Publications

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems. In this paper, we fill this gap by showing that proximal methods provide an efficient framework to model and solve problems involving perspective functions. We study the construction of the proximity operator of a perspective function under general assumptions and present important instances in which the proximity operator can be computed explicitly or via straightforward numerical operations. These results constitute central building blocks in the design of proximal optimization algorithms. We showcase the versatility of the framework by designing novel proximal algorithms for state-of-the-art regression and variable selection schemes in high-dimensional statistics.

\textbf{Background:} No microbe exists in isolation, and few live in environments with only members of their own kingdom or domain. As microbiome studies become increasingly more interested in the interactions between microbes than in cataloging which microbes are present, the variety of microbes in the community should be considered. However, the majority of ecological interaction networks for microbiomes built to date have included only bacteria. Joint association inference across multiple domains of life, e.g., fungal communities (the mycobiome) and bacterial communities, has remained largely elusive. \textbf{Results:} Here, we present a novel extension of the SParse InversE Covariance estimation for Ecological ASsociation Inference (SPIEC-EASI) framework that allows statistical inference of cross-domain associations from targeted amplicon sequencing data. For human lung and skin micro- and mycobiomes, we show that cross-domain networks exhibit higher connectivity, increased network stability, and similar topological re-organization patterns compared to single-domain networks. We also validate in vitro a small number of cross-domain interactions predicted by the skin association network. \textbf{Conclusions:} For the human lung and skin micro- and mycobiomes, our findings suggest that fungi play a stabilizing role in ecological network organization. Our study suggests that computational efforts to infer association networks that include all forms of microbial life, paired with large-scale culture-based association validation experiments, will help formulate concrete hypotheses about the underlying biological mechanisms of species interactions and, ultimately, help understand microbial communities as a whole.

Determining the three dimensional arrangement of proteins in a complex is highly beneficial for uncovering mechanistic function and interpreting genetic variation in coding genes comprising protein complexes. There are several methods for determining co-complex interactions between proteins, among them co-fractionation / mass spectrometry (CF-MS), but it remains difficult to identify directly contacting subunits within a multi-protein complex. Correlation analysis of CF-MS profiles shows promise in detecting protein complexes as a whole but is limited in its ability to infer direct physical contacts among proteins in sub-complexes. To identify direct protein-protein contacts within human protein complexes we learn a sparse conditional dependency graph from approximately 3,000 CF-MS experiments on human cell lines. We show substantial performance gains in estimating direct interactions compared to correlation analysis on a benchmark of large protein complexes with solved three-dimensional structures. We demonstrate the method's value in determining the three dimensional arrangement of proteins by making predictions for complexes without known structure (the exocyst and tRNA multi-synthetase complex) and by establishing evidence for the structural position of a recently discovered component of the core human EKC/KEOPS complex, GON7/C14ORF142, providing a more complete 3D model of the complex. Direct contact prediction provides easily calculable additional structural information for large-scale protein complex mapping studies and should be broadly applicable across organisms as more CF-MS datasets become available.

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.

Broad-spectrum antibiotics are frequently prescribed to children. Early childhood represents a dynamic period for the intestinal microbial ecosystem, which is readily shaped by environmental cues; antibiotic-induced disruption of this sensitive community may have long-lasting host consequences. Here we demonstrate that a single pulsed macrolide antibiotic treatment (PAT) course early in life is sufficient to lead to durable alterations to the murine intestinal microbiota, ileal gene expression, specific intestinal T-cell populations, and secretory IgA expression. A PAT-perturbed microbial community is necessary for host effects and sufficient to transfer delayed secretory IgA expression. Additionally, early-life antibiotic exposure has lasting and transferable effects on microbial community network topology. Our results indicate that a single early-life macrolide course can alter the microbiota and modulate host immune phenotypes that persist long after exposure has ceased.High or multiple doses of macrolide antibiotics, when given early in life, can perturb the metabolic and immunological development of lab mice. Here, Ruiz et al. show that even a single macrolide course, given early in life, leads to long-lasting changes in the gut microbiota and immune system of mice.

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

We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and non-convex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, each least squares calculation is well-conditioned and involves the solution of a large number of forward scattering problems, for which we employ a recently developed, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately one million partial differential equations were solved, requiring approximately two days to compute using a parallel MATLAB implementation on a multi-core workstation.

The design of systems or models that work robustly under uncertainty and environmental fluctuations is a key challenge in both engineering and science. This is formalized in the design-centering problem, which is defined as finding a design that fulfills given specifications and has a high probability of still doing so if the system parameters or the specifications fluctuate randomly. Design centering is often accompanied by the problem of quantifying the robustness of a system. Here we present a novel adaptive statistical method to simultaneously address both problems. Our method, L p-Adaptation, is inspired by the evolution of robustness in biological systems and by randomized schemes for convex volume computation. It is able to address both problems in the general, non-convex case and at low computational cost. We describe the concept and the algorithm, test it on known benchmarks, and demonstrate its real-world applicability in electronic and biological systems. In all cases, the present method outperforms the previous state of the art. This enables re-formulating optimization problems in engineering and biology as design centering problems, taking global system robustness into account.

We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O(n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples