Self-Similar Tilings of Fractal Blow-Ups

New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produces a usually infinite family of tilings that satisfy the following properties: (1) the prototile set is finite; (2) the tilings are repetitive (quasiperiodic); (3) each family contains self-similartilings, usually infinitely many; and (4) when the IFS is rigid in an appropriate sense, the tiling has no non-trivial symmetry; in particular the tiling is non-periodic

A Realistic Neural Mass Model of the Cortex with Laminar-Specific Connections and Synaptic Plasticity – Evaluation with Auditory Habituation

<div><p>In this work we propose a biologically realistic local cortical circuit model (LCCM), based on neural masses, that incorporates important aspects of the functional organization of the brain that have not been covered by previous models: (1) activity dependent plasticity of excitatory synaptic couplings via depleting and recycling of neurotransmitters and (2) realistic inter-laminar dynamics via laminar-specific distribution of and connections between neural populations. The potential of the LCCM was demonstrated by accounting for the process of auditory habituation. The model parameters were specified using Bayesian inference. It was found that: (1) besides the major serial excitatory information pathway (layer 4 to layer 2/3 to layer 5/6), there exists a parallel “short-cut” pathway (layer 4 to layer 5/6), (2) the excitatory signal flow from the pyramidal cells to the inhibitory interneurons seems to be more intra-laminar while, in contrast, the inhibitory signal flow from inhibitory interneurons to the pyramidal cells seems to be both intra- and inter-laminar, and (3) the habituation rates of the connections are unsymmetrical: forward connections (from layer 4 to layer 2/3) are more strongly habituated than backward connections (from Layer 5/6 to layer 4). Our evaluation demonstrates that the novel features of the LCCM are of crucial importance for mechanistic explanations of brain function. The incorporation of these features into a mass model makes them applicable to modeling based on macroscopic data (like EEG or MEG), which are usually available in human experiments. Our LCCM is therefore a valuable building block for future realistic models of human cognitive function.</p></div

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Visualization S2: Raw data from monochrome senso

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Visualization S4: Reconstructed multi-spectral vide

Supplement 1: Ultra-high-sensitivity color imaging via a transparent diffractive-filter array and computational optics

Supplemental document Originally published in Optica on 20 November 2015 (optica-2-11-933

Identification and Bayesian Estimation of Dynamic Factor Models

<div><p>We consider a set of minimal identification conditions for dynamic factor models. These conditions have economic interpretations and require fewer restrictions than the static factor framework. Under these restrictions, a standard structural vector autoregression (SVAR) with measurement errors can be embedded into a dynamic factor model. More generally, we also consider overidentification restrictions to achieve efficiency. We discuss general linear restrictions, either in the form of known factor loadings or cross-equation restrictions. We further consider serially correlated idiosyncratic errors with heterogeneous dynamics. A numerically stable Bayesian algorithm for the dynamic factor model with general parameter restrictions is constructed for estimation and inference. We show that a square-root form of the Kalman filter improves robustness and accuracy when sampling the latent factors. Confidence intervals (bands) for the parameters of interest such as impulse responses are readily computed. Similar identification conditions are also exploited for multilevel factor models, and they allow us to study the “spill-over” effects of the shocks arising from one group to another. Supplementary materials for technical details are available online.</p></div

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Visualization S3: Reconstructed RGB video from multi-spectral data

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Visualization S1: Original video on LCD scree

Priors of parameters.

<p><i>Note.</i> Re-parameterization for uncertain connections used: <i>φ</i> = <i>θ²</i>, <i>p</i>(<i>θ</i>)∝N(0, 10⁴) for uninformative prior. Re-parameterization for other parameters use: <i>φ</i> = <i>u</i>⋅exp(<i>θ</i>),<i>u</i> is the expectation. The un-informative priors are <i>p</i>(<i>θ</i>)∝N(0, 1/2), the informative priors are <i>p</i>(<i>θ</i>)∝N(0, 1/16). EIN = excitatory interneurons, sPC = superficial pyramidal cells, sIIN = superficial inhibitory interneurons, dPC = deep pyramidal cells, dIIN = deep inhibitory interneurons. U = uninformative prior, I = informative prior, C = constant.</p

Habituation of the N100m source.

<p>The amplitudes are normalized to the responses to the first stimulus.</p