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We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of new memory traces caused by learning a certain fragment of information pattern and affected by the fragments of this pattern already retained by the current moment of time. Using the available psychological and physiological data these constructions are justified. The final equation governing the learning and forgetting processes is constructed in the form of the differential equation with the Caputo type fractional time derivative. Several characteristic situations of the learning (continuous and discontinuous) and forgetting processes are studied numerically. In particular, it is demonstrated that, first, the learning and forgetting exponents of the corresponding power laws of the memory fractional dynamics should be regarded as independent system parameters. Second, as far as the spacing effects are concerned, the longer the discontinuous learning process, the longer the time interval within which a subject remembers the information without its considerable lost. Besides, the latter relationship is a linear proportionality.
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The understanding of neural activity patterns is fundamentally linked to an understanding of how the brains network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs, or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings, lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatiotemporal pattern formation and propose a novel perspective for analyzing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.
Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake brain remains controversial. Here, we compared avalanche analyses performed on different in vivo preparations during wakefulness, slow-wave sleep and REM sleep, using high-density electrode arrays in cat motor cortex (96 electrodes), monkey motor cortex and premotor cortex and human temporal cortex (96 electrodes) in epileptic patients. In neuronal avalanches defined from units (up to 160 single units), the size of avalanches never clearly scaled as power-law, but rather scaled exponentially or displayed intermediate scaling. We also analyzed the dynamics of local field potentials (LFPs) and in particular LFP negative peaks (nLFPs) among the different electrodes (up to 96 sites in temporal cortex or up to 128 sites in adjacent motor and pre-motor cortices). In this case, the avalanches defined from nLFPs displayed power-law scaling in double log representations, as reported previously in monkey. However, avalanche defined as positive LFP (pLFP) peaks, which are less directly related to neuronal firing, also displayed apparent power-law scaling. Closer examination of this scaling using more reliable cumulative distribution functions (CDF) and other rigorous statistical measures, did not confirm power-law scaling. The same pattern was seen for cats, monkey and human, as well as for different brain states of wakefulness and sleep. We also tested other alternative distributions. Multiple exponential fitting yielded optimal fits of the avalanche dynamics with bi-exponential distributions. Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man.
When one is presented with an item or a face, one can sometimes have a sense of recognition without being able to recall where or when one has encountered it before. This sense of recognition is known as familiarity. Following previous computational models of familiarity memory we investigate the dynamical properties of familiarity discrimination, and contrast two different familiarity discriminators: one based on the energy of the neural network, and the other based on the time derivative of the energy. We show how the familiarity signal decays after a stimulus is presented, and examine the robustness of the familiarity discriminator in the presence of random fluctuations in neural activity. For both discriminators we establish, via a combined method of signal-to-noise ratio and mean field analysis, how the maximum number of successfully discriminated stimuli depends on the noise level.
Urban housing markets, along with markets of other assets, universally exhibit periods of strong price increases followed by sharp corrections. The mechanisms generating such non-linearities are not yet well understood. We develop an agent-based model populated by a large number of heterogeneous households. The agents behavior is compatible with economic rationality, with the trend-following behavior found to be essential in replicating market dynamics. The model is calibrated using several large and distributed datasets of the Greater Sydney region (demographic, economic and financial) across three specific and diverse periods since 2006. The model is not only capable of explaining price dynamics during these periods, but also reproduces the novel behavior actually observed immediately prior to the market peak in 2017, namely a sharp increase in the variability of prices. This novel behavior is related to a combination of trend-following aptitude of the household agents (rational herding) and their propensity to borrow.
In nature and human societies, the effects of homogeneous and heterogeneous characteristics on the evolution of collective behaviors are quite different from each other. It is of great importance to understand the underlying mechanisms of the occurrence of such differences. By incorporating pair pattern strategies and reference point strategies into an agent-based model, we have investigated the coupled effects of heterogeneous investment strategies and heterogeneous risk tolerance on price fluctuations. In the market flooded with the investors with homogeneous investment strategies or homogeneous risk tolerance, large price fluctuations are easy to occur. In the market flooded with the investors with heterogeneous investment strategies or heterogeneous risk tolerance, the price fluctuations are suppressed. For a heterogeneous population, the coexistence of investors with pair pattern strategies and reference point strategies causes the price to have a slow fluctuation around a typical equilibrium point and both a large price fluctuation and a no-trading state are avoided, in which the pair pattern strategies push the system far away from the equilibrium while the reference point strategies pull the system back to the equilibrium. A theoretical analysis indicates that the evolutionary dynamics in the present model is governed by the competition between different strategies. The strategy that causes large price fluctuations loses more while the strategy that pulls the system back to the equilibrium gains more. Overfrequent trading does harm to ones pursuit for more wealth.
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