Fading Memory Research Articles

Volterra-Prabhakar function of distributed order and some applications

The paper studies the exact solution of two kinds of generalized Fokker–Planck equations in which the integral kernels are given either by the distributed order function k1(t)=∫01t−μ/Γ(1−μ)dμ or the distributed order Prabhakar function k2(α,γ;λ;t)=∫01eα,1−μ−γ(λ;t)dμ, where the Prabhakar function is denoted as eα,1−μ−γ(λ;t). Both of these integral kernels can be called the fading memory functions and are the Stieltjes functions. It is also shown that their Stieltjes character is enough to ensure the non-negativity of the mean square values and higher even moments. The odd moments vanish. Thus, the solution of generalized Fokker–Planck equations can be called the probability density functions. We introduce also the Volterra-Prabhakar function and its generalization which are involved in the definition of k2(α,γ;λ;t) and generated by it the probability density function p2(x,t).

Robust UKF Relative Positioning Approach for Tightly Coupled Vehicle Ad Hoc Networks Based on Adaptive M-Estimation

Huber M-estimation, as an estimation method based on mixed norm as cost function, provides an effective method for robust filtering to deal with measurement outliers. Based on statistical linear regression model approximating nonlinear measurement model, M-estimation algorithm is used to realize measurement update of states. However, when the measurement noise pollution rate is high, the filtering performance will be seriously degraded. In order to further improve the actual performance of data fusion under abnormal measurement noise, a vehicle cooperative positioning scheme based on adaptive M-estimation robust unscented Kalman filter (AMRUKF) was proposed. This algorithm combines Huber’s linear regression problem with covariance matching method, and calculates the adaptive matrix through the innovation covariance estimator based on fading memory index weighting to adaptively adjust the measurement noise covariance used in Huber M estimation method. The analytical and experimental results of tightly-coupled vehicle relative positioning show that the proposed AMRUKF method can effectively improve the robustness and accuracy of relative positioning and provide a practical control scheme for vehicle cooperative positioning.

Hybrid MoS2/PbS Quantum Dots Toward In-Sensor Reservoir Computing

Neuromorphic visual systems are potential to overcome the von Neumann bottleneck, emulating the human retina to implement in situ vision preprocessing. Specifically, in-sensor reservoir computing (RC) is capable of processing spatio-temporal vision information with high efficiency. However, traditional photodetectors are incapable of the fading memory ability, which is the core of the RC systems for temporal information processing. Here, we report a hybrid MoS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /PbS quantum dots based optoelectronic device with short-term memory properties for RC demonstration. The photogating effect induced dynamic temporal photoresponse behavior can be effectively regulated by the incident optical intensity and time. As a proof of concept, image classifying with a high accuracy of 95.8% and time series prediction are demonstrated, paving a way for intelligent edge computing.

The Eastern Australian Floods of February 2022 and Its Relationship with Climate Change

During February 2022 major riverine flooding occurred in an area which has the fastest population growth in Australia. This extended from the Mary River in Southeast Queensland (SEQ) to the Clarence River in Northeast NSW (NENSW). Two centres within this area were devastated by floods unprecedented in living memory. One was the Brisbane Metropolitan area where all-time record daily rainfall in the suburbs flooded creeks. This creek flooding was much worse than that caused by the Brisbane River itself where Wivenhoe Dam played a role in preventing more disastrous flooding. The other was in the Northern New South Wales city of Lismore where rainfall in the Wilsons River catchment exceeded all known rainfall rates there. The structure of the weather system generating the rainfall responsible for these two floods is studied along with the climatology of such events. One event which occurred during 1954 stands out and is examined in detail. A climate shift in 1976 resulted in two decades of relatively benign weather in the region and tourism flourished there due to mild summers and warm winters. The area experienced a huge growth in population with fading memories of past disastrous weather events and huge residential development occurred in flood plain areas. During the twenty-first century these extreme events have returned although so far not as frequent as earlier decades but still result in some residents experiencing multiple flooding events. The 1954 event occurred during an extended period of devastating flood events not experienced in recent decades. With the huge increase in population in this area since the 1970s such a series of events like those in the 1950s would stretch the resources of disaster managers given the problems, they faced in 2022.

Quantum reservoir computing in finite dimensions.

Most existing results in the analysis of quantum reservoir computing (QRC) systems with classical inputs have been obtained using the density matrix formalism. This paper shows that alternative representations can provide better insight when dealing with design and assessment questions. More explicitly, system isomorphisms are established that unify the density matrix approach to QRC with the representation in the space of observables using Bloch vectors associated with Gell-Mann bases. It is shown that these vector representations yield state-affine systems previously introduced in the classical reservoir computing literature and for which numerous theoretical results have been established. This connection is used to show that various statements in relation to the fading memory property (FMP) and the echo state property (ESP) are independent of the representation and also to shed some light on fundamental questions in QRC theory in finite dimensions. In particular, a necessary and sufficient condition for the ESP and FMP to hold is formulated using standard hypotheses, and contractive quantum channels that have exclusively trivial semi-infinite solutions are characterized in terms of the existence of input-independent fixed points.

The Fading Memory Formalism with Mittag-Leffler-Type Kernels as A Generator of Non-Local Operators

Transient heat conduction problems are systematically applied to the fading memory formalism with different Mittag-Leffler-type memory kernels. With such an approach, using various memories naturally results in definitions of various fractional operators. Six examples are given and interpreted from a common perspective, covering the most well-liked versions of the Mittag-Leffler function. The fading memory approach was used as a template and demonstrated that, if the constitutive equations are correctly built, it is also possible to directly determine where the hereditary terms are located in the models.

Optimization of the memory reset rate of a quantum echo-state network for time sequential tasks

Quantum reservoir computing is a class of quantum machine learning algorithms involving a reservoir of an echo state network based on a register of qubits, but the dependence of its memory capacity on the hyperparameters is still rather unclear. In order to maximize its accuracy in time–series predictive tasks, we investigate the relation between the memory of the network and the reset rate of the evolution of the quantum reservoir. We benchmark the network performance by three non–linear maps with fading memory on IBM quantum hardware. The memory capacity of the quantum reservoir is maximized for central values of the memory reset rate in the interval [0,1]. As expected, the memory capacity increases approximately linearly with the number of qubits. After optimization of the memory reset rate, the mean squared errors of the predicted outputs in the tasks may decrease by a factor ∼1/5 with respect to previous implementations.

A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model

Abstract The stress-strain constitutive law for viscoelastic materials such as soft tissues, metals at high temperature, and polymers can be written as a Volterra integral equation of the second kind with a fading memory kernel. This integral relationship yields current stress for a given strain history and can be used in the momentum balance law to derive a mathematical model for the resulting deformation. We consider such a dynamic linear viscoelastic model problem resulting from using a Dirichlet–Prony series of decaying exponentials to provide the fading memory in the Volterra kernel. We introduce two types of internal variable to replace the Volterra integral with a system of auxiliary ordinary differential equations and then use a spatially discontinuous symmetric interior penalty Galerkin (SIPG) finite element method and – in time – a Crank–Nicolson method to formulate the fully discrete problems: one for each type of internal variable. We present a priori stability and error analyses without using Grönwall’s inequality and with the result that the constants in our estimates grow linearly with time rather than exponentially. In this sense, the schemes are therefore suited to simulating long time viscoelastic response, and this (to our knowledge) is the first time that such high quality estimates have been presented for SIPG finite element approximation of dynamic viscoelasticity problems. We also carry out a number of numerical experiments using the FEniCS environment (https://fenicsproject.org), describe a simulation using “real” material data, and explain how the codes can be obtained and all of the results reproduced.

Uniform general stability of a coupled Volterra integro-differential equations with fading memories

Uniform general stability of a coupled Volterra integro-differential equations with fading memories

Novel pedestrian navigation system based on zero velocity update procedure technology and improved Sage‐Husa adaptive Kalman filter with index fading memory factor

AbstractTo acquire an accurate location on the occasions, such as in an indoor, tunnel, and valley, where satellite navigation signals fail. The paper designs a pedestrian navigation system by using the zero velocity update procedure technology (ZUPT) and Kalman filter to reduce the location error. The measurement noise characteristic (mean and variance) of the micro electro mechanical systems gyros is unknown and time variant, but in traditional studies, it is usually thought and calculated as a constant. So the optimality of the error estimation of the Kalman filter cannot be reached. To address this question, this paper proposes the improved Sage–Husa Adaptive Kalman Filter (SHAKF) based on the index fading memory factor to realise the state estimation of the Kalman filter and navigation error correction. The advantage of improved SHAKF is it can accurately estimate the state vector when the measurement noise is unknown and time variant. To verify the validity of novel navigation methods, walking experiments under outdoor environments and indoor environments are carried out. The results of actual walking experiments demonstrate that the proposed method can effectively reduce the pedestrian location error compared with the traditional ZUPT method. The mean location error is reduced by more than 10%, and the variance of the location error is reduced by more than 5%.

High Frequency Response of Non-Volatile Memristors

This paper presents an analytical investigation of the transient and steady-state response of non-volatile memristors to high frequency periodic inputs, using as a case study a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {TaO}_{\textrm {x}}$ </tex-math></inline-formula> -based nano-scale memristor model derived at HP Labs. For the first time, we provide a mathematical proof for the fading memory phenomenon in memristors stimulated by periodic inputs in the high frequency limit. Specifically, we demonstrate that the steady-state response of a non-volatile memristor, exhibiting asymmetric switching kinetics with respect to the polarity of the input, depends only on the amplitude of the testing signal and not on the device initial conditions. Based on the results of our analyses, we provide an alternative method for tuning the memristor state by using high-frequency AC inputs, and introduce a new system-theoretic visualization tool, namely the input-referred High-Frequency Dynamic Route Map (HF-DRM), that allows the reproduction of the memristor time-response to any high-frequency periodic input from each admissible initial condition. The purely theoretical results introduced in this paper could inspire new approaches for modulating the memory states of practical non-volatile memristors.

All-optical reservoir computing system based on polarization dynamics

Reservoir computing (RC) is a simplified recurrent neural network and can be implemented by using a nonlinear system with delay feedback, thus it is called delay-based RC. Various nonlinear nodes and feedback loop structures have been proposed. Most of existing researches are based on the dynamical responses in intensity of the nonlinear systems. There are also a photoelectric RC system based on wavelength dynamics and an all-optical RC based on the phase dynamics of a semiconductor laser with optical feedback, as well as so-called polarization dynamics of a vertical cavity surface emitting laser (VCSEL). However, these VCSEL-RCs actually are based on the intensity dynamics of two mutually orthogonal polarization modes, or polarization-resolved intensity dynamics. The RC based on rich dynamical responses in polarization has not yet been found. A semiconductor optical amplifier (SOA) fiber ring laser can produce rich dynamical states in polarization, and is used in optical chaotic secure communication and distributed optical fiber sensing. To further expand the application of polarization dynamics of the SOA fiber ring laser and open up a new direction for the research of optical RC neural network, an all-optical RC system based on polarization dynamics of the ring laser is proposed. The ring laser is used as the reservoir, and the SOA as the nonlinear node. After the input signal is masked according to a synchronization scheme, it is injected into the reservoir by intensity modulation for a continuous wave generated by a superluminescent light emitting diode (SLED). The dynamical response in polarization of the ring laser is detected by a polarizer and a photodetector. The influences of the SOA operation current, output power of the SLED and attenuation of a variable optical attenuator (VOA) in the fiber loop on the polarization dynamic characteristic (mainly referring to the output degree of polarization) of the laser are analyzed experimentally. The fading memory and nonlinear response of the RC system based on the polarization dynamic response and intensity dynamic response are compared experimentally. The influences of output power of the SLED and attenuation of the VOA on fading memory, consistency and separation of the RC system based on the two kinds of dynamic responses are investigated experimentally. Thus the range of the VOA attenuation is determined. The network performance of the polarization dynamics RC system is evaluated by processing a Santa Fe time series prediction task and a multi-waveform recognition task. The normalized mean square error can be as low as 0.0058 for the time series prediction task, and the identification rate can be as high as 100% for the recognition task under the appropriate system parameters and only 30 virtual nodes. The experimental results show that the polarization dynamics RC system has good prediction performance and classification capability, which are comparable to the existing RC system based on intensity dynamics of the ring laser. The system can be expected to process two tasks in parallel when the polarization dynamics and intensity dynamics are used at the same time.

On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations

In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations.

Remembering Welfare as We Knew It: Understanding Neoliberalism through Histories of Welfare

AbstractThe political transformation that culminated in the Personal Responsibility and Work Opportunity Reconciliation Act fueled scholarly interest in welfare history. As politicians dismantled welfare, scholars discovered long histories of raced and gendered social control, intertwined public and private interests, and fixations on work and personal responsibility. They also recovered more promising possibilities of cash assistance. This article examines foundational welfare histories published between 1971 and 2018. I suggest that this somewhat isolated body of work has shed bright light on the history of neoliberalism from the perspective of people never fully included into social citizenship. It exposes how neoliberalism is and is not different from mid-century liberalism and recovers a long history of resistance. In an era when few talk about cash assistance, welfare historiography is vital for restoring fading memory of its redistributive potential.

Geriatric Friendly Medicine Reminder Device Powered by Visual, Voice and IOT Assistance System

Any medical care must include regular consumption of the correct dose at the precise time. Because they are more likely to have chronic conditions, older persons consume more medications than younger adults. The majority of medications are used for years, while only a few are used for a brief period. Based on many research investigations, it has been discovered that on average, older individuals take 3 to 5 prescription drugs, and that owing to fading memory impairments, it becomes difficult for them to remember the dosage time and quantity. The dose is effective if it is given at the precise time and in the correct quantity; otherwise, the patient's health would deteriorate. This study proposes a medicine reminder device based on an algorithm that addresses and eliminates difficulties experienced by older adults, such as remembering time, name, quantity or amount of dose, with some specific description, feedback and assistance mechanisms. The device employs a system clock for reminders based on the time inputted, a television display for presenting medicine and meal images, and a speaker for voice help. Finally, a rack of devices is used to pick up the right dose, and a trigger feedback device is employed to notify the website that the drug has been taken.

Clinical Application of the Persian Version of Buffalo Model Questionnaire by examining Its correlation with the Buffalo Model Test Battery

Background and Aim: The Buffalo Model Questionnaire (BMQ) has been proposed for the screening, helping to diagnose and also monitoring the effect of rehabilitation on the improvement of Central Auditory Processing Disorder ((C)APD). In this regard, the applicability and accuracy of Persian-BMQ (P-BMQ) are evaluated by examining the correlation between the results of this questionnaire and the Buffalo model test battery. Methods: Overall, 254 children, normal and with Specific Learning Disorder (SLD) aged between 7–12 years old participated in this cross-sectional study. The questionnaire was completed by the parents of children who were subjected to the Buffalo model test battery evaluations. Results: In the normal group, the highest correlation (0.648) was shown between the Decoding (D) component of the P-BMQ with the Row Staggered Spondaic Word (RSSW) variable. In the SLD group, the highest correlation (0.318) was shown between the Variance-tolerance fading memory (V) component of the P-BMQ and the qualitative Persian version of the Phonemic Sentence Test (P-PST) variable. The highest correlation was considered to be between the D component of the P-BMQ with the Right Competitive word, started in the Left ear (RC-LEF) variable in the SSW test (0.498), and qualitative P-PST variable (0.471); and 0.360 between the V component of the P-BMQ and Persian version of the Speech in Noise with S/N=4 in the Left ear (P-SIN4L) of variable in the P-SIN test. Conclusion: P-BMQ is a useful screening tool complementing the Persian Buffalo model test battery for evaluating auditory processing evaluation in children. Keywords: Central auditory processing disorder; specific learning disorder; Buffalo model questionnaire

Robust sequential adaptive Kalman filter algorithm for ultrashort baseline underwater acoustic positioning

Affected by dynamic changes in the complex marine environment, ultrashort baseline (USBL) systems may exhibit continuous gross errors in underwater target positioning, resulting in the distortion of the target coordinates. To effectively detect and eliminate continuous gross errors in USBL underwater acoustic positioning, a robust sequential adaptive Kalman filter (RSAKF) algorithm is proposed in this paper. The RSAKF algorithm employs sequential filtering to decompose all measurement updates into multiple submeasurement updates and uses the fading memory weighted average method to estimate the one-step prediction mean square error of the metrics for each submeasurement update. Then, the RSAKF algorithm adopts an adaptive correction method of submeasurement noise variance, which eliminates the influence of continuous gross errors through a more targeted adaptive correction of each submeasurement noise variance. The effectiveness of the algorithm was quantitatively analyzed using a USBL positioning simulation experiment, and the results showed that the continuous gross errors rejection rate of the RSAKF algorithm reached 84.12%. The point error of the RSAKF algorithm is improved by 62.65%, 46.76%, 36.09%, and 26.48% compared with the Kalman filter (KF), KF based on Huber, KF based on Institute of Geodesy and Geophysics, and the maximum correntropy KF, respectively. The USBL positioning remotely operated vehicle experiment was conducted in the South China Sea, and the results showed that the RSAKF has the best filtering accuracy. Simulation and actual measurement experiments verified that the RSAKF algorithm can effectively eliminate the influence of continuous gross errors.

Plasticity of conducting polymer dendrites to bursts of voltage spikes in phosphate buffered saline

The brain capitalizes on the complexity of both its biochemistry for neurons to encode diverse pieces of information with various neurotransmitters and its morphology at multiple scales to route different pathways for neural interconnectivity. Conducting polymer dendrites can show similar features by differentiating between cations and anions thanks to their charge accumulation profile and the asymmetry in their dendriticity that allows projecting spike signals differently. Here, we exploit such mimicry for in materio classification of bursting activity and investigate, in phosphate buffered saline, the capability of such object to sense bursts of voltage pulses of 100 mV amplitude, emitted by a local gate in the vicinity of the dendrite. The dendrite integrates the different activities with a fading memory time window that is characteristic of both the polarity of the spikes and the temporality of the burst. By this first demonstration, the ‘material-object’ definitely shows great potential to be a node halfway between the two realms of brain and electronic communication.

THE LEFTISM IDEOLOGY OR NOSTALGIA FOR THE SOCIALIST PAST? SEARCHING FOR LIEUX DE MÉMOIRE IN THE POST-SOVIET CULTURAL SPACES

The concept lieu de mémoire (site of memory) was developed by the French historian Pierre Nora in the 1970–90s, who suggests to use the term to refer to “any significant entity, whether material or non-material in nature, which by dint of human will or the work of time has become a symbolic element of the memorial heritage of any community” [Nora, Kritzman 1996:18]. Lieux de mémoire function as an array of mnemonic techniques, which are necessary when the real memory (milieux de mémoire) fades. Lieux de mémoire are repeatedly employed in referring back to the past, thus sustaining the actual identity of a community and laying a solid foundation for developing the existing identity or re-shaping it. In the Post-Soviet cultural space of Latvia lieux de mémoire, which are associated with the Soviet past, can be encountered everywhere, from the “The Government Inspector”, staged by Alvis Hermanis and performed during the 2010s, to the nostalgic interior objects in cafés, the hullabaloo stirred by the contest New Wave, the popularity of Karosta Prison in Liepāja, and social media users’ commentaries on the Internet about the topical events in contemporary society. The article discusses the potential links of these phenomena to contemporary socio-political events and attempts to establish if they hide any efforts to restore collective and individual memory, which were split alongside the so-called rewriting of history that took place as a result of the collapse of the Soviet Union, or indications of flaws in Western neoliberalism and neoconservativism while seeking opportunities for renewal of society by way of indirect leftist ideological implications.

Development of adaptive dual predictive control schemes based on Wiener–Hammerstein models

Adaptive MPC schemes often employ local linear approximation of the system dynamics, which may not be adequate to capture the dynamic behavior of systems exhibiting strongly nonlinear dynamics. In particular, it is challenging to control a system exhibiting input multiplicity behavior at its optimum operating point as the steady-state gain matrix can smoothly become singular at the optimum operating point. In this work, with the aim of controlling systems with fading memory that exhibit such strongly nonlinear dynamics, a novel adaptive dual nonlinear MPC (ADNMPC) formulation is developed based on discrete-time block-oriented models. The block-oriented models are parameterized using the generalized orthonormal basis filters (GOBF). The nonlinear black-box model is further used to formulate a stochastic optimal control problem. A deterministic approximation to the stochastic optimal control problem is then systematically derived. Subsequently, an ADNMPC scheme is developed using the deterministic approximation as a basis. The efficacy of the proposed approach is demonstrated by simulating the problem of controlling a continuously operated fermenter system at its optimum operating point. Analysis of the simulation study shows that in contrast to the conventional nonlinear MPC (NMPC), the proposed ADNMPC scheme injects perturbation to the process whenever a model update is needed while meeting the control objectives. Moreover, with reference to a non-adaptive NMPC controller, the proposed ADNMPC schemes achieve better servo control performance while controlling the fermenter at the singular optimum operating point.