Linguistic Summaries of Static and Dynamic Data: Computing with Words and Granularity

<title>Abstract</title> This study explores the put-call duality under the Truncated Normal Distribution (TND) model in option pricing which assumes that the log-prices of the underlying assets are bounded above and below. The model is compared with famous Black \&amp; Scholes Model which has been consistently been considered as the benchmark model for option pricing. Using the model, we derived a model-consistent put-call duality identity and applied it in the construction of an objective function that improves the accuracy and consistency of option pricing. This is in conjunction with the various modifications that have been put forward to "improve" the option price. The purpose of this study was to extend Zhu \&amp; He's work by studying the the put-call duality relation of the proposed model and compare it with the results obtained using the classical Black \&amp; Scholes (BS) Model. Similarly, this study investigated the implied volatility of the proposed model and compared it with the BS model. From the duality constraint calibration, the proposed model performed significantly better than the traditional Black-Scholes model. A numerical analysis was done using real market data for S\&amp;P 500 stock price data retrieved on June 27, 2025. Model performance check such as AIC, BIC and pricing errors indicated that outstanding performance of the TND model. From the methodology and numerical analysis, there is evidence that the duality relation holds for the Truncated Normal Distribution model as is the case with the Black \&amp; Scholes model. The implied volatility indicated that the TND model was sensitive for in-the-money and out-of-the money options. Therefore, the enforcement of the duality constraint in the pricing of European option improved the market consistency ensures that no arbitrage opportunities exist in the market that cab provide enormous risk-free earnings in the market.

House price forecasting with neural networks

This paper reports results with ABI, a portable noninvasive brain-computer interface. It uses 8 scalp electrodes to measure spontaneous EEG signals from which we extract simple power spectral features. The features are fed to a simple local neural network that recognizes reliably 3 different mental states. We compare the performance of this local classifier to more complex time-processing neural networks. We also illustrate the control of a complex brain-actuated device; i.e., a robot moving along smooth and safe paths between rooms.

In this paper, we showed a method to forecast the stock price using neural networks. Predicting the stock market is very difficult since it depends on several known and unknown factors. In recent years, one of the techniques that have been used popularly in this area is artificial neural network. The power of neural network is its ability to model a nonlinear process without a priori knowledge about the nature of the process. We used both feed forward neural network and simple recurrent neural network, trained by time and profit based back propagation algorithm with early stopping to make the prediction. The integration of profit and time factors with training procedure made an improvement in forecasted results for feed forward neural network. Moreover, the simple recurrent neural network with its ` time capture' capabilities had better forecasted results than feed forward neural network in all experiments.

We have investigated selective learning techniques for improving the ability of back-propagation neural networks to predict large changes. The prediction of daily stock prices was taken as an example of a noisy real-world problem. We previously proposed the selective-presentation and selective-learning-rate approaches and applied them into feed-forward neural networks. This paper applies the selective-learning-rate approach into three types of simple recurrent neural networks. We evaluated their performances through experimental stock-price prediction. Using selective-learning-rate approach, the network can learn the large changes well and profit per trade was improved in all of simple recurrent neural networks.

The author considers a discrete-time neural network which consists of only two neurons with the sigmoidal nonlinear function as the neuron activation function and has no external inputs and no time delay. He treats the simple network as a one-parameter family of two-dimensional maps with the neuron gain as the parameter, and mathematically proves the existence of period-doublings to chaos in the network with an excitatory neuron and an inhibitory neuron. Specifically, it is proved that, for a certain class of singular connection weight matrices, the simple neural network is dynamically equivalent to a one-parameter full family of (one-dimensional) S-unimodal maps on the interval which is well-known to become chaotic through the period-doubling route as the parameter varies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.

Leaky integrate-and-fire neurons based on perovskite memristor for spiking neural networks

In this paper, we propose and demonstrate a low-complexity fiber nonlinearity impairments compensation (NLC) scheme based on simple recurrent neural network (SRNN), combining with the triplets derived from the first-order perturbation solution of the coupled nonlinear Schrodinger equation. Benefitting from the time memory of SRNN, the proposed NLC can reduce the computational complexity without sacrificing the compensation performance compared with the schemes based on memoryless feedforward neural networks. To verify the feasibility of the proposed NLC, the simulation systems of single channel and three channel 30 GBaud polarization division multiplexing (PDM) 16 quadrature amplitude modulation (QAM) over 2400 km standard single mode fiber transmission are constructed respectively. Comprehensive numerical simulation results demonstrate that although the NLC performance of proposed scheme is inferior to that of digital back propagation (DBP) with much higher complexity and impracticality, it can still achieve the competitive NLC performance with lower computational complexity compared to the schemes based on deep neural network (DNN) and artificial neural network (ANN). Moreover, it is further proved that using triplets as the feature required for NLC can cause the pattern of pseudo random bit sequence to be destroyed, resulting in the neural network-based NLC scheme not suffering from the problem of overestimation for performance. Additionally, the time memory of SRNN enables the number of triplets in training set required by the SRNN-based NLC to be reduced by 169% compared to that of DNN and ANN. The experimental results of 16 GBaud PDM-16QAM wavelength division multiplexing coherent systems demonstrate that compared to with ANN and DNN, the comparable NLC performance can also be achieved by the proposed scheme with lower complexity.

In the 21st century marine navigation has become dominated by satellite positioning systems and automated navigational processes. Today, global navigation satellite systems (GNSS) play a central role in the process of carrying out basic navigational tasks, e.g. determining the coordinates of a vessel’s position at sea. Since satellite systems are being used increasingly more often in everyday life, the signals they send are becoming more and more prone to jamming. Therefore there is a need to search for other positioning systems and methods that would be as accurate and fast as the existing satellite systems. On the other hand, the automation process makes it possible to conduct navigational tasks more quickly. Due to the development of this technology, all kinds of navigation equipment can be used in the process of automating navigation. This also applies to marine radars, which are characterised by a relatively high accuracy that allows them to replace satellite systems in performing classic navigational tasks. By employing M-estimation methods that are used in geodesy as well as simple neural networks, a software package can be created that will aid in automating navigation and will provide highly accurate information about a given object’s position at sea by making use of radar in comparative navigation. This paper presents proposals for automating the process of determining a vessel’s position at sea by using comparative navigation methods that are based on simple neural networks and geodetic M-estimation methods.

Due to their synaptic-like characteristics and memory properties, memristors are often used in neuromorphic circuits, particularly neural network circuits. However, most of the existing neural network circuits that can generate complex dynamics have high dimensions and excessive connections, which is not conducive to implementation. This article introduces a memristor containing an arctangent function into a simple cyclic neural network (SCNN) circuit to design a simple cyclic memristive neural network (SCMNN) circuit capable of generating complex multiscroll chaotic attractors. The designed SCMNN contains an external stimulus current and generates multiscroll attractors, with the number of scrolls expanding as the switches in the memristor equivalent circuit are activated. By varying the parameters, the multiscroll attractors can be broken into different numbers of coexisting attractors, which also depends on the switch, and it can achieve multivariable amplitude control when there is only one scroll. The anti-interference ability of the circuit is tested. A low-cost circuit-based microcontroller suitable for engineering applications is designed for it, and multiscroll attractors are successfully captured in an oscilloscope. The National Institute of Standards and Technology (NIST) test is carried out to verify its application value.

This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent unpredictability of market volatility by setting upper and lower bounds on volatility and the correlation among underlying assets. By leveraging historical data and extreme values of estimated volatilities and correlations, the model establishes a confidence interval for future volatility and correlations, thus providing a more realistic approach to option pricing. By integrating advanced Machine Learning algorithms, we aim to enhance the accuracy and efficiency of option pricing under the UVM, especially when the option price depends on a large number of variables, such as in basket or path-dependent options. In this paper, we consider two approaches based on Machine Learning. The first one, termed GTU, evolves backward in time, dynamically selecting at each time step the most expensive volatility and correlation for each market state. Specifically, it identifies the particular values of volatility and correlation that maximize the expected option value at the next time step, and therefore, an optimization problem must be solved. This is achieved through the use of Gaussian Process regression, the computation of expectations via a single step of a multidimensional tree and the Sequential Quadratic Programming optimization algorithm. The second approach, referred to as NNU, leverages neural networks and frames pricing in the UVM as a control problem. Specifically, we train a neural network to determine the most adverse volatility and correlation for each simulated market state, generated via random simulations. The option price is then obtained through Monte Carlo simulations, which are performed using the values for the uncertain parameters provided by the neural network. The numerical results demonstrate that the proposed approaches can significantly improve the precision of option pricing and risk management strategies compared with methods already in the literature, particularly in high-dimensional contexts.

One important issue in the motion planning of kinematic redundant manipulators is the online obstacle-avoidance. For such purposes, we proposed and unified the scheme formulation based on general quadratic-programs (QP), which incorporates physical constraints such as joint physical limits and collision-avoidance inequality. In this paper, a simplified primal-dual neural network based on linear variational inequalities (LVI) is presented for the real-time solution of such a collision-free inverse-kinematic planning scheme. The neural network solves the strictly-convex QP in an inverse-free manner, in addition to the simple piecewise-linear dynamics and global exponential convergence to optimal solutions. Further computer-simulations based on PA10 redundant robot manipulator substantiate the efficacy of the scheme formulation and its neural-network solver on window-shaped obstacle avoidance.

ABSTRACTIn human speech, the timing function is important for determining its duration, stress and rhythm; however, little attention has been paid to these issues when building a speech synthesis system. In the human brain, the cerebellum plays a key role in the coordination, precision and timing of motor responses. We have developed a talking robot, which generates human-like vocal sounds using a simplified cerebellum-like neural network model as the timing function. The model was designed using the System Generator software in Matlab environment and the timing duration of trained speech was estimated using hardware co-simulated with a field programmable gate array board (FPGA). The timing information obtained from the co-simulation, together with the output motor vector, is sent to the talking robot controller in order to generate vowels of short, medium and long duration. Using this model for short-range timing of less than 1200 milliseconds, we verify that the short-range learning capability of the cerebellar-like neural network is applicable to the speaking robot for generating a human-like speech with prosodic features.

This paper presents a risk neutral binomial process as an alternative approach for the derivation of analytic pricing equation called “Black - Scholes Partial differential Equation” in the theory of option pricing. Binomial option pricing is a powerful technique that can be used to solve many complex option pricing problems. In contra st to the Black - Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial model is mathematically simple. Binomial model is based on the assumption of no arbitrage. The assumption of no arbitra ge implies that all risk - free investments earn the risk - free rate of return and no investment opportunity exists that requires zero amounts of investment but yield positive returns.