Approximate solutions of dual fuzzy polynomials by feed-back neural networks

Recently, artificial neural networks (ANNs) have been extensively studied and used in different areas such as pattern recognition, associative memory, combinatorial optimization, etc. In this paper, we investigate the ability of fuzzy neural networks to approximate solution of a dual fuzzy polynomial of the form a1x+...+anx n = b1x+...+bnx n +d, where aj , bj , d ϵ E1 (for j = 1, ..., n). Since the operation of fuzzy neural networks is based on Zadeh’s extension principle. For this scope we train a fuzzified neural network by backpropagation-type learning algorithm which has five layer where connection weights arecrisp numbers. This neural network can get a crisp input signal and then calculates itscorresponding fuzzy output. Presented method can give a real approximate solution for given polynomial by using a cost function which is defined for the level sets of fuzzy output and target output. The simulation results are presented to demonstrate the efficiency and effectiveness of the proposed approach

A new computational method for solving fully fuzzy nonlinear matrix equations

Multi formulations and computational methodologies have been suggested to extract solution of fuzzy nonlinear programming problems. However, in some cases the methods which have been utilised in order to find the solution of these problems involve greater complexity. On the basis of the mentioned reason, the current research work is intended towards introduction of a simple method for finding the fuzzy optimal solution related to fuzzy nonlinear issues. The proposed method is validated and is confirmed to be applicable by suggesting some demonstrated examples. The results confirm that the proposed method is so easy to understand and to apply for solving fully fuzzy nonlinear system (FFNS)

Solving fully fuzzy polynomials using feed-back neural networks

Recently, there has been a considerable amount of interest and practice in solving many problems of several applied fields by fuzzy polynomials. In this paper, we have designed an artificial fuzzified feed-back neural network. With this design, we are able to find a solution of fully fuzzy polynomial with degree n. This neural network can get a fuzzy vector as an input, and calculates its corresponding fuzzy output. It is clear that the input–output relation for each unit of fuzzy neural network is defined by the extension principle of Zadeh. In this work, a cost function is also defined for the level sets of fuzzy output and fuzzy target. Next a learning algorithm based on the gradient descent method will be defined that can adjust the fuzzy connection weights. Finally, our approach is illustrated by computer simulations on numerical examples. It is worthwhile to mention that application of this method in fluid mechanics has been shown by an example

Slow-Fast Duffing Neural Mass Model

Epileptic seizures may be initiated by random neuronal fluctuations and/or by pathological slow regulatory dynamics of ion currents. This paper presents extensions to the Jansen and Rit neural mass model (JRNMM) to replicate paroxysmal transitions in intracranial electroencephalogram (iEEG) recordings. First, the Duffing NMM (DNMM) is introduced to emulate stochastic generators of seizures. The DNMM is constructed by applying perturbations to linear models of synaptic transmission in each neural population of the JRNMM. Then, the slow-fast DNMM is introduced by considering slow dynamics (relative to membrane potential and firing rate) of some internal parameters of the DNMM to replicate pathological evolution of ion currents. Through simulation, it is illustrated that the slow-fast DNMM exhibits transitions to and from seizures with etiologies that are linked either to random input fluctuations or pathological evolution of slow states. Estimation and optimization of a log likelihood function (LLF) using a continuous-discrete unscented Kalman filter (CD-UKF) and a genetic algorithm (GA) are performed to capture dynamics of iEEG data with paroxysmal transitions

Identification of A Neural Mass Model of Burst Suppression

Burst suppression includes alternating patterns of silent and fast spike activities in neuronal activities observable (in micro or macro scale) electro-physiological recordings. Biological models of burst suppression are given as dynamical systems with slow and fast states. The aim of this paper is to give a method to identify parameters of a mesoscopic model of burst suppression that can provide insights into study underlying generators of intracranial electroencephalogram (iEEG) data. An optimisation technique based upon a genetic algorithm (GA) is employed to find feasible model parameters to replicate burst patterns in the iEEG data with paroxysmal transitions. Then, a continuous-discrete unscented Kalman filter (CD-UKF) is used to infer hidden states of the model and to enhance the identification results from the GA. The results show promise in finding the model parameters of a partially observed mesoscopic model of burst suppression

Propofol-alfentanil vs propofol-remifentanil for posterior spinal fusion including wake-up test

Background. Wake-up test can be used during posterior spinal fusion (PSF) to ensure that spinal function remains intact. This study aims at assessing the characteristics of the wake-up test during propofol-alfentanil (PA) vs propofol-remifentanil (PR) infusions for PSF surgery. Methods. Sixty patients with scoliosis and candidates for PSF surgery were randomly allocated in either alfentanil (PA) or remifentanil (PR) group. After an i.v. bolus of alfentanil 30 μg kg-1 in the PA group or remifentanil 1 μg kg-1 in the PR group, anaesthesia was induced with thiopental and atracurium. During maintenance, opioid infusion consisted of alfentanil 1 μg kg-1 min-1 or remifentanil 0.2 μg kg-1 min-1, in the PA group and the PR group, respectively. All patients received propofol 50 μg kg-1 min-1. Atracurium was given to maintain the required surgical relaxation. At the surgeon's request, all infusions were discontinued. Patients were asked to move their hands and feet. Time from anaesthetic discontinuation to spontaneous ventilation (T1), and from then until movement of the hands and feet (T2), and its quality were recorded. Results. The average T1 and T2 were significantly shorter in the PR group 3.6 (2.5) and 4.1 (2) min than the PA group 6.1 (4) and 7.5 (4.5) min. Quality of wake-up test, however, did not show significant difference between the two groups studied. Conclusion. Wake-up test can be conducted faster with remifentanil compared with alfentanil infusion during PSF surgery. © 2006 Oxford University Press

Investigation on microstructure and oxidation behavior of Cr-modified aluminide coating on γ-TiAl alloys

Microstructure and oxidation behavior of aluminide coating has been investigated. The layers were examined by optical microscopy, scanning electron microscopy (SEM) equipped with EDS and X-ray diffraction method. The isothermal oxidation behaviors of samples were investigated at 950°C for 200 h. The results indicated that TiAl₃ were formed on substrate. In addition, aluminide coating improved the oxidation resistance of γ-TiAl alloys by forming a protective alumina scale. Moreover, during oxidation treatment the interdiffusion of TiAl₃ layer with γ-TiAl substrate results in depletion of aluminum in the TiAl₃ layer and growth of TiAl₂ layer. After oxidation treatment the coating layer maintained a microstructure with phases including TiAl₃, TiAl₂ and Al₂O₃.Досліджено мікроструктуру алюмінідного покриву та його поведінку під час високотемпературного окислення. Шари алюмінідів титану вивчали за допомогою оптичної мікроскопії, сканівної електронної мікроскопії (SЕМ) з використанням дисперсного рентгеноспектрометра (EDS) та рентгенівським дифракційним методом. Випробовування проводили при 950°C впродовж 200 h. Встановлено, що на підкладці з титанового сплаву утворився TiAl₃. Покрив з алюмініду титану покращує стійкість до окислення сплавів з γ-TiAl, утворюючи захисну плівку з оксиду алюмінію. Під час окислення дифузійна взаємодія TiAl₃ з підкладкою γ-TiAl спричиняє зменшення кількості алюмінію у шарі TiAl₃ та збільшення шару TiAl₂. Після окислення в покриві утворюється мікроструктура з фазами, що містять TiAl₃, TiAl₂ та Al₂O₃.Исследовано микроструктуру алюминидного покрытия и его поведение при высокотемпературном окислении. Слои алюминида титана изучали с помощью оптической микроскопии, сканирующей электронной микроскопии (SЕМ) с использованием дисперсного рентгеноспектрометра (EDS) и рентгеновским дифракционным методом. Испытания проводили при 950°C в течение 200 h. Установлено, что на подкладке из титанового сплава образовался TiAl₃. Покрытие из алюминида титана улучшает стойкость к окислению сплавов из γ-TiAl, образовывая защитную пленку из окисла алюминия. Во время окисления диффузионное взаимодействие TiAl₃ с подкладкой γ-TiAl влечет уменьшение количества алюминия в слое TiAl₃ и увеличение слоя TiAl₂. После окисления в покрытии образуется микроструктура с фазами, которые содержат TiAl₃, TiAl₂ и Al₂O₃

A novel computational approach to approximate fuzzy interpolation polynomials

This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form yp=anxnp+⋯+a1xp+a0 where aj is crisp number (for j=0,…,n), which interpolates the fuzzy data (xj,yj)(forj=0,…,n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient

Adiabatic dynamic causal modelling

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity