Scattering from large, open cavity structures is of importance in a variety of \href{https://www.sciencedirect.com/topics/physics-and-astronomy/electromagnetism}{electromagnetic} applications. In this paper, we propose a new well conditioned integral equation for scattering from general open cavities embedded in an infinite, perfectly conducting half-space. The integral representation permits the stable evaluation of both the electric and \href{https://www.sciencedirect.com/topics/physics-and-astronomy/magnetic-fields}{magnetic field}, even in the low-frequency regime, using the \href{https://www.sciencedirect.com/topics/physics-and-astronomy/continuity-equation}{continuity equation} in a \href{https://www.sciencedirect.com/topics/computer-science/postprocessing-step}{post-processing step}. We establish existence and uniqueness results, and demonstrate the performance of the scheme in the cavity-of-revolution case. High-order accuracy is obtained using a Nyström \href{https://www.sciencedirect.com/topics/computer-science/discretization}{discretization} with generalized Gaussian \href{https://www.sciencedirect.com/topics/physics-and-astronomy/quadratures}{quadratures}.
Understanding the detailed dynamics of neuronal networks will require the simultaneous measurement of spike trains from hundreds of neurons (or more). Currently, approaches to extracting spike times and labels from raw data are time consuming, lack standardization, and involve manual intervention, making it difficult to maintain data provenance and assess the quality of scientific results. Here, we describe an automated clustering approach and associated software package that addresses these problems and provides novel cluster quality metrics. We show that our approach has accuracy comparable to or exceeding that achieved using manual or semi-manual techniques with desktop central processing unit (CPU) runtimes faster than acquisition time for up to hundreds of electrodes. Moreover, a single choice of parameters in the algorithm is effective for a variety of electrode geometries and across multiple brain regions. This algorithm has the potential to enable reproducible and automated spike sorting of larger scale recordings than is currently possible.
Determining the three-dimensional (3D) structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using “single particle” cryo-electron microscopy (cryo-EM) for this purpose. In cryo-EM, hundreds of thousands of two-dimensional (2D) images are obtained of individual copies of the same particle, each held in a thin sheet of ice at some unknown orientation. Each image corresponds to the noisy projection of the particle's electron-scattering density. The reconstruction of a high-resolution image from this data is typically formulated as a nonlinear, nonconvex optimization problem for unknowns which encode the angular pose and lateral offset of each particle. Since there are hundreds of thousands of such parameters, this leads to a very CPU-intensive task---limiting both the number of particle images which can be processed and the number of independent reconstructions which can be carried out for the purpose of statistical validation. Moreover, existing reconstruction methods typically require a good initial guess to converge. Here, we propose a deterministic method for high-resolution reconstruction that operates in an ab initio manner---that is, without the need for an initial guess. It requires a predictable and relatively modest amount of computational effort, by marching out radially in the Fourier domain from low to high frequency, increasing the resolution by a fixed increment at each step.
Read More: http://epubs.siam.org/doi/abs/10.1137/16M1097171
Background
The throughput of electrophysiological recording is growing rapidly, allowing thousands of simultaneous channels, and there is a growing variety of spike sorting algorithms designed to extract neural firing events from such data. This creates an urgent need for standardized, automatic evaluation of the quality of neural units output by such algorithms.
New method
We introduce a suite of validation metrics that assess the credibility of a given automatic spike sorting algorithm applied to a given dataset. By rerunning the spike sorter two or more times, the metrics measure stability under various perturbations consistent with variations in the data itself, making no assumptions about the internal workings of the algorithm, and minimal assumptions about the noise.
Results
We illustrate the new metrics on standard sorting algorithms applied to both in vivo and ex vivo recordings, including a time series with overlapping spikes. We compare the metrics to existing quality measures, and to ground-truth accuracy in simulated time series. We provide a software implementation.
Comparison with existing methods
Metrics have until now relied on ground-truth, simulated data, internal algorithm variables (e.g. cluster separation), or refractory violations. By contrast, by standardizing the interface, our metrics assess the reliability of any automatic algorithm without reference to internal variables (e.g. feature space) or physiological criteria.
Conclusions
Stability is a prerequisite for reproducibility of results. Such metrics could reduce the significant human labor currently spent on validation, and should form an essential part of large-scale automated spike sorting and systematic benchmarking of algorithms.