Publications

High-throughput microbial sequencing techniques, such as targeted amplicon-based and metagenomic profiling, provide low-cost genomic survey data of microbial communities in their natural environment, ranging from marine ecosystems to host-associated habitats. While standard microbiome profiling data can provide sparse relative abundances of operational taxonomic units or genes, recent advances in experimental protocols give a more quantitative picture of microbial communities by pairing sequencing-based techniques with orthogonal measurements of microbial cell counts from the same sample. These tandem measurements provide absolute microbial count data albeit with a large excess of zeros due to limited sequencing depth. In this contribution we consider the fundamental statistical problem of estimating correlations and partial correlations from such quantitative microbiome data. To this end, we propose a semi-parametric rank-based approach to correlation estimation that can naturally deal with the excess zeros in the data. Combining this estimator with sparse graphical modeling techniques leads to the Semi-Parametric Rank-based approach for INference in Graphical model (SPRING). SPRING enables inference of statistical microbial association networks from quantitative microbiome data which can serve as high-level statistical summary of the underlying microbial ecosystem and can provide testable hypotheses for functional species-species interactions. Due to the absence of verified microbial associations we also introduce a novel quantitative microbiome data generation mechanism which mimics empirical marginal distributions of measured count data while simultaneously allowing user-specified dependencies among the variables. SPRING shows superior network recovery performance on a wide range of realistic benchmark problems with varying network topologies and is robust to misspecifications of the total cell count estimate. To highlight SPRING's broad applicability we infer taxon-taxon associations from the American Gut Project data and genus-genus associations from a recent quantitative gut microbiome dataset. We believe that, as quantitative microbiome profiling data will become increasingly available, the semi-parametric estimators for correlation and partial correlation estimation introduced here provide an important tool for reliable statistical analysis of quantitative microbiome data.

Most vertebrates use active sensing strategies for perception, cognition and control of motor activity. These strategies include directed body/sensor movements or increases in discrete sensory sampling events. The weakly electric fish, \textit{Gymnotus sp.}, uses its active electric sense during navigation in the dark. Electric organ discharge rate undergoes transient increases during navigation to increase electrosensory sampling. \textit{Gymnotus} also use stereotyped backward swimming as an important form of active sensing that brings objects toward the electroreceptor dense fovea-like head region. We wirelessly recorded neural activity from the pallium of freely swimming \textit{Gymnotus}. Spiking activity was sparse and occurred only during swimming. Notably, most units tended to fire during backward swims and their activity was on average coupled to increases in sensory sampling. Our results provide the first characterization of neural activity in a hippocampal (CA3)-like region of a teleost fish brain and connects it to active sensing of spatial environmental features.

We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called "geometrically-induced stiffness," meaning that formally high-order accurate methods require excessively small time steps before the rapid convergence rate is observed. This can be overcome by analytic integration in time, requiring the evaluation of a collection of spatial boundary integral operators with non-physical, weakly singular kernels. In our hybrid scheme, we combine a local asymptotic approximation with the evaluation of a few boundary integral operators involving only Gaussian kernels, which are easily accelerated by a new version of the fast Gauss transform. This new scheme is robust, avoids geometrically-induced stiffness, and is easy to use in the presence of moving geometries. Its extension to three dimensions is natural and straightforward, and should permit layer heat potentials to become flexible and powerful tools for modeling diffusion processes.

Current mechanisms for knowledge transfer in deep networks tend to either share the lower layers between tasks, or build upon representations trained on other tasks. However, existing work in non-deep multi-task and lifelong learning has shown success with using factorized representations of the model parameter space for transfer, permitting more flexible construction of task models. Inspired by this idea, we introduce a novel architecture for sharing latent factorized representations in convolutional neural networks (CNNs). The proposed approach, called a deconvolutional factorized CNN, uses a combination of deconvolutional factorization and tensor contraction to perform flexible transfer between tasks. Experiments on two computer vision data sets show that the DF-CNN achieves superior performance in challenging lifelong learning settings, resists catastrophic forgetting, and exhibits reverse transfer to improve previously learned tasks from subsequent experience without retraining.

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation-dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.

The brain is a massive neuronal network, organized into anatomically distributed sub-circuits, with functionally relevant activity occurring at timescales ranging from milliseconds to years. Current methods to monitor neural activity, however, lack the necessary conjunction of anatomical spatial coverage, temporal resolution, and long-term stability to measure this distributed activity. Here we introduce a large-scale, multi-site, extracellular recording platform that integrates polymer electrodes with a modular stacking headstage design supporting up to 1,024 recording channels in freely behaving rats. This system can support months-long recordings from hundreds of well-isolated units across multiple brain regions. Moreover, these recordings are stable enough to track large numbers of single units for over a week. This platform enables large-scale electrophysiological interrogation of the fast dynamics and long-timescale evolution of anatomically distributed circuits, and thereby provides a new tool for understanding brain activity.

For smooth bounded domains in ℝn, we prove upper and lower L2 bounds on the boundary data of Neumann eigenfunctions, and we prove quasiorthogonality of this boundary data in a spectral window. The bounds are tight in the sense that both are independent of the eigenvalues; this is achieved by working with an appropriate norm for boundary functions, which includes a spectral weight, that is, a function of the boundary Laplacian. This spectral weight is chosen to cancel concentration at the boundary that can happen for whispering gallery-type eigenfunctions. These bounds are closely related to wave equation estimates due to Tataru. Using this, we bound the distance from an arbitrary Helmholtz parameter E>0 to the nearest Neumann eigenvalue in terms of boundary normal derivative data of a trial function u solving the Helmholtz equation (Δ−E)u=0. This inclusion bound improves over previously known bounds by a factor of E5/6, analogously to a recently improved inclusion bound in the Dirichlet case due to the first two authors. Finally, we apply our theory to present an improved numerical implementation of the method of particular solutions for computation of Neumann eigenpairs on smooth planar domains. We show that the new inclusion bound improves the relative accuracy in a computed Neumann eigenvalue (around the 42000th) from nine to fourteen digits, with negligible extra numerical effort.

Two fundamental difficulties are encountered in the numerical evaluation of time-dependent layer potentials. One is the quadratic cost of history dependence, which has been successfully addressed by splitting the potentials into two parts - a local part that contains the most recent contributions and a history part that contains the contributions from all earlier times. The history part is smooth, easily discretized using high-order quadratures, and straightforward to compute using a variety of fast algorithms. The local part, however, involves complicated singularities in the underlying Green's function. Existing methods, based on exchanging the order of integration in space and time, are able to achieve high order accuracy, but are limited to the case of stationary boundaries. Here, we present a new quadrature method that leaves the order of integration unchanged, making use of a change of variables that converts the singular integrals with respect to time into smooth ones. We have also derived asymptotic formulas for the local part that lead to fast and accurate hybrid schemes, extending earlier work for scalar heat potentials and applicable to moving boundaries. The performance of the overall scheme is demonstrated via numerical examples.

The emerging field of computational acoustic monitoring aims at retrieving high-level information from acoustic scenes recorded by some network of sensors. These networks gather large amounts of data requiring analysis. To decide which parts to inspect further, we need tools that automatically mine the data, identifying recurring patterns and isolated events. This requires a similarity measure for acoustic scenes that does not impose strong assumptions on the data. The state of the art in audio similarity measurement is the “bag-of-frames” approach, which models a recording using summary statistics of short-term audio descriptors, such as mel-frequency cepstral coefficients (MFCCs). They successfully characterise static scenes with little variability in auditory content, but cannot accurately capture scenes with a few salient events superimposed over static background. To overcome this issue, we propose a two-scale representation which describes a recording using clusters of scattering coefficients. The scattering coefficients capture short-scale structure, while the cluster model captures longer time scales, allowing for more accurate characterization of sparse events. Evaluation within the acoustic scene similarity framework demonstrates the interest of the proposed approach.

A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and others showed that Fourier analysis combined with contour integration provides a systematic and broadly effective approach, leading to what is generally referred to as the Sommerfeld integral representation. When either the source or target is at some distance from an infinite boundary, the number of degrees of freedom needed to resolve the scattering response is very modest. When both are near an interface, however, the Sommerfeld integral involves a very large range of integration and its direct application becomes unwieldy. Historically, three schemes have been employed to overcome this difficulty: the method of images, contour deformation, and asymptotic methods of various kinds. None of these methods make use of classical layer potentials in physical space, despite their advantages in terms of adaptive resolution and high-order accuracy. The reason for this is simple: layer potentials are impractical in layered media or half-space geometries since they require the discretization of an infinite boundary. In this paper, we propose a hybrid method which combines layer potentials (physical-space) on a finite portion of the interface together with a Sommerfeld-type (Fourier) correction. We prove that our method is efficient and rapidly convergent for arbitrarily located sources and targets, and show that the scheme is particularly effective when solving scattering problems for objects which are close to the half-space boundary or even embedded across a layered media interface.