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We propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to estimate transformation coefficients using unordered multisets of covariates and responses. Previous theoretical analysis of the problem has been done in a setting where the responses are a complete permutation of the regressed covariates. This paper expands the problem setting by analyzing the cases where only a subset of the responses is a permutation of the regressed covariates in addition to some covariates possibly being adversarial outliers. We term this problem robust regression without correspondence and provide several algorithms based on random sample consensus for exact and approximate recovery in a noiseless and noisy one-dimensional setting as well as an approximation algorithm for multiple dimensions. The theoretical guarantees of the algorithms are verified in simulated data. We demonstrate an important computational neuroscience application of the proposed framework by demonstrating its effectiveness in a Caenorhabditis elegans neuron matching problem where the presence of outliers in both the source and target nematodes is a natural tendency 

Sex differences in the brain are prevalent throughout the animal kingdom and particularly well appreciated in the nematode C. elegans, where male animals contain a little studied set of 93 male-specific neurons. To make these neurons amenable for future study, we describe here how a multicolor reporter transgene, NeuroPAL, is capable of visualizing the distinct identities of all male specific neurons. We used NeuroPAL to visualize and characterize a number of features of the male-specific nervous system. We provide several proofs of concept for using NeuroPAL to identify the sites of expression of gfp-tagged reporter genes and for cellular fate analysis by analyzing the effect of removal of several developmental patterning genes on neuronal identity acquisition. We use NeuroPAL and its intrinsic cohort of more than 40 distinct differentiation markers to show that, even though male-specific neurons are generated throughout all four larval stages, they execute their terminal differentiation program in a coordinated manner in the fourth larval stage. This coordinated wave of differentiation, which we call “just-in-time" differentiation, couples neuronal maturation programs with the appearance of sexual organs. 

Spatial transcriptomics techniques such as STARmap [15] enable the subcellular detection of RNA transcripts within complex tissue sections. The data from these techniques are impacted by optical microscopy limitations, such as shading or vignetting effects from uneven illumination during image capture. Downstream analysis of these sparse spatially resolved transcripts is dependent upon the correction of these artefacts. This paper introduces a novel non-parametric vignetting correction tool for spatial transcriptomic images, which estimates the illumination field and background using an efficient iterative sliced histogram normalization routine. We show that our method outperforms the state-of-the-art shading correction techniques both in terms of illumination and background field estimation and requires fewer input images to perform the estimation adequately. We further demonstrate an important downstream application of our technique, showing that spatial transcriptomic volumes corrected by our method yield a higher and more uniform gene expression spot-calling in the rodent hippocampus. Python code and a demo file to reproduce our results are provided in the supplementary material and at this github page: https://github.com/BoveyRao/Non-parametric-vc-for-sparse-st. 

Multi-electrode arrays such as "Neuropixels" probes enable the study of neuronal voltage signals at high temporal and single-cell spatial resolution. However, in vivo recordings from these devices often experience some shifting of the probe (due e.g. to animal movement), resulting in poorly localized voltage readings that in turn can corrupt estimates of neural activity. We introduce a new registration method to partially correct for this motion. In contrast to previous template-based registration methods, the proposed approach is decentralized, estimating shifts of the data recorded in multiple timebins with respect to one another, and then extracting a global registration estimate from the resulting estimated shift matrix. We find that the resulting decentralized registration is more robust and accurate than previous template-based approaches applied to both simulated and real data, but nonetheless some significant non-stationarity in the recovered neural activity remains that should be accounted for by downstream processing pipelines. Open source code is available at https://github.com/evarol/NeuropixelsRegistration.