Memory and forgetting constitute two sides of the same coin, and although the first has been extensively investigated, the latter is often overlooked. A possible approach to better understand forgetting is to develop phenomenological models that implement its putative mechanisms in the most elementary way possible, and then experimentally test the theoretical predictions of these models. One such mechanism proposed in previous studies is retrograde interference, stating that a memory can be erased due to subsequently acquired memories. In the current contribution, we hypothesize that retrograde erasure is controlled by the relevant “importance” measures such that more important memories eliminate less important ones acquired earlier. We show that some versions of the resulting mathematical model are broadly compatible with the previously reported power-law forgetting time course and match well the results of our recognition experiments with long, randomly assembled streams of words.
Decoding approaches provide a useful means of estimating the information contained in neuronal circuits. In this work, we analyze the expected classification error of a decoder based on Fisher linear discriminant analysis. We provide expressions that relate decoding error to the specific parameters of a population model that performs linear integration of sensory input. Results show conditions that lead to beneficial and detrimental effects of noise correlation on decoding. Further, the proposed framework sheds light on the contribution of neuronal noise, highlighting cases where, counter-intuitively, increased noise may lead to improved decoding performance. Finally, we examined the impact of dynamical parameters, including neuronal leak and integration time constant, on decoding. Overall, this work presents a fruitful approach to the study of decoding using a comprehensive theoretical framework that merges dynamical parameters with estimates of readout error.
The brain is intrinsically organized into large-scale networks that constantly re-organize on multiple timescales, even when the brain is at rest. The timing of these dynamics is crucial for sensation, perception, cognition, and ultimately consciousness, but the underlying dynamics governing the constant reorganization and switching between networks are not yet well understood. Electroencephalogram (EEG) microstates are brief periods of stable scalp topography that have been identified as the electrophysiological correlate of functional magnetic resonance imaging defined resting-state networks. Spatiotemporal microstate sequences maintain high temporal resolution and have been shown to be scale-free with long-range temporal correlations. Previous attempts to model EEG microstate sequences have failed to capture this crucial property and so cannot fully capture the dynamics; this paper answers the call for more sophisticated modeling approaches. We present a dynamical model that exhibits a noisy network attractor between nodes that represent the microstates. Using an excitable network between four nodes, we can reproduce the transition probabilities between microstates but not the heavy tailed residence time distributions. We present two extensions to this model: first, an additional hidden node at each state; second, an additional layer that controls the switching frequency in the original network. Introducing either extension to the network gives the flexibility to capture these heavy tails. We compare the model generated sequences to microstate sequences from EEG data collected from healthy subjects at rest. For the first extension, we show that the hidden nodes 'trap' the trajectories allowing the control of residence times at each node. For the second extension, we show that two nodes in the controlling layer are sufficient to model the long residence times. Finally, we show that in addition to capturing the residence time distributions and transition probabilities of the sequences, these two models capture additional properties of the sequences including having interspersed long and short residence times and long range temporal correlations in line with the data as measured by the Hurst exponent.
The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and hence with the principle of stationary action. Taking the Dynamic Causal Modelling (DCM) neuronal state equation as an instructive archetype of the first-order linear differential equations commonly found in computational neuroscience, we show that it is possible to make certain modifications to this equation to render it compatible with the principle of stationary action. Specifically, we show that a Lagrangian formulation of the DCM neuronal state equation is facilitated using a complex dependent variable, an oscillatory solution, and a Hermitian intrinsic connectivity matrix. We first demonstrate proof of principle by using Bayesian model inversion to show that both the original and modified models can be correctly identified via in silico data generated directly from their respective equations of motion. We then provide motivation for adopting the modified models in neuroscience by using three different types of publicly available in vivo neuroimaging datasets, together with open source MATLAB code, to show that the modified (oscillatory) model provides a more parsimonious explanation for some of these empirical timeseries. It is our hope that this work will, in combination with existing techniques, allow people to explore the symmetries and associated conservation laws within neural systems – and to exploit the computational expediency facilitated by direct variational techniques.
We report two cases of eccrine syringofibroadenoma. Both patients had a large, solitary hyperkeratotic nodular lesion over the extremities. Histologic sections showed spongelike masses of small cuboidal acrosyringeal cells. Fibrovascular connective tissue stroma resembling premalignant fibroepithelial tumor of Pinkus filled the spaces between the masses.
