Sine-skewed toroidal distributions and their application in protein bioinformatics

In the bioinformatics field, there has been a growing interest in modeling dihedral angles of amino acids by viewing them as data on the torus. This has motivated, over the past years, new proposals of distributions on the torus. The main drawback of most of these models is that the related densities are (pointwise) symmetric, despite the fact that the data usually present asymmetric patterns. This motivates the need to find a new way of constructing asymmetric toroidal distributions starting from a symmetric distribution. We tackle this problem in this article by introducing the sine-skewed toroidal distributions. The general properties of the new models are derived. Based on the initial symmetric model, explicit expressions for the shape and dependence measures are obtained, a simple algorithm for generating random numbers is provided, and asymptotic results for the maximum likelihood estimators are established. An important feature of our construction is that no extra normalizing constant needs to be calculated, leading to more flexible distributions without increasing the complexity of the models. The benefit of employing these new sine-skewed toroidal distributions is shown on the basis of protein data, where, in general, the new models outperform their symmetric antecedents.

Modeling of spike trains in auditory nerves with self-exciting point processes of the von Mises type

This article presents the modeling of spike trains in auditory nerve fiber (ANF) models with a one-memory self-exciting point process (SEPP) of the von Mises type. The ANF models were acoustically stimulated by a synaptic current of inner hair cells, or electrically stimulated by sinusoidally amplitude-modulated pulsatile waveforms. It has been shown that the parameters of one-memory SEPP of the von Mises type could be estimated by numerically maximizing the likelihood function from sample realizations of the spike trains in response to acoustic or electric stimulus. Furthermore, it was found that period histograms of the one-memory SEPP generated artificially on the basis of the estimated von Mises parameters agreed well with those of acoustic or electric stimulus, by performing the uniform-scores test. It implies that the waveforms of pulsatile electric stimuli should be selected such that the spike trains can be represented by one-memory SEPP of the von Mises type with appropriate parameters, efficiently carrying information to the cochlear implant user's brain, like that in acoustic stimulation of the healthy ear. The findings presented in this paper may play an important role in determining optimal parameters of pulsatile electric stimuli by using one-memory SEPP of the von Mises type, and further in the design of better cochlear prostheses.

Geometric classification of brain network dynamics via conic derivative discriminants

BACKGROUND

Over the past decade, pattern decoding techniques have granted neuroscientists improved anatomical specificity in mapping neural representations associated with function and cognition. Dynamical patterns are of particular interest, as evidenced by the proliferation and success of frequency domain methods that reveal structured spatiotemporal rhythmic brain activity. One drawback of such approaches, however, is the need to estimate spectral power, which limits the temporal resolution of classification.

NEW METHOD

We propose an alternative method that enables classification of dynamical patterns with high temporal fidelity. The key feature of the method is a conversion of time-series data into temporal derivatives. By doing so, dynamically-coded information may be revealed in terms of geometric patterns in the phase space of the derivative signal.

RESULTS

We derive a geometric classifier for this problem which simplifies into a straightforward calculation in terms of covariances. We demonstrate the relative advantages and disadvantages of the technique with simulated data and benchmark its performance with an EEG dataset of covert spatial attention. We reveal the timecourse of covert spatial attention and, by mapping the classifier weights anatomically, its retinotopic organization.

COMPARISON WITH EXISTING METHOD

We especially highlight the ability of the method to provide strong group-level classification performance compared to existing benchmarks, while providing information that is complementary with classical spectral-based techniques. The robustness and sensitivity of the method to noise is also examined relative to spectral-based techniques.

CONCLUSION

The proposed classification technique enables decoding of dynamic patterns with high temporal resolution, performs favorably to benchmark methods, and facilitates anatomical inference.

Dendritic-branching angles of pyramidal neurons of the human cerebral cortex

In this article, we analyze branching angles of the basal dendrites of pyramidal neurons of layers III and V of the human temporal cortex. For this, we use a novel probability directional statistical distribution called truncated von Mises distribution that is able to describe more accurately the dendritic-branching angles than the previous proposals. Then, we perform comparative studies using this statistical method to determine similarities and/or differences between branches and branching angles that belong to different cortical layers and regions. Using this methodology, we found that common design principles exist and govern the patterns found in the different branches that compose the basal dendrites of human pyramidal cells of the temporal cortex. However, particular differences were found between supra and infragranular cells. Furthermore, we compared the branching angles of human layer III pyramidal neurons with data obtained in the previous studies in layer III of both the rat somatosensory cortex and of several cortical areas of the mouse. Finally, we study the branching angle differences between the humans that compose our data.

A framework for optimal whole-sample histological quantification of neurite orientation dispersion in the human spinal cord

BACKGROUND

The complexity of fibre distributions in tissues is an important microstructural feature, now measurable in vivo by magnetic resonance imaging (MRI) through orientation dispersion (OD) indices. OD metrics have gained popularity for the characterisation of neurite morphology, but they still lack systematic validation. This paper demonstrates a framework for whole-sample histological quantification of OD in spinal cord specimens, potentially useful for validating MRI-derived OD estimates.

NEW METHOD

Our methodological framework is based on (i) sagittal sectioning; (ii) Palmgren's silver staining; (iii) structure tensor (ST) analysis; (iv) directional statistics. Novel elements are the data-driven optimisation of the spatial scale of ST analysis, and a new multivariate, weighted directional statistical approach for anisotropy-informed quantification of OD.

RESULTS

Palmgren's silver staining of sagittal spinal cord sections provides robust visualisation of neuronal elements, enabling OD quantification. The choice of spatial scale of ST analysis influences OD values, and weighted directional statistics provide OD maps with high contrast-to-noise. Segmentation of neurites prior to OD quantification is recommended.

COMPARISON WITH EXISTING METHODS

Our framework can potentially provide OD even in demyelinating diseases, where myelin-based histology is not suitable. As compared to conventional univariate approaches, our multivariate weighted directional statistics improve the contrast-to-noise of OD maps and more accurately describe the distribution of ST metrics.

CONCLUSIONS

Our framework enables practical whole-specimen characterisation of OD in the spinal cord. We recommend tuning the scale of ST analysis for optimal OD quantification, as well as neurite segmentation and weighted directional statistics, of which examples are provided herein.