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In this paper we discuss the details, limitations, and difficulties of the implementation in hardware of a memristor-based random number generator that exhibits monofractal/multifractal behavior. To do so, the components and selection criteria of a reference memristor and one proposed by the authors, the chaotic circuit leveraging them, and the processing that is performed on the chaotic signals to achieve the random discrete sequences are described. After applying the estimation tools, findings indicate that more than 60% of the proposed combinations allow generating random discrete sequences, with long-range dependence, and that both monofractal and multifractal behaviors can also be obtained. Consequently, a hardware system was achieved that can be used as a source of entropy in future synthetic biological signal generators.

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[This corrects the article DOI: 10.3389/fnbot.2023.1211570.].

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Introduction: We introduce a bio-inspired navigation system for a robot to guide a social agent to a target location while avoiding static and dynamic obstacles. Robot navigation can be accomplished through a model of ring attractor neural networks. This connectivity pattern between neurons enables the generation of stable activity patterns that can represent continuous variables such as heading direction or position. The integration of sensory representation, decision-making, and motor control through ring attractor networks offers a biologically-inspired approach to navigation in complex environments. Methods: The navigation system is divided into perception, planning, and control stages. Our approach is compared to the widely-used Social Force Model and Rapidly Exploring Random Tree Star methods using the Social Individual Index and Relative Motion Index as metrics in simulated experiments. We created a virtual scenario of a pedestrian area with various obstacles and dynamic agents. Results: The results obtained in our experiments demonstrate the effectiveness of this architecture in guiding a social agent while avoiding obstacles, and the metrics used for evaluating the system indicate that our proposal outperforms the widely used Social Force Model. Discussion: Our approach points to improving safety and comfort specifically for human-robot interactions. By integrating the Social Individual Index and Relative Motion Index, this approach considers both social comfort and collision avoidance features, resulting in better human-robot interactions in a crowded environment.

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Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi-Sugeno (T-S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

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In this paper we analyze the behavior of the COVID-19 pandemic during a certain period of the year 2020 in the state of Mexico, Mexico. For this, we will use the discrete models obtained by the first, third and fourth authors of this work. The first is a one-dimensional model, and the second is two-dimensional, both non-linear. It is assumed that the population of the state of Mexico is constant and that the parameters used are the infection capacity, which we will initially assume to be constant, and the recovery and mortality parameters in that state. We will show that even when the statistical data obtained are disperse, and the process could be stabilized, this has been slow due to chaotic mitigation, creating situations of economic, social, health and political deterioration in that region of the country. We note that the observed results of the behavior of the epidemic during that period for the first variants of the virus have continued to be observed for the later variants, which has not allowed the eradication of the pandemic.

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Autoassociative neural networks provide a simple model of how memories can be stored through Hebbian synaptic plasticity as retrievable patterns of neural activity. Although progress has been made along the last decades in understanding the biological implementation of autoassociative networks, their modest theoretical storage capacity has remained a major constraint. While most previous approaches utilize randomly connected networks, here we explore the possibility of optimizing network performance by selective connectivity between neurons, that could be implemented in the brain through creation and pruning of synaptic connections. We show through numerical simulations that a reconfiguration of the connectivity matrix can improve the storage capacity of autoassociative networks up to one order of magnitude compared to randomly connected networks, either by reducing the noise or by making it reinforce the signal. Our results indicate that the signal-reinforcement scenario is not only the best performing but also the most adequate for brain-like highly diluted connectivity. In this scenario, the optimized network tends to select synapses characterized by a high consensus across stored patterns. We also introduced an online algorithm in which the network modifies its connectivity while learning new patterns. We observed that, similarly to what happens in the human brain, creation of connections dominated in an initial stage, followed by a stage characterized by pruning, leading to an equilibrium state that was independent of the initial connectivity of the network. Our results suggest that selective connectivity could be a key component to make attractor networks in the brain viable in terms of storage capacity.

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Systemic blood pressure (BP) may oscillate for homeostatic needs (equilibrium by constancy) or just as shifts in other intrinsic and extrinsic variables known as allostatic changes. This transitory pressure often rises alerts physicians to out-of-control hypertension or even hypertensive crisis. There is a very complex theory underlying these stochastic phenomena, which physicists and mathematicians translate into a single word: chaos. These changes happen according to a stochastic probabilistic pattern that presumes chaotic but somewhat predictable and nonlinear modeling of BP-related dynamics as a mathematical approach. Based on the chaos theory, small changes at the initial BP (baseline overtime) values could disturb the homeostasis leading to extreme BP chaotic shifts. These almost insignificant oscillations may also affect other variables and systems, leading to the misdiagnosis of hypertension, "out-of-control" BP levels, and resistant hypertension (RHT). Thus, these unpredictable and transient increases in BP values may be improperly diagnosed as the white coat and masked or resistant hypertension. Indeed, the interference of the chaos in any phenotype of (true or false) hard to control BP is not considered in clinical settings. This review provides some basic concepts on chaos theory and BP regulation. Besides pseudoresistant hypertension (lack of adherence, circadian variations, and others (white-coat, masked, early morning effects or hypertension), chaotic changes can be responsible for out-of-control hypertension.

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In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane'-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

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Antecedentes: la teoría de los sistemas dinámicos estudia la evolución de los sistemas. Mediante esta teoría y la geometría fractal se desarrolló una ley matemática de ayuda diagnóstica a los sistemas dinámicos cardiacos, que permite diferenciar entre normalidad y enfermedad, y la evolución entre los dos estados. Objetivo: confirmar la capacidad diagnóstica de la ley matemática exponencial desarrollada inicialmente para dinámicas cardiacas en 21 horas, para dinámicas evaluadas en 18 horas. Método: se tomaron 400 registros electrocardiográficos, 80 de dinámicas normales y 320 de dinámicas anormales. Se generó una sucesión pseudoaleatoria con el número de latidos/hora y las frecuencias máximas y mínimas cada hora; luego, se construyó el atractor de cada dinámica, para así calcular los espacios de ocupación y la dimensión fractal. Finalmente, se estableció el diagnóstico físico-matemático en 18 y 21 horas y se comparó con el diagnóstico clínico tomado como Gold Standard, obteniendo valores de sensibilidad, especificidad y coeficiente Kappa. Resultados: se encontraron valores de ocupación espacial en la rejilla Kp para normalidad entre 236 y 368 y para estados patológicos entre 22 y 189, lo que permitió diferenciar entre normalidad, enfermedad, y estados de evolución hacia la enfermedad en 18 horas. Se obtuvieron valores de sensibilidad y especificidad del 100 por ciento y coeficiente Kappa igual a 1. Conclusión: la ley matemática permitió dictaminar diagnósticos reduciendo el tiempo de evaluación a 18 horas confirmando así su aplicabilidad clínica(AU)

Dynamical systems theory aims to study the evolution of systems. With this theory and fractal geometry, it was developed a mathematical law of diagnostic utility in cardiac dynamical systems that may differentiate normality from disease and evolution between these two states. Objective: To confirm the diagnostic capacity of the exponential mathematical law initially developed for cardiac dynamics in 21 hours, for dynamics evaluated in 18 hours. Method: There were taken 400 electrocardiographic records, 80 from normal dynamics and 320 from abnormal dynamics. A pseudorandom sequence was generated with the number of beats per hour and the maximum and minimum frequencies each hour; then, the attractors were built for each dynamic, in order to calculate the space occupation and the fractal dimension. Finally the physical and mathematical diagnosis in 18 and 21 hours was established, and compared to clinical diagnosis taken as Gold Standard, obtaining values of sensitivity, specificity and Kappa coefficient. Results: There were found values for spatial occupation in the Kp grid between 236 and 368 for normal cases, and between 22 and 189 for pathological states, which allowed distinguish normality from disease and states of progression to disease in 18 hours. There were obtained values for sensitivity and specificity of 100 percent and a Kappa coefficient equal to 1. Conclusion: The mathematical law allowed to stablish diagnostics by reducing the evaluation time to 18 hours confirming its clinical applicability(AU)

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El objetivo del presente escrito consiste en investigar la constitución subjetiva desde una nueva perspectiva a fin de abordar las estructuras psicopatológicas, con miras a una terapéutica que incluya una noción de salud acorde a la ética psicoanalítica. Desarrollaremos el concepto de agujero en la estructura: proponemos que en un primer momento de la enseñanza de Lacan el agujero originario es leído en términos de falta y luego se concibe como un vacío. En este sentido, realizaremos un recorrido que nos permita argumentar qué se concibe por agujero desde el psicoanálisis y diferenciar distintos tipos de agujeros. Postulamos que el agujero, que llamaremos inicial, requerirá ser redoblado por otras operaciones tanto como para vaciarse, como para transformarse en un agujero con bordes. Para ello señalaremos la importancia de diferenciar el concepto de vacío y de agujero, y luego los tratamientos posibles de éste. Por último consideramos que la concepción que se tenga de la estructuración subjetiva tiene consecuencias en la praxis. En este recorrido nos serviremos de algunas nociones de la física para articular el concepto de estructura disipativa y desde allí pensar la orientación analítica.

The aim of this paper is to investigate the subjective constitution from a new perspective in order to approach psychopathological structures looking forward to a kind of practice that includes a notion of health consistent with psychoanalytic ethics. We will develop the concept of hole in the structure: we propose that in Lacan' s first teachings the originary hole is read in terms of lack, while in his last teachings it is conceived as a void. In this sense, we will follow a path that will allow us to argue what is the concept of hole in psychoanalysis and identify the different types of holes. We postulate that the hole, which we call originary, will need to be reinforced by other operations in order to be emptied or to become a hole with edges. And to do that, we will stress the importance of differentiating the concepts of void and hole, and then lay out the possible treatments for the latter. Finally, we consider that the concept that one may have of subjective structuring has consequences for the practice. On the course of this investigation we will use some notions of physics to articulate the concept of dissipative structure and think the analytical orientation from there.

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Mathematical models based on dynamical systems theory are well-suited tools for the integration of available molecular experimental data into coherent frameworks in order to propose hypotheses about the cooperative regulatory mechanisms driving developmental processes. Computational analysis of the proposed models using well-established methods enables testing the hypotheses by contrasting predictions with observations. Within such framework, Boolean gene regulatory network dynamical models have been extensively used in modeling plant development. Boolean models are simple and intuitively appealing, ideal tools for collaborative efforts between theorists and experimentalists. In this chapter we present protocols used in our group for the study of diverse plant developmental processes. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature.

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ResumenIntroducción:La dinámica cardíaca ha sido caracterizada a partir de la teoría de los sistemas dinámicos y la geometría fractal, permitiendo generar metodologías de aplicación clínica.Objetivo:desde los sistemas dinámicos, se desarrollará una metodología de evaluación de los pH y presiones de dióxido de carbono arteriales y venosos para pacientes de la Unidad de Cuidados Intensivos.Materiales y Métodos:se escogieron 10 pacientes con diversas patologías de la Unidad de Cuidados Intensivos Postqui rúrgicos del Hospital Militar Central, registrando pH y presiones de dióxido de carbono arteriales y venosas durante su tiempo de estancia; posteriormente se construyeron atractores, determinando su tipo de trayectoria y estableciendo los valores máximos y mínimos de estas variables en el mapa de retardo.Resultados:se encontró un comportamiento caótico de las variables evaluadas, hallando valores mínimos y máximos de 7,01 y 7,59 para pH arterial, 6,97 y 7,53 para pH venoso, 14,40 y 73,70 para presión arterial de dióxido de carbono, y 19,20 y 97,90 para presión venosa de dióxido de carbono.Conclusiones:La evaluación de los valores máximos y mínimos del atractor en el mapa de retardo constituye un nuevo método, objetivo y reproducible, para la evaluación matemática de cada una de las variables estudiadas, de utilidad para el seguimiento de pacientes en UCI.

SummaryIntroduction:Cardiac dynamics has been characterized from the theory of dynamical systems and fractal geometry, allowing to generate methodologies with clinical application. Objective: from dynamic systems, a methodology for evaluating the arterial and venous pH and dioxide of carbon pressures for patient in Intensive Care Unit will be developed.Materials and Methods:10 patients with various pathologies were selected from Post-surgical Intensive Care Unit of the Central Military Hospital, recording arterial and venous pH and dioxide of carbon pressures of during its stay; attractors were built subsequently, determining the type of path and setting the maximum and minimum values of these variables on the delay map.Results:chaotic behavior of the variables evaluated was found, finding maximum and minimum values of 7,01 and 7,59 for arterial pH values, 6,97 and 7,53 for venous pH, 14,40 and 73,70 for arterial dioxide of carbon pressure, and 19,20 and 97,90 for venous dioxide of carbon pressure.Conclusions:The evaluation of the maximum and minimum values of the attractor on the delay map is a new method, objective and reproducible for the mathematical evaluation of each of the variables studied, useful for monitoring patients in Intensive Care Unit.

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This work experimentally analyzes the learning and retrieval capabilities of the diluted metric attractor neural network when applied to collections of fingerprint images. The computational cost of the network decreases with the dilution, so we can increase the region of interest to cover almost the complete fingerprint. The network retrieval was successfully tested for different noisy configurations of the fingerprints, and proved to be robust with a large basin of attraction. We showed that network topologies with a 2D-Grid arrangement adapt better to the fingerprints spatial structure, outperforming the typical 1D-Ring configuration. An optimal ratio of local connections to random shortcuts that better represent the intrinsic spatial structure of the fingerprints was found, and its influence on the retrieval quality was characterized in a phase diagram. Since the present model is a set of nonlinear equations, it is possible to go beyond the naïve static solution (consisting in matching two fingerprints using a fixed distance threshold value), and a crossing evolution of similarities was shown, leading to the retrieval of the right fingerprint from an apparently more distant candidate. This feature could be very useful for fingerprint verification to discriminate between fingerprints pairs.

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Behavioral observations suggest that multiple sensory elements can be maintained for a short time, forming a perceptual buffer which fades after a few hundred milliseconds. Only a subset of this perceptual buffer can be accessed under top-down control and broadcasted to working memory and consciousness. In turn, single-cell studies in awake-behaving monkeys have identified two distinct waves of response to a sensory stimulus: a first transient response largely determined by stimulus properties and a second wave dependent on behavioral relevance, context and learning. Here we propose a simple biophysical scheme which bridges these observations and establishes concrete predictions for neurophsyiological experiments in which the temporal interval between stimulus presentation and top-down allocation is controlled experimentally. Inspired in single-cell observations, the model involves a first transient response and a second stage of amplification and retrieval, which are implemented biophysically by distinct operational modes of the same circuit, regulated by external currents. We explicitly investigated the neuronal dynamics, the memory trace of a presented stimulus and the probability of correct retrieval, when these two stages were bracketed by a temporal gap. The model predicts correctly the dependence of performance with response times in interference experiments suggesting that sensory buffering does not require a specific dedicated mechanism and establishing a direct link between biophysical manipulations and behavioral observations leading to concrete predictions.