Narrow Results

In the framework of open-ended learning cognitive architectures for robots, this paper deals with the design of a Long-Term Memory (LTM) structure that can accommodate the progressive acquisition of experience-based decision capabilities, or what different authors call “automation” of what is learnt, as a complementary system to more common prospective functions. The LTM proposed here provides for a relational storage of knowledge nuggets given the form of artificial neural networks (ANNs) that is representative of the contexts in which they are relevant in a configural associative structure. It also addresses the problem of continuous perceptual spaces and the task- and context-related generalization or categorization of perceptions in an autonomous manner within the embodied sensorimotor apparatus of the robot. These issues are analyzed and a solution is proposed through the introduction of two new types of knowledge nuggets: P-nodes representing perceptual classes and C-nodes representing contexts. The approach is studied and its performance evaluated through its implementation and application to a real robotic experiment.

Continuum temperature variability represents the response of the Earth's climate to deterministic external forcing. Scaling regimes are observed which range from hours to millennia with low frequency fluctuations characterizing long-term memory. The presence of 1/f power spectra in weather and climate is noteworthy: (i) In the tropical atmosphere 1/f scaling ranging from hours to weeks is found for several variables; it emerges as superposition of uncorrelated pulses with individual 1/f spectra. (ii) The daily discharge of the Yangtze shows 1/f within one week to one year, although the precipitation spectrum is white. (iii) Beyond one year mid-latitude sea surface temperatures reveal 1/f scaling in large parts of the global ocean. The spectra can be simulated by complex atmosphere-ocean general circulation models and understood as a two layer heat diffusion process forced by an uncorrelated stochastic atmospheric. Long-term memory on time scales up to millennia are the global sea surface temperatures and the Greenland ice core records (GISP2, GRIP) with δ¹⁸O temperature proxy data during the Holocene. Complex atmosphere ocean general circulation models reproduce this behavior quantitatively up to millennia without solar variability, interacting land-ice and vegetation components.

Long-term memory (LTM ) and short-term memory (STM ) and their evolution from one to the other are important mechanisms to understand brain memory. We use the Hodgkin–Huxley (HH ) model, a well-tested and closest model to biological neurons and synapses, to shine some light on LTM and STM memorization mechanisms. The role of ${\mathrm{\text{Na}}}^{+}$ and ${\mathrm{\text{K}}}^{+}$ion channels playing in LTM and STM process is carefully examined by using three different types of input signals, namely, a step DC voltage, a positive part of sinusoidal wave and periodic square signal with read voltage. Results are analyzed based on first-order${\mathrm{\text{K}}}^{+}$memristor and second-order${\mathrm{\text{Na}}}^{+}$memristor.

We consider a class of abstract evolutionary variational inequalities arising in the study of frictionless contact problems for linear viscoelastic materials with long-term memory. We prove an existence and uniqueness result, by using arguments of time-dependent elliptic variational inequalities and Banach's fixed point theorem. We then consider numerical approximation of the problem by introducing spatially semi-discrete, time semi-discrete and fully discrete schemes. For both schemes, we show the existence of a unique solution and derive error estimates. Finally, we apply the abstract results to the analysis and numerical approximation of the Signorini frictionless contact problem between two viscoelastic bodies with long-term memory.

The notion of long-term memory has received considerable attention in empirical finance. This paper makes two main contributions. First one is, the paper provides evidence of long-term memory dynamics in the equity market of China. An analysis of market patterns in the Chinese market (a typical emerging market) instead of US market (a developed market) will be meaningful because little research on the behaviors of emerging markets has been carried out previously. Second one is, we present a comprehensive research on the long-term memory characteristics in the Chinese stock market returns as well as volatilities. While many empirical results have been obtained on the detection of long-term memory in returns series, very few investigations are focused on the market volatility, though the long-term dependence in volatility may lead to some types of volatility persistence as observed in financial markets and affect volatility forecasts and derivative pricing formulas. By means of using modified rescaled range analysis and Autoregressive Fractally Integrated Moving Average model testing, this study examines the long-term dependence in Chinese stock market returns and volatility. The results show that although the returns themselves contain little serial correlation, the variability of returns has significant long-term dependence. It would be beneficial to encompass long-term memory structure to assess the behavior of stock prices and to research on financial market theory.

Several attempts have been made to reconcile a number of rival theories on the role of the hippocampus in long-term memory. Those attempts fail to explain the basic effects of the theories from the same point of view. We are reviewing the four major theories, and shall demonstrate, with the use of mathematical models of attention and memory, that only one theory is capable of reconciling all of them by explaining the basic effects of each theory in a unified fashion, without altogether sacrificing their individual contributions. The key issue here is whether or not a memory trace is ever stored in the hippocampus itself, and there is no reconciliation unless the answer to that question is that there is not. As a result of the reconciliation that we are proposing, there is a simple solution to several outstanding problems concerning the neurobiology of memory such as: consolidation and reconsolidation, persistency of long term memory, novelty detection, habituation, long-term potentiation, and the multifrequency oscillatory self-organization of the brain.

In this chapter, we shall study the mathematical construction of a random walk and how this has been a workhorse for developing the concept of market efficiency in the finance literature. While market efficiency (or informational efficiency, to be more precise about the type of market efficiency discussed here) is a benchmark consideration in an economy with rational agents or investors, it is also important to realise that anomalies and deviations from the benchmark such as in behavioural finance are plausible and possible.