Search results for: huxley

Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: all-or-none, computational modelling, mathematical model, transmembrane voltage, action potential

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Firas Al-Jubouri

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Literature has been a subject of studying English at secondary, university, and postgraduate levels in many countries and for several decades. One of the prominent literary genres, which is being increasingly used in the literature classrooms, is dystopian literature. However, since teachers usually address the educational requirements of teaching canonical English literature to meet the expected objectives of the particular 1organisation, and the learner’s needs in the non- Anglophone context, they must also negotiate the issues of cultural differences, aesthetic values, literary significance, and the rationale of storytelling. This paper examines how teaching certain dystopian themes in Aldous Huxley’s Brave New World (1932), an extremely influential dystopian canon, has to take into consideration the ideas, traditions, cultures, and means of literary interpretation inherent in the Arab Muslim world, with specific emphasis on the GCC region. It suggests the use of DionýzĎurišin’s (1929-1997) system of interliterariness in teaching world and comparative literature to help improve the interpretation of canonical literary texts in the international and inter-ethnic classrooms and contexts. Thus, this study helps to define a means of integrating global content and cross-cultural experiences into an effective teaching methodology that helps mitigate the major divides between the Anglophone text and the non-Anglophone readers.

Keywords: anglophone, dystopia, brave new world, huxley, interliterariness

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Authors: Aamna Lawrence, Ashutosh Mishra

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Tremors occur in 60% of the patients who have Multiple Sclerosis (MS), the most common demyelinating disease that affects the central and peripheral nervous system, and are the primary cause of disability in young adults. While pharmacological agents provide minimal benefits, surgical interventions like Deep Brain Stimulation and Thalamotomy are riddled with dangerous complications which make non-invasive electrical stimulation an appealing treatment of choice for dealing with tremors. Hence, we hypothesized that if the non-invasive electrical stimulation parameters (mainly frequency) can be computed by mathematically modeling the nerve fibre to take into consideration the minutest details of the axon morphologies, tremors due to demyelination can be optimally alleviated. In this computational study, we have modeled the random demyelination pattern in a nerve fibre that typically manifests in MS using the High-Density Hodgkin-Huxley model with suitable modifications to account for the myelin. The internode of the nerve fibre in our model could have up to ten demyelinated regions each having random length and myelin thickness. The arrival time of action potentials traveling the demyelinated and the normally myelinated nerve fibre between two fixed points in space was noted, and its relationship with the nerve fibre radius ranging from 5µm to 12µm was analyzed. It was interesting to note that there were no overlaps between the arrival time for action potentials traversing the demyelinated and normally myelinated nerve fibres even when a single internode of the nerve fibre was demyelinated. The study gave us an opportunity to design DC pulses whose frequency of application would be a function of the random demyelination pattern to block only the delayed tremor-causing action potentials. The DC pulses could be delivered to the peripheral nervous system non-invasively by an electrode bracelet that would suppress any shakiness beyond it thus paving the way for wearable neuro-rehabilitative technologies.

Keywords: demyelination, Hodgkin-Huxley model, non-invasive electrical stimulation, tremor

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Authors: Le Zhao, Alain Nogaret

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We have built universal Central Pattern Generator (CPG) hardware by interconnecting Hodgkin-Huxley neurons with reciprocally inhibitory synapses. We investigate the dynamics of neuron oscillations as a function of the time delay between current steps applied to individual neurons. We demonstrate stimulus dependent switching between spiking polyrhythms and map the phase portraits of the neuron oscillations to reveal the basins of attraction of the system. We experimentally study the dependence of the attraction basins on the network parameters: the neuron response time and the strength of inhibitory connections.

Keywords: central pattern generator, winnerless competition principle, artificial neural networks, synapses

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Zeina Bou Diab, Arij Daou

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The neural mechanisms of sequential behaviors are intensively studied, with songbirds a focus for learned vocal production. We are studying the premotor nucleus HVC at a nexus of multiple pathways contributing to song learning and production. The HVC consists of multiple classes of neuronal populations, each has its own cellular, electrophysiological and functional properties. During singing, a large subset of motor cortex analog-projecting HVCRA neurons emit a single 6-10 ms burst of spikes at the same time during each rendition of song, a large subset of basal ganglia-projecting HVCX neurons fire 1 to 4 bursts that are similarly time locked to vocalizations, while HVCINT neurons fire tonically at average high frequency throughout song with prominent modulations whose timing in relation to song remains unresolved. This opens the opportunity to define models relating explicit HVC circuitry to how these neurons work cooperatively to control learning and singing. We developed conductance-based Hodgkin-Huxley models for the three classes of HVC neurons (based on the ion channels previously identified from in vitro recordings) and connected them in several physiologically realistic networks (based on the known synaptic connectivity and specific glutaminergic and gabaergic pharmacology) via different architecture patterning scenarios with the aim to replicate the in vivo firing patterning behaviors. We are able, through these networks, to reproduce the in vivo behavior of each class of HVC neurons, as shown by the experimental recordings. The different network architectures developed highlight different mechanisms that might be contributing to the propagation of sequential neural activity (continuous or punctate) in the HVC and to the distinctive firing patterns that each class exhibits during singing. Examples of such possible mechanisms include: 1) post-inhibitory rebound in HVCX and their population patterns during singing, 2) different subclasses of HVCINT interacting via inhibitory-inhibitory loops, 3) mono-synaptic HVCX to HVCRA excitatory connectivity, and 4) structured many-to-one inhibitory synapses from interneurons to projection neurons, and others. Replication is only a preliminary step that must be followed by model prediction and testing.

Keywords: computational modeling, neural networks, temporal neural sequences, ionic currents, songbird

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Authors: Yuko Ishiwaka, Tomohiro Yoshida, Tadateru Itoh

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Human makes preparation called readiness potential unconsciously (RP) before awareness of their own decision. For example, when recognizing a button and pressing the button, the RP peaks are observed 200 ms before the initiation of the movement. It has been known that the preparatory movements are acquired before actual movements, but it has not been still well understood how humans can obtain the RP during their growth. On the proposition of why the brain must respond earlier, we assume that humans have to adopt the dangerous environment to survive and then obtain the behavior to cover the various time lags distributed in the body. Without RP, humans cannot take action quickly to avoid dangerous situations. In taking action, the brain makes decisions, and signals are transmitted through the Spinal Cord to the muscles to the body moves according to the laws of physics. Our research focuses on the time lag of the neuron signal transmitting from a brain to muscle via a spinal cord. This time lag is one of the essential factors for readiness potential. We propose a firing pattern controller model of a motor nerve system considered innervation and jitter, which produces time lag. In our simulation, we adopt innervation and jitter in our proposed muscle-skeleton model, because these two factors can create infinitesimal time lag. Q10 Hodgkin Huxley model to calculate action potentials is also adopted because the refractory period produces a more significant time lag for continuous firing. Keeping constant power of muscle requires cooperation firing of motor neurons because a refractory period stifles the continuous firing of a neuron. One more factor in producing time lag is slow or fast-twitch. The Expanded Hill Type model is adopted to calculate power and time lag. We will simulate our model of muscle skeleton model by controlling the firing pattern and discuss the relationship between the time lag of physics and neurons. For our discussion, we analyze the time lag with our simulation for knee bending. The law of inertia caused the most influential time lag. The next most crucial time lag was the time to generate the action potential induced by innervation and jitter. In our simulation, the time lag at the beginning of the knee movement is 202ms to 203.5ms. It means that readiness potential should be prepared more than 200ms before decision making.

Keywords: firing patterns, innervation, jitter, motor nerve system, readiness potential

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Authors: Johan Anker

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The purpose of this paper is to discuss the nature of gender construction in modern dystopian fiction, the development of this genre in Young Adult Literature and reasons for the enormous appeal on the adolescent readers. A recent award winning South African text in this genre, The Mark by Edith Bullring (2014), will be used as example while also comparing this text to international bestsellers like Divergent (Roth:2011), The Hunger Games (Collins:2008) and others. Theoretical insights from critics and academics in the field of children’s literature, like Ames, Coats, Bradford, Booker, Basu, Green-Barteet, Hintz, McAlear, McCallum, Moylan, Ostry, Ryan, Stephens and Westerfield will be referred to and their insights used as part of the analysis of The Mark. The role of relevant and recurring themes in this genre, like global concerns, environmental destruction, liberty, self-determination, social and political critique, surveillance and repression by the state or other institutions will also be referred to. The paper will shortly refer to the history and emergence of dystopian literature as genre in adult and young adult literature as part of the long tradition since the publishing of Orwell’s 1984 and Huxley’s Brave New World. Different factors appeal to adolescent readers in the modern versions of this hybrid genre for young adults: teenage protagonists who are questioning the underlying values of a flawed society like an inhuman or tyrannical government, a growing understanding of the society around them, feelings of isolation and the dynamic of relationships. This unease leads to a growing sense of the potential to act against society (rebellion), and of their role as agents in a larger community and independent decision-making abilities. This awareness also leads to a growing sense of self (identity and agency) and the development of romantic relationships. The specific modern tendency of a female protagonist as leader in the rebellion against state and state apparatus, who gains in agency and independence in this rebellion, an important part of the identification with and construction of gender, while being part of the traditional coming-of-age young adult novel will be emphasized. A comparison between the traditional themes, structures and plots of young adult literature (YAL) with adult dystopian literature and those of recent dystopian YAL will be made while the hybrid nature of this genre and the 'sense of unease' but also of hope, as an essential part of youth literature, in the closure to these novels will be discussed. Important questions about the role of the didactic nature of these texts and the political issues and the importance of the formation of agency and identity for the young adult reader, as well as identification with the protagonists in this genre, are also part of this discussion of The Mark and other YAL novels.

Keywords: agency, dystopian literature, gender construction, young adult literature

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Authors: Turky Al-Qahtani, Roustem Miftahof

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Introduction: Under common assumptions of excitabi-lity, morphological (cellular) homogeneity, and spatial structural anomalies added as required, it has been shown that biological systems are able to display travelling wave dynamics. Being not self-sustainable, existence depends on the electrophysiological state of transmembrane ion channels and it requires an extrinsic/intrinsic periodic source. However, organs in the body are highly multicellular, heterogeneous, and their functionality is the outcome of electro-mechanical conjugation, rather than excitability only. Thus, peristalsis in the gut relies on spatiotemporal myoelectrical pattern formations between the mechanical, represented by smooth muscle cells (SM), and the control, comprised of a chain of primary sensory and motor neurones, components. Synaptically linked through the afferent and efferent pathways, they form a functional unit (FU) of the gut. Aims: These are: i) to study numerically the complex dynamics, and ii) to investigate the possibility of self-sustained myoelectrical activity in the FU. Methods: The FU recreates the following sequence of physiological events: deformation of mechanoreceptors of located in SM; generation and propagation of electrical waves of depolarisation - spikes - along the axon to the soma of the primary neurone; discharge of the primary neurone and spike propagation towards the motor neurone; burst of the motor neurone and transduction of spikes to SM, subsequently producing forces of contraction. These are governed by a system of nonlinear partial and ordinary differential equations being a modified version of the Hodgkin-Huxley model and SM fibre mechanics. In numerical experiments; the source of excitation is mechanical stretches of SM at a fixed amplitude and variable frequencies. Results: Low frequency (0.5 < v < 2 Hz) stimuli cause the propagation of spikes in the neuronal chain and, finally, the generation of active forces by SM. However, induced contractions are not sufficient to initiate travelling wave dynamics in the control system. At frequencies, 2 < v < 4 Hz, multiple low amplitude and short-lasting contractions are observed in SM after the termination of stretching. For frequencies (0.5 < v < 4 Hz), primary and sensory neurones demonstrate strong connectivity and coherent electrical activity. Significant qualitative and quantitative changes in dynamics of myoelectical patterns with a transition to a self-organised mode are recorded with the high degree of stretches at v = 4.5 Hz. Increased rates of deformation lead to the production of high amplitude signals at the mechanoreceptors with subsequent self-sustained excitation within the neuronal chain. Remarkably, the connection between neurones weakens resulting in incoherent firing. Further increase in a frequency of stimulation (v > 4.5 Hz) has a detrimental effect on the system. The mechanical and control systems become disconnected and exhibit uncoordinated electromechanical activity. Conclusion: To our knowledge, the existence of periodic activity in a multicellular, functionally heterogeneous biological system with mechano-electrical dynamics, such as the FU, has been demonstrated for the first time. These findings support the notion of possible peristalsis in the gut even in the absence of intrinsic sources - pacemaker cells. Results could be implicated in the pathogenesis of intestinal dysrythmia, a medical condition associated with motor dysfunction.

Keywords: complex dynamics, functional unit, the gut, dysrythmia

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