Publications

Background Accurate high-resolution EEG source reconstruction (localization) is important for several tasks, including rigorous and rapid mental health screening.Objective The present study has developed, validated, and applied a new source localization algorithm utilizing a charge-based boundary element fast multipole method (BEM-FMM) coupled with the Helmholtz reciprocity principle and the transcranial electrical stimulation (TES) forward solution.Methods The unknown cortical dipole density is reconstructed over the entire cortical surface by expanding into global basis functions in the form of cortical fields of active TES electrode pairs. These pairs are constructed from the reading electrodes. An analog of the minimum norm estimation (MNE) equation is obtained after substituting this expansion into the reciprocity principle written in terms of measured electrode voltages. Delaunay (geometrically balanced) triangulation of the electrode cap is introduced first. Basis functions for all electrode pairs connected by the edges of a triangular mesh are precomputed and stored in memory. A smaller set of independent basis functions is then selected and employed at every time instant. This set is based on the highest voltage differences measured.Results The method is validated against the classic, yet challenging problem of median nerve stimulation and the tangential cortical sources located at the posterior wall of the central sulcus for an N20/P20 peak (2 scanned subjects). The method is further applied to perform source reconstruction of synthesized tangential cortical sources located at the posterior wall of the central sulcus (12 different subjects). In the second case, an average source reconstruction error of 7 mm is reported for the best possible noiseless scenario.Conclusions Once static preprocessing with TES electrodes has been done (the basis functions have been computed), our method requires fractions of a second to complete the accurate high-resolution source localization.Competing Interest StatementThe authors have declared no competing interest.

Two groups have visualized actin — the protein polymer that gives cells their shape — at high resolution. The structures provide in-depth views of the polymer as it adopts fleeting states and undergoes conformational changes.

Peptides are commonly used as therapeutic agents. However, they suffer from easy degradation and instability. Replacing natural by non-natural amino acids can avoid these problems, and potentially improve the affinity towards the target protein. Here, we present a computational pipeline to optimize peptides based on adding non-natural amino acids while improving their binding affinity. The workflow is an iterative computational evolution algorithm, inspired by the PARCE protocol, that performs single-point mutations on the peptide sequence using modules from the Rosetta framework. The modifications can be guided based on the structural properties or previous knowledge of the biological system. At each mutation step, the affinity to the protein is estimated by sampling the complex conformations and applying a consensus metric using various open protein-ligand scoring functions. The mutations are accepted based on the score differences, allowing for an iterative optimization of the initial peptide. The sampling/scoring scheme was benchmarked with a set of protein-peptide complexes where experimental affinity values have been reported. In addition, a basic application using a known protein-peptide complex is also provided. The structure- and dynamic-based approach allows users to optimize bound peptides, with the option to personalize the code for further applications. The protocol, called mPARCE, is available at: https://github.com/rochoa85/mPARCE/.

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.

In fluid dynamics, constitutive models are often used to describe the unresolved turbulence and to close the Reynolds averaged Navier–Stokes (RANS) equations. Traditional PDE-based constitutive models are usually too rigid to calibrate with a large set of high-fidelity data. Moreover, commonly used turbulence models are based on the weak equilibrium assumption, which cannot adequately capture the nonlocal physics of turbulence. In this work, we propose using a vector-cloud neural network (VCNN) to learn the nonlocal constitutive model, which maps a regional mean flow field to the local turbulence quantities without solving the transport PDEs. The network is strictly invariant to coordinate translation, rotation, and uniform motion, as well as ordering of the input points. The VCNN-based nonlocal constitutive model is trained and evaluated on flows over a family of parameterized periodic hills. Numerical results demonstrate its predictive capability on target turbulence quantities of turbulent kinetic energy k and dissipation ɛ. More importantly, we investigate the robustness and stability of the method by coupling the trained model back to RANS solver. The solver shows good convergence with the simulated velocity field comparable to that based on k–ɛ model when starting from a reasonable initial condition. This study, as a proof of concept, highlights the feasibility of using a nonlocal, frame-independent, neural network-based constitutive model to close the RANS equations, paving the way for the further emulation of the Reynolds stress transport models.

Self-supervised learning (SSL) is currently one of the premier techniques to create data representations that are actionable for transfer learning in the absence of human annotations. Despite their success, the underlying geometry of these representations remains elusive, which obfuscates the quest for more robust, trustworthy, and interpretable models. In particular, mainstream SSL techniques rely on a specific deep neural network architecture with two cascaded neural networks: the encoder and the projector. When used for transfer learning, the projector is discarded since empirical results show that its representation generalizes more poorly than the encoder's. In this paper, we investigate this curious phenomenon and analyze how the strength of the data augmentation policies affects the data embedding. We discover a non-trivial relation between the encoder, the projector, and the data augmentation strength: with increasingly larger augmentation policies, the projector, rather than the encoder, is more strongly driven to become invariant to the augmentations. It does so by eliminating crucial information about the data by learning to project it into a low-dimensional space, a noisy estimate of the data manifold tangent plane in the encoder representation. This analysis is substantiated through a geometrical perspective with theoretical and empirical results.

Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is analyzed in the limit of slow surface diffusion. Using the tools of formal asymptotics and calculus of variations, we study the characteristic wave-pinning behavior of this system on three dynamical timescales. On the short timescale, generation of an interface separating high- and low-concentration domains is established under suitable conditions. Intermediate timescale dynamics is shown to lead to a uniform growth or shrinking of these domains to sizes which are fixed by global parameters. Finally, the long time dynamics reduces to area-preserving geodesic curvature flow that may lead to multi-interface steady state solutions. These results provide a foundation for studying cell polarization and related phenomena in biologically relevant geometries.

Speckle or multiplicative noise is a critical issue in coherence-based imaging systems, such as synthetic aperture radar and optical coherence tomography. Existence of speckle noise considerably limits the applicability of such systems by degrading their performance. On the other hand, the sophistications that arise in the study of multiplicative noise have so far impeded theoretical analysis of such imaging systems. As a result, the current acquisition technology relies on heuristic solutions, such as oversampling the signal and converting the problem into a denoising problem with multiplicative noise. This paper attempts to bridge the gap between theory and practice by providing the first theoretical analysis of such systems. To achieve this goal the log-likelihood function corresponding to measurement systems with speckle noise is characterized. Then employing compression codes to model the source structure, for the case of under-sampled measurements, a compression-based maximum likelihood recovery method is proposed. The mean squared error (MSE) performance of the proposed method is characterized and is shown to scale as O(klognm−−−−−√) , where k , m and n denote the intrinsic dimension of the signal class according to the compression code, the number of observations, and the ambient dimension of the signal, respectively. This result, while in contrast to imaging systems with additive noise in which MSE scales as O(klognm) , suggests that if the signal class is structured (i.e., k≪n ), accurate recovery of a signal from under-determined measurements is still feasible, even in the presence of speckle noise. Simulation results are presented that suggest image recovery under multiplicative noise is inherently more challenging than additive noise, and that the derived theoretical results are sharp

We perform a data-driven dimensionality reduction of the scale-dependent four-point vertex function characterizing the functional renormalization group (FRG) flow for the widely studied two-dimensional \(t−t′\) Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a neural ordinary differential equation solver in a low-dimensional latent space efficiently learns the FRG dynamics that delineates the various magnetic and d-wave superconducting regimes of the Hubbard model. We further present a dynamic mode decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the FRG dynamics. Our Letter demonstrates the possibility of using artificial intelligence to extract compact representations of the four-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.

We investigate the effects of non-zero spatial curvature on cosmic inflation in the light of cosmic microwave background (CMB) anisotropy measurements from the Planck 2018 legacy release and from the 2015 observing season of BICEP2 and the Keck Array. Even a small percentage of non-zero curvature today would significantly limit the total number of e-folds of the scale factor during inflation, rendering just-enough inflation scenarios with a kinetically dominated or fast-roll stage prior to slow-roll inflation more likely. Finite inflation leads to oscillations and a cutoff towards large scales in the primordial power spectrum and curvature pushes them into the CMB observable window. Using nested sampling, we carry out Bayesian parameter estimations and model comparisons taking into account constraints from reheating and horizon considerations. We confirm the preference of CMB data for closed universes with Bayesian odds of over 100:1 and with a posterior on the curvature density parameter of ΩK,0=−0.051±0.017 for a curvature extension of LCDM and ΩK,0=−0.031±0.014 for Starobinsky inflation. Model comparisons of various inflation models give similar results as for flat universes with the Starobinsky model outperforming most other models.