern Portugal. METHODS: A total of 256 community representative SICH patients aged ≥ 75 years (2009-2016) were included. Multiple logistic regression was used to identify predictors of 30-day mortality. RESULTS: Mean age was 82.1 years; 57.4% males. The 30-day case fatality was 38.7%. The frequency of patients taking anticoagulants (29.3% vs. 11.5%); comatose (46.9% vs. 2.5%); with hematoma volume ≥ 30 mL (64.6% vs. 13.4%); intraventricular dissection (78.8% vs. 27.4%) was higher in deceased patients (p < 0.05). Survivors were more often admitted to stroke unit (SU) (68.2 vs. 31.3%) and had lower mean admission glycaemia values (p < 0.05). The likelihood of death was increased in patients with higher admission hematoma volume (≥ 30 mL) (OR: 8.817, CI 1.753-44.340, p = 0.008) and with prior to SICH history of ≥ 2 hospitalizations OR = 1.022, CI 1.009-1.069, p = 0.031). Having higher Glasgow coma scale score, OR: 0.522, CI 0.394-0.692, p < 0.001, per unit was associated with reduced risk of death. Age was not an independent risk factor of short-term death. CONCLUSIONS: The short-term mortality is high in very elderly SICH. Prior to SICH history of hospitalization, an indirect and gross marker of coexistent functional reserve, not age per se, increases the risk of short-term death. Other predictors of short-term death are potentially manageable reinforcing the message against any defeatist attitude toward elderly patients with SICH.

Emergence of Neuronal Synchronisation in Coupled Areas.

One of the most fundamental questions in the field of neuroscience is the emergence of synchronous behaviour in the brain, such as phase, anti-phase, and shift-phase synchronisation. In this work, we investigate how the connectivity between brain areas can influence the phase angle and the neuronal synchronisation. To do this, we consider brain areas connected by means of excitatory and inhibitory synapses, in which the neuron dynamics is given by the adaptive exponential integrate-and-fire model. Our simulations suggest that excitatory and inhibitory connections from one area to another play a crucial role in the emergence of these types of synchronisation. Thus, in the case of unidirectional interaction, we observe that the phase angles of the neurons in the receiver area depend on the excitatory and inhibitory synapses which arrive from the sender area. Moreover, when the neurons in the sender area are synchronised, the phase angle variability of the receiver area can be reduced for some conductance values between the areas. For bidirectional interactions, we find that phase and anti-phase synchronisation can emerge due to excitatory and inhibitory connections. We also verify, for a strong inhibitory-to-excitatory interaction, the existence of silent neuronal activities, namely a large number of excitatory neurons that remain in silence for a long time.

Curry-Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems.

The routes to chaos play an important role in predictions about the transitions from regular to irregular behavior in nonlinear dynamical systems, such as electrical oscillators, chemical reactions, biomedical rhythms, and nonlinear wave coupling. Of special interest are dissipative systems obtained by adding a dissipation term in a given Hamiltonian system. If the latter satisfies the so-called twist property, the corresponding dissipative version can be called a "dissipative twist system." Transitions to chaos in these systems are well established; for instance, the Curry-Yorke route describes the transition from a quasiperiodic attractor on torus to chaos passing by a chaotic banded attractor. In this paper, we study the transitions from an attractor on torus to chaotic motion in dissipative nontwist systems. We choose the dissipative standard nontwist map, which is a non-conservative version of the standard nontwist map. In our simulations, we observe the same transition to chaos that happens in twist systems, known as a soft one, where the quasiperiodic attractor becomes wrinkled and then chaotic through the Curry-Yorke route. By the Lyapunov exponent, we study the nature of the orbits for a different set of parameters, and we observe that quasiperiodic motion and periodic and chaotic behavior are possible in the system. We observe that they can coexist in the phase space, implying in multistability. The different coexistence scenarios were studied by the basin entropy and by the boundary basin entropy.

Mandibular First Molar with Six Canals: Case Report of Radix Entomolaris and Middle Mesial Canal.

The purpose of this article is to report a successful endodontic treatment of a mandibular first molar with six canals; three root canals in the mesial root, two root canals in the distal root, and one radix entomolaris. The incidence of two anatomical variations presented in this report, middle mesial canal and radix entomolaris, is generally low. Knowledge of the internal anatomy of the root canals and their possible variations, and use of magnification, such as the operating microscope or loupes, can increase the chances of finding additional canals, contributing to the success of endodontic treatment.

Dynamics of epidemics: Impact of easing restrictions and control of infection spread.

During an infectious disease outbreak, mathematical models and computational simulations are essential tools to characterize the epidemic dynamics and aid in design public health policies. Using these tools, we provide an overview of the possible scenarios for the COVID-19 pandemic in the phase of easing restrictions used to reopen the economy and society. To investigate the dynamics of this outbreak, we consider a deterministic compartmental model (SEIR model) with an additional parameter to simulate the restrictions. In general, as a consequence of easing restrictions, we obtain scenarios characterized by high spikes of infections indicating significant acceleration of the spreading disease. Finally, we show how such undesirable scenarios could be avoided by a control strategy of successive partial easing restrictions, namely, we tailor a successive sequence of the additional parameter to prevent spikes in phases of low rate of transmissibility.

Influence of Autapses on Synchronization in Neural Networks With Chemical Synapses.

A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronization. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behavior. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behavior depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.

Ratchet current in nontwist Hamiltonian systems.

Non-monotonic area-preserving maps violate the twist condition locally in phase space, giving rise to shearless invariant barriers surrounded by twin island chains in these regions of phase space. For the extended standard nontwist map, with two resonant perturbations with distinct wave numbers, we investigate the presence of such barriers and their associated island chains and compare our results with those that have been reported for the standard nontwist map with only one perturbation. Furthermore, we determine in the control parameter space the existence of the shearless barrier and the influence of the additional wave number on this condition. We show that only for odd second wave numbers are the twin island chains symmetrical. Moreover, for even wave numbers, the lack of symmetry between the chains of twin islands generates a ratchet effect that implies a directed transport in the phase space.

Influence of Delayed Conductance on Neuronal Synchronization.

In the brain, the excitation-inhibition balance prevents abnormal synchronous behavior. However, known synaptic conductance intensity can be insufficient to account for the undesired synchronization. Due to this fact, we consider time delay in excitatory and inhibitory conductances and study its effect on the neuronal synchronization. In this work, we build a neuronal network composed of adaptive integrate-and-fire neurons coupled by means of delayed conductances. We observe that the time delay in the excitatory and inhibitory conductivities can alter both the state of the collective behavior (synchronous or desynchronous) and its type (spike or burst). For the weak coupling regime, we find that synchronization appears associated with neurons behaving with extremes highest and lowest mean firing frequency, in contrast to when desynchronization is present when neurons do not exhibit extreme values for the firing frequency. Synchronization can also be characterized by neurons presenting either the highest or the lowest levels in the mean synaptic current. For the strong coupling, synchronous burst activities can occur for delays in the inhibitory conductivity. For approximately equal-length delays in the excitatory and inhibitory conductances, desynchronous spikes activities are identified for both weak and strong coupling regimes. Therefore, our results show that not only the conductance intensity, but also short delays in the inhibitory conductance are relevant to avoid abnormal neuronal synchronization.

Basin of attraction for chimera states in a network of Rössler oscillators.

Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rössler oscillators. The Rössler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.