Long-term Memory Properties Research Articles

Cortical, striatal, and thalamic populations self-organize into a functionally connected circuit with long-term memory properties

The human brain is a complex organ with an intricate neuronal connectivity and diverse functional regions. Neurological disorders often disrupt the delicate balance among these anatomical compartments, resulting in severe impairments. The available therapeutic options constitute an incomplete solution as many patients respond partially, highlighting the need for continued research into causes and treatments. Bottom-up approaches, like in vitro models, offer insights into brain functions as they recreate the in vivo microenvironment that allows studying how specific features affect physiological and pathological conditions. In this work, we engineered the cortical-striatal-thalamic (CST) circuit, involved in many brain functions such as action initiation and selection, using a three-compartment polymeric device. We characterized the emerging spontaneous electrophysiological activity by using Micro-Electrode Arrays (MEAs). Cortical neurons exhibited complex bursting activity, which influenced the entire circuit. Striatal and thalamic neurons displayed predominantly tonic firing when isolated, while interconnections with the cortex synchronized and organized their neuronal activity, highlighting the cortical pivotal role in bursting activity and information processing. The CST circuit demonstrated self-organization abilities and displayed high entropy values, indicative of dynamic richness and information encoding potential. Furthermore, we proved the CST’s involvement in learning and memory. Our CST model provides a platform for further exploration into brain circuitry and potential therapeutic interventions, underscoring the necessity of realistic in vitro models to fully understand neurological diseases' pathophysiology.

Enhancing Long-Term Memory in Carbon-Nanotube-Based Optoelectronic Synaptic Devices for Neuromorphic Computing.

This study investigates the impact of spin-coating speed on the performance of carbon nanotube (CNT)-based optoelectronic synaptic devices, focusing on their long-term memory properties. CNT films fabricated at lower spin speeds exhibited a greater thickness and density compared to those at higher speeds. These denser films showed enhanced persistent photoconductivity, resulting in higher excitatory postsynaptic currents (EPSCs) and the prolonged retention of memory states after UV stimulation. Devices coated at a lower spin-coating speed of 2000 RPM maintained EPSCs above 70% for 3600 s, outperforming their higher-speed counterparts in long-term memory retention. Additionally, the study demonstrated that the learning efficiency improved with repeated UV stimulation, with fewer pulses needed to achieve the maximum EPSC in successive learning cycles. These findings highlight that optimizing spin-coating speeds can significantly enhance the performance of CNT-based synaptic devices, making them suitable for applications in neuromorphic computing and artificial neural networks requiring robust memory retention and efficient learning.

A novel fractional-order memristive Hopfield neural network for traveling salesman problem and its FPGA implementation

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

Fractional Approximation of Broad Learning System.

Approximation ability is of much importance for neural networks. The broad learning system (BLS) (Chen and Liu, 2018), widely used in the industry with good performance, has been proved to be a universal approximator from the aspect of density. This kind of approximation property is very important, which proves the existence of the desired network but does not provide a means of construction that is commonly implemented through complexity aspect. Thus, such an approach lacks the advantage of determining constructively the network architecture and its weights. To the best of our knowledge, for a BLS, there is a few theory providing a constructive approach to obtain the network structure along with weights ensuring the approximation properties. By virtue of the long-term memory and nonlocality properties, fractional calculus has observed many distinctive applications. The purpose of this article is to study the BLS approximation ability constructively, which is valid for fractional case as well. Specifically, first we introduce two simplified BLSs by means of extending functions. For each of the simplified BLSs, an upper bound of error is derived through the modulus of continuity of Caputo fractional derivatives. As a result, two types of fractional convergent behaviors of BLS, that is: 1) pointwise and 2) uniform convergence, have been rigorously proved as well. Finally, some numerical experiments are conducted to demonstrate the approximation capabilities of BLSs.

Short-Term to Long-Term Plasticity Transition Behavior of Memristive Devices with Low Power Consumption via Facilitating Ionic Drift of Implanted Lithium

Recent innovations in information technology have encouraged extensive research into the development of future generation memory and computing technologies. Memristive devices based on resistance switching are not only attractive because of their multi-level information storage, but they also display fascinating neuromorphic behaviors. We investigated the basic human brain’s learning and memory algorithm for “memorizing” as a feature for memristive devices based on Li-implanted structures with low power consumption. A topographical and surface chemical functionality analysis of an Li:ITO substrate was conducted to observe its characterization. In addition, a switching mechanism of a memristive device was theoretically studied and associated with ion migrations into a polymeric insulating layer. Biological short-term and long-term memory properties were imitated with the memristive device using low power consumption.

Fuzzy simulation of European option pricing using sub-fractional Brownian motion

On the basis of the sub-fractional Black-Scholes model, considering that the financial market is uncertain with randomness and fuzziness, we used stochastic analysis, fractal theory and fuzzy set theory to construct European option pricing model based on the long-term memory property of the financial market in an uncertain environment. Afterwards the influence of Hurst index H, a measure of long-term memory in financial market, on European option pricing is analyzed. Finally, the rationality and feasibility of the pricing model are demonstrated by numerical experiment. The obtained results show that the European options pricing model with long-term memory property is more suitable for financial markets under uncertain environment.

Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging

In this paper, we introduce and analyze the fractional Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. The proposed model is based upon two desirable properties of the long-term variance process suggested by the empirical data: long-term memory and jumps. The proposed model incorporates the long-term memory and positive autocorrelation properties of fractional Brownian motion with $H>1/2$, and the jump properties of the BN-S model. We find arbitrage-free prices for variance and volatility swaps for this new model. Because fractional Brownian motion is still a Gaussian process, we derive some new expressions for the distributions of integrals of continuous Gaussian processes as we work towards an analytic expression for the prices of these swaps. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The amount of derivatives required to minimize a quadratic hedging error is obtained. Finally, we provide some numerical analysis based on the VIX data. Numerical results show the efficiency of the proposed model compared to the Heston model and the classical BN-S model.

Could network analysis of horizontal visibility graphs be faithfully used to infer long-term memory properties in real-world time series?

Mapping time series to complex networks has great potential to investigate their temporal structures. Some previous studies have been carried on time series generated from idealized stochastic models and found that there are inherent associations between long-term memory (LTM) of pure long-range correlated time series and topological parameters (TPs) of their networks, which is thought as a new prospective to extract information from time series. However, output time series from natural systems seldom take so idealized structures as those from idealized stochastic models, and there is usually some unconsidered information inherited in them, which makes these derived associations questionable. To check and generalize these conclusions acquired from idealized stochastic models, horizontal visibility graph (HVG) algorithm is employed to map time series to their horizontal visibility networks. Firstly synthetic time series with known mixed correlations (apart from LTM) have been analyzed and results indicate that topological parameters (TPs) of HVG networks are not solely dominated by the strength of LTM, other factors such as white noise, short-term correlation (STC) and nonlinear correlations are also playing crucial roles. Taking this fact into account, after some preprocessing treatments have been carried out, the LTM of daily mean air temperature series can indeed be inferred by means of the inherent associations between LTM of pure long-range correlated time series and TPs of their networks.

A meta extreme learning machine method for forecasting financial time series

In the last decade, the problem of forecasting time series in very different fields has received increasing attention due to its many real-world applications. In particular, in the very challenging case of financial time series, the underlying phenomenon of stock time series exhibits complex behaviors, including non-stationary, non-linearity and non-trivial scaling properties. In the literature, a wide-used strategy to improve the forecasting capability is the combination of several models. However, the majority of the published researches in the field of financial time series use different machine learning models where only one type of predictor, either linear or nonlinear, is considered. In this paper we first measure relevant features present in the underlying process to propose a forecast method. We select the Sample Entropy and Hurst Exponent to characterize the behavior of stock time series. The characterization reveals the presence of moderate randomness, long-term memory and scaling properties. Thus, based on the measured properties, this paper proposes a novel one-step-ahead off-line meta-learning model, called μ-XNW, for the prediction of the next value xt+1 of a financial time series $x_{t}$ , t = 1, 2, 3, … , that integrates a naive or linear predictor (LP), for which the predicted value of $x_{t + 1}$ is just repeating the last value $x_{t}$ , an extreme learning machine (ELM) and a discrete wavelet transform (DWT), both based on the nprevious values of $x_{t + 1}$ . LP, ELM and DWT are the constituent of the proposed model μ-XNW. We evaluate the proposed model using four well-known performance measures and validated the usefulness of the model using six high-frequency stock time series belong to the technology sector. The experimental results validate that including internal estimators that are able to the capture the relevant features measured (randomness, long-term memory and scaling properties) successfully improve the accuracy of the forecasting over methods that do not include them.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

In the past few decades, it has been recognized that 1∕f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1∕f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic–stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Market efficiency of traditional stock market indices and social responsible indices: the role of sustainability reporting

Corporate social responsibility, disclosed in sustainability reporting, influences the financial performance of companies. As a result, traditional stock market indices (TI) are expanded with the social responsible stock market indices (SRI). The aim of this study was to establish whether there are any differences in the behavior of the TI and SRI. To do this, the authors analyzed their efficiency. They used R/S analysis to calculate the Hurst exponent as a measure of persistence (long-term memory property). The presence of persistence was evidence in favor of less efficiency. According to empirical results, SRI has lower efficiency, in particular the Dow Jones Sustainability Index. Lower efficiency was also observed in the emerging markets with a responsible investment segment, compared to the traditional stock market indices. Further standardization and a common methodological approach to corporate sustainability reporting disclosure are proposed.

Dynamic properties of calcium-activated chloride currents in Xenopus laevis oocytes

Chloride is the most abundant permeable anion in the cell, and numerous studies in the last two decades highlight the great importance and broad physiological role of chloride currents mediated anion transport. They participate in a multiplicity of key processes, as for instance, the regulation of electrical excitability, apoptosis, cell cycle, epithelial secretion and neuronal excitability. In addition, dysfunction of Cl− channels is involved in a variety of human diseases such as epilepsy, osteoporosis and different cancer types. Historically, chloride channels have been of less interest than the cation channels. In fact, there seems to be practically no quantitative studies of the dynamics of chloride currents. Here, for the first time, we have quantitatively studied experimental calcium-activated chloride fluxes belonging to Xenopus laevis oocytes, and the main results show that the experimental Cl− currents present an informational structure characterized by highly organized data sequences, long-term memory properties and inherent “crossover” dynamics in which persistent correlations arise at short time intervals, while anti-persistent behaviors become dominant in long time intervals. Our work sheds some light on the understanding of the informational properties of ion currents, a key element to elucidate the physiological functional coupling with the integrative dynamics of metabolic processes.

How long will the traffic flow time series keep efficacious to forecast the future?

Abstract This paper investigate how long will the historical traffic flow time series keep efficacious to forecast the future. In this frame, we collect the traffic flow time series data with different granularity at first. Then, using the modified rescaled range analysis method, we analyze the long memory property of the traffic flow time series by computing the Hurst exponent. We calculate the long-term memory cycle and test its significance. We also compare it with the maximum Lyapunov exponent method result. Our results show that both of the freeway traffic flow time series and the ground way traffic flow time series demonstrate positively correlated trend (have long-term memory property), both of their memory cycle are about 30 h. We think this study is useful for the short-term or long-term traffic flow prediction and management.

Chaos recognition and fractal analysis in the term structure of Shanghai Interbank Offered Rate

In this paper, we investigate the Shanghai Interbank Offered Rate (SHIBOR) employing the chaos recognition and fractal analysis. We find that all interest rates of SHIBOR are chaotic systems with multifractal nature. The volatilities of the short-term interest rates are larger than the medium- and long-term interest rates and the magnitudes of these fluctuations decrease with the term increases. The smaller fluctuations of all interest rates have long-term memory property. The larger fluctuations of medium- or long-term interest rates have also long-term memory property but not for those of short-term rates. Moreover, there is long-term memory property between the two interest rates of SHIBOR with one medium- or long-term, but not for both short-term interest rates. Especially, there is also long-term memory between SHIBOR and USD LIBOR. These findings are beneficial not only to understand well the SHIBOR’s running but also to price accurately financial products.

A review of aggregation techniques for agent-based models: understanding the presence of long-term memory

A key feature of agent-based modeling is the understanding of the macroscopic behavior based on data at the microscopic level. In this respect, financial market models are requested to replicate, at the aggregate level, the stylized facts of empirical data. Among them, a remarkable role is played by the long term behavior. Indeed, the study of the long-term memory is relevant, in that it describes if and how past events continue to maintain their influence for the future evolution of a system. In economic applications, this is relevant for understanding the reaction of the system to micro- and macro-economic shocks. Moreover, further information on the long-term memory properties of a system can be obtained by analyzing agents heterogeneity and the outcome of their aggregation. The aim of this paper is to review a few techniques—though the most relevant in our opinion—for studying the long-term memory as emergent property of systems composed by heterogeneous agents. Theorems relevant to the present analysis are summarized and their applications in four structural models with long-term memory are shown. This property is assessed through the analysis of the functional relation between model parameters.

REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of noninteger order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.

The role of diversity in persistence aggregation

This paper deals with the theoretical analysis of the long-term memory property of time series generated by the aggregation of heterogeneous terms. The diversity is captured by the different features, regarding the persistence of each component. It is shown that the memory of the aggregation is driven by the one related to some key components. The argument is carried out by developing an equilibrium model for asset prices in a financial market with heterogeneous agents. © 2011 Wiley Periodicals, Inc.

The properties and mechanism of long-term memory in nonparametric volatility

Recent empirical literature documents the presence of long-term memory in return volatility. But the mechanism of the existence of long-term memory is still unclear. In this paper, we investigate the origin and properties of long-term memory with nonparametric volatility, using high-frequency time series data of the Chinese Shanghai Composite Stock Price Index. We perform Detrended Fluctuation Analysis (DFA) on three different nonparametric volatility estimators with different sampling frequencies. For the same volatility series, the Hurst exponents reduce as the sampling time interval increases, but they are still larger than 1/2, which means that no matter how the interval changes, it still cannot change the existence of long memory. RRV presents a relatively stable property on long-term memory and is less influenced by sampling frequency. RV and RBV have some evolutionary trends depending on time intervals, which indicating that the jump component has no significant impact on the long-term memory property. This suggests that the presence of long-term memory in nonparametric volatility can be contributed to the integrated variance component. Considering the impact of microstructure noise, RBV and RRV still present long-term memory under various time intervals. We can infer that the presence of long-term memory in realized volatility is not affected by market microstructure noise. Our findings imply that the long-term memory phenomenon is an inherent characteristic of the data generating process, not a result of microstructure noise or volatility clustering.

Long-term memory and volatility clustering in high-frequency price changes

We studied the long-term memory in diverse stock market indices and foreign exchange rates using Detrended Fluctuation Analysis (DFA). For all high-frequency market data studied, no significant long-term memory property was detected in the return series, while a strong long-term memory property was found in the volatility time series. The possible causes of the long-term memory property were investigated using the return data filtered by the AR(1) model, reflecting the short-term memory property, the GARCH(1,1) model, reflecting the volatility clustering property, and the FIGARCH model, reflecting the long-term memory property of the volatility time series. The memory effect in the AR(1) filtered return and volatility time series remained unchanged, while the long-term memory property diminished significantly in the volatility series of the GARCH(1,1) filtered data. Notably, there is no long-term memory property, when we eliminate the long-term memory property of volatility by the FIGARCH model. For all data used, although the Hurst exponents of the volatility time series changed considerably over time, those of the time series with the volatility clustering effect removed diminish significantly. Our results imply that the long-term memory property of the volatility time series can be attributed to the volatility clustering observed in the financial time series.