arXiv subjects

Peter C. Doerschuk

Publications and source records attributed to Peter C. Doerschuk.

3 recordsLinked to original sources

arXiv2021

Computation of real-valued basis functions which transform as irreducible representations of the polyhedral groups

Basis functions which are invariant under the operations of a rotational point group $G$ are able to describe any 3-D object which exhibits the rotational point group symmetry. However, in order to characterize the spatial statistics of an ensemble of objects in which each object is different but the statistics exhibit the symmetry, a complete set of basis functions is required. In particular, for each irreducible representation (irrep) of $G$, it is necessary to include basis functions that transform according to that irrep. This complete set of basis functions is a basis for square-integrable functions on the surface of the sphere in 3-D. Because the objects are real-valued, it is convenient to have real-valued basis functions. In this paper, the existence of such real-valued bases is proven and an algorithm for their computation is provided for the icosahedral $I$ and the octahedral $O$ symmetries. Furthermore, it is proven that such a real-valued basis does not exist for the tetrahedral $T$ symmetry because some irreps of $T$ are essentially complex. The importance of these basis functions to computations in single-particle cryo-electron microscopy is described.

math.GR↗

arXiv2018

Learning Compositional Visual Concepts with Mutual Consistency

Compositionality of semantic concepts in image synthesis and analysis is appealing as it can help in decomposing known and generatively recomposing unknown data. For instance, we may learn concepts of changing illumination, geometry or albedo of a scene, and try to recombine them to generate physically meaningful, but unseen data for training and testing. In practice however we often do not have samples from the joint concept space available: We may have data on illumination change in one data set and on geometric change in another one without complete overlap. We pose the following question: How can we learn two or more concepts jointly from different data sets with mutual consistency where we do not have samples from the full joint space? We present a novel answer in this paper based on cyclic consistency over multiple concepts, represented individually by generative adversarial networks (GANs). Our method, ConceptGAN, can be understood as a drop in for data augmentation to improve resilience for real world applications. Qualitative and quantitative evaluations demonstrate its efficacy in generating semantically meaningful images, as well as one shot face verification as an example application.

cs.CV↗

arXiv2017

Initial validation for the estimation of resting-state fMRI effective connectivity by a generalization of the correlation approach

Resting-state functional MRI (rs-fMRI) is widely used to noninvasively study human brain networks. Network functional connectivity is often estimated by calculating the timeseries correlation between blood-oxygen-level dependent (BOLD) signal from different regions of interest. However, standard correlation cannot characterize the direction of information flow between regions. In this paper, we introduce and test a new concept, prediction correlation, to estimate effective connectivity in functional brain networks from rs-fMRI. In this approach, the correlation between two BOLD signals is replaced by a correlation between one BOLD signal and a prediction of this signal via a causal system driven by another BOLD signal. Three validations are described: (1) Prediction correlation performed well on simulated data where the ground truth was known, and outperformed four other methods. (2) On simulated data designed to display the "common driver" problem, prediction correlation did not introduce false connections between non-interacting driven ROIs. (3) On experimental data, prediction correlation recovered the previously identified network organization of human brain. Prediction correlation scales well to work with hundreds of ROIs, enabling it to assess whole brain interregional connectivity at the single subject level. These results provide an initial validation that prediction correlation can capture the direction of information flow and estimate the duration of extended temporal delays in information flow between regions of interest based on BOLD signal. This approach not only maintains the high sensitivity to network connectivity provided by the correlation analysis, but also performs well in the estimation of causal information flow in the brain.

q-bio.QM↗