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In the initial article [Phys. Rev. Lett. 110, 044301 (2013), arXiv:1208.4611] it was claimed that human hearing can beat the Fourier uncertainty principle. In this Comment, we demonstrate that the experiment designed and implemented in the original article was ill-chosen to test Fourier uncertainty in human hearing.
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This comment is aimed to point out that the recent work due to Kim, et al. in which the clinical and experiential assessment of a brain network model suggests that asymmetry of synchronization suppression is the key mechanism of hysteresis has coupling with our theoretical hysteresis model of unconscious-conscious interconnection based on dynamics on m-adic trees.
One manifestation of quantum resonances is a large sojourn time, or autocorrelation, for states which are initially localized. We elaborate on Lavines time-energy uncertainty principle and give an estimate on the sojourn time. For the case of perturbed embedded eigenstates the bound is explicit and involves Fermis Golden Rule. It is valid for a very general class of systems. We illustrate the theory by applications to resonances for time dependent systems including the AC Stark effect as well as multistate systems.
Spatial Semantic Pointers (SSPs) have recently emerged as a powerful tool for representing and transforming continuous space, with numerous applications to cognitive modelling and deep learning. Fundamental to SSPs is the notion of similarity between vectors representing different points in $n$-dimensional space -- typically the dot product or cosine similarity between vectors with rotated unit-length complex coefficients in the Fourier domain. The similarity measure has previously been conjectured to be a Gaussian function of Euclidean distance. Contrary to this conjecture, we derive a simple trigonometric formula relating spatial displacement to similarity, and prove that, in the case where the Fourier coefficients are uniform i.i.d., the expected similarity is a product of normalized sinc functions: $prod_{k=1}^{n} operatorname{sinc} left( a_k right)$, where $mathbf{a} in mathbb{R}^n$ is the spatial displacement between the two $n$-dimensional points. This establishes a direct link between space and the similarity of SSPs, which in turn helps bolster a useful mathematical framework for architecting neural networks that manipulate spatial structures.
The frequency-specific coupling mechanism of the functional human brain networks underpins its complex cognitive and behavioral functions. Nevertheless, it is not well unveiled what are the frequency-specific subdivisions and network topologies of the human brain. In this study, we estimated functional connectivity of the human cerebral cortex using spectral connection, and conducted frequency-specific parcellation using eigen-clustering and gradient-based methods, and then explored their topological structures. 7T fMRI data of 184 subjects in the HCP dataset were used for parcellation and exploring the topological properties of the functional networks, and 3T fMRI data of another 890 subjects were used to confirm the stability of the frequency-specific topologies. Seven to ten functional networks were stably integrated by two to four dissociable hub categories at specific frequencies, and we proposed an intrinsic functional atlas containing 456 parcels according to the parcellations across frequencies. The results revealed that the functional networks contained stable frequency-specific topologies, which may imply more abundant roles of the functional units and more complex interactions among them.
The aim of this paper is to leverage the free-energy principle and its corollary process theory, active inference, to develop a generic, generalizable model of the representational capacities of living creatures; that is, a theory of phenotypic representation. Given their ubiquity, we are concerned with distributed forms of representation (e.g., population codes), whereby patterns of ensemble activity in living tissue come to represent the causes of sensory input or data. The active inference framework rests on the Markov blanket formalism, which allows us to partition systems of interest, such as biological systems, into internal states, external states, and the blanket (active and sensory) states that render internal and external states conditionally independent of each other. In this framework, the representational capacity of living creatures emerges as a consequence of their Markovian structure and nonequilibrium dynamics, which together entail a dual-aspect information geometry. This entails a modest representational capacity: internal states have an intrinsic information geometry that describes their trajectory over time in state space, as well as an extrinsic information geometry that allows internal states to encode (the parameters of) probabilistic beliefs about (fictive) external states. Building on this, we describe here how, in an automatic and emergent manner, information about stimuli can come to be encoded by groups of neurons bound by a Markov blanket; what is known as the neuronal packet hypothesis. As a concrete demonstration of this type of emergent representation, we present numerical simulations showing that self-organizing ensembles of active inference agents sharing the right kind of probabilistic generative model are able to encode recoverable information about a stimulus array.
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