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Item A Branch Decomposition Algorithm for the p-Median Problem(INFORMS, 2017) Fast, Caleb C.; Hicks, Illya V.Show more In this paper, we use a branch decomposition technique to improve approximations to the p-median problem. Starting from a support graph produced either by a combination of heuristics or by linear programming, we use dynamic programming guided by a branch decomposition of that support graph to find the best p-median solution on the support graph. Our results show that when heuristics are used to build the support graph and the support graph has branchwidth at most 7, our algorithm is able to provide a solution of lower cost than any of the heuristic solutions. When linear programming is used to build the support graph and the support graph has branchwidth at most 7, then our algorithm provides better solutions than popular heuristics and is faster than integer programming. Thus, our algorithm is a useful practical tool when support graphs have branchwidth at most 7.Show more Item A discrepancy-based penalty method for extended waveform inversion(Society of Exploration Geophysicists, 2017) Fu, Lei; Symes, William W.; The Rice Inversion ProjectShow more Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These extra degrees of freedom must be curtailed at the solution, for example, by penalizing them as part of an optimization formulation. For separable (partly linear) models, a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical (linear) degrees of freedom. The linear variables are eliminated in an inner optimization step, leaving a function of the outer (nonlinear) variables to be optimized. This variable projection method is convenient for computation, but it requires that the penalty weight be increased as the estimated model tends to the (physical) solution. We describe an algorithm based on discrepancy, that is, maintaining the data residual at the inner optimum within a prescribed range, to control the penalty weight during the outer optimization. We evaluate this algorithm in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting bandlimited waveform data in the Born approximation.Show more Item A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions(Society for Industrial and Applied Mathematics, 2017) Xin, Zixing; Xia, Jianlin; de Hoop, Maarten V.; Cauley, Stephen; Balakrishnan, VenkataramananShow more We design a distributed-memory randomized structured multifrontal solver for large sparse matrices. Two layers of hierarchical tree parallelism are used. A sequence of innovative parallel methods are developed for randomized structured frontal matrix operations, structured update matrix computation, skinny extend-add operation, selected entry extraction from structured matrices, etc. Several strategies are proposed to reuse computations and reduce communications. Unlike an earlier parallel structured multifrontal method that still involves large dense intermediate matrices, our parallel solver performs the major operations in terms of skinny matrices and fully structured forms. It thus significantly enhances the efficiency and scalability. Systematic communication cost analysis shows that the numbers of words are reduced by factors of about $O(\sqrt{n}/r)$ in two dimensions and about $O(n^{2/3}/r)$ in three dimensions, where $n$ is the matrix size and $r$ is an off-diagonal numerical rank bound of the intermediate frontal matrices. The efficiency and parallel performance are demonstrated with the solution of some large discretized PDEs in two and three dimensions. Nice scalability and significant savings in the cost and memory can be observed from the weak and strong scaling tests, especially for some 3D problems discretized on unstructured meshes.Show more Item A Topological Model of the Hippocampal Cell Assembly Network(Frontiers Media S.A., 2016) Babichev, Andrey; Ji, Daoyun; Mémoli, Facundo; Dabaghian, Yuri A.Show more It is widely accepted that the hippocampal place cells' spiking activity produces a cognitive map of space. However, many details of this representation's physiological mechanism remain unknown. For example, it is believed that the place cells exhibiting frequent coactivity form functionally interconnected groups—place cell assemblies—that drive readout neurons in the downstream networks. However, the sheer number of coactive combinations is extremely large, which implies that only a small fraction of them actually gives rise to cell assemblies. The physiological processes responsible for selecting the winning combinations are highly complex and are usually modeled via detailed synaptic and structural plasticity mechanisms. Here we propose an alternative approach that allows modeling the cell assembly network directly, based on a small number of phenomenological selection rules. We then demonstrate that the selected population of place cell assemblies correctly encodes the topology of the environment in biologically plausible time, and may serve as a schematic model of the hippocampal network.Show more Item An adaptive multiscale algorithm for efficient extended waveform inversion(Society of Exploration Geophysicists, 2017) Fu, Lei; Symes, William W.; The Rice Inversion ProjectShow more Subsurface-offset extended full-waveform inversion (FWI) may converge to kinematically accurate velocity models without the low-frequency data accuracy required for standard data-domain FWI. However, this robust alternative approach to waveform inversion suffers from a very high computational cost resulting from its use of nonlocal wave physics: The computation of strain from stress involves an integral over the subsurface offset axis, which must be performed at every space-time grid point. We found that a combination of data-fit driven offset limits, grid coarsening, and low-pass data filtering can reduce the cost of extended inversion by one to two orders of magnitude.Show more Item An Algebraic Exploration of Dominating Sets and Vizing's Conjecture(The Electronic Journal of Combinatorics, 2012) Margulies, S.; Hicks, I.V.Show more Systems of polynomial equations are commonly used to model combinatorial problems such as independent set, graph coloring, Hamiltonian path, and others. We formulate the dominating set problem as a system of polynomial equations in two di erent ways: rst, as a single, high-degree polynomial, and second as a collection of polynomials based on the complements of domination-critical graphs. We then provide a su cient criterion for demonstrating that a particular ideal representation is already the universal Gr obner bases of an ideal, and show that the second representation of the dominating set ideal in terms of domination-critical graphs is the universal Gr obner basis for that ideal. We also present the rst algebraic formulation of Vizing's conjecture, and discuss the theoretical and computational rami cations to this conjecture when using either of the two dominating set representations described above.Show more Item An accelerated Poisson solver based on multidomain spectral discretization(Springer, 2018) Babb, Tracy; Gillman, Adrianna; Hao, Sijia; Martinsson, Per-GunnarShow more This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The method works best for domains that can readily be mapped onto a rectangle, or a collection of nonoverlapping rectangles. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and higher have been tested and work well). Local mesh refinement results in highly accurate solutions even in the presence of local irregular behavior due to corner singularities, localized loads, etc. The system of linear equations attained upon discretization is solved using a direct (as opposed to iterative) solver with O(N1.5)O(N1.5) complexity for the factorization stage and O(NlogN)O(NlogN) complexity for the solve. The scheme is ideally suited for executing the elliptic solve required when parabolic problems are discretized via time-implicit techniques. In situations where the geometry remains unchanged between time-steps, very fast execution speeds are obtained since the solution operator for each implicit solve can be pre-computed.Show more Item An alternating direction and projection algorithm for structure-enforced matrix factorization(Springer, 2017) Xu, Lijun; Yu, Bo; Zhang, YinShow more Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.Show more Item An exact redatuming procedure for the inverse boundary value problem for the wave equation(Society for Industrial and Applied Mathematics, 2018) de Hoop, Maarten V.; Kepley, Paul; Oksanen, LauriShow more Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. We consider a redatuming problem for a wave equation on a bounded domain, or on a manifold with boundary, and model data acquisition by a restriction of the associated Neumann-to-Dirichlet map. This map models measurements with sources and receivers on an open subset $\Gamma$ contained in the boundary of the manifold. We model the wavespeed by a Riemannian metric and suppose that the metric is known in some coordinates in a neighborhood of $\Gamma$. Our goal is to move sources and receivers into this known near boundary region. We formulate redatuming as a collection of unique continuation problems and provide a two-step procedure to solve the redatuming problem. We investigate the stability of the first step in this procedure, showing that it enjoys conditional Hölder stability under suitable geometric hypotheses. In addition, we provide computational experiments that demonstrate our redatuming procedure.Show more Item Angola Cameia Development Casing-Settlement Calculations(Society of Petroleum Engineers, 2017) Akin, J. Ed; Dove, N. Roland; Ruddy, KenShow more The amount of axial settlement of casings supported by regions of axial elastic foundations is computed. The differential equation of axial equilibrium, including the foundation stiffnesses, is solved by use of cubic axial finite elements. The analysis is applied to 101 m of a vertical 914-mm (36-in.) casing supporting a 559-mm (22-in.) casing running from 3 m above the mudline to near the bottom of the 1201-m hole. The upper casing is supported by a region of layered clay sediments. The lower casing has a long openhole region, followed by a bottom region encased in cement. A series of loading increments is applied, with the connection of the tree/blowout preventer (BOP) as the last. The settlement at the mudline was calculated to be less than 0.1 m. This study shows that for weak upper foundations, a good cement job is needed to support the tree/BOP without large mudline settlements.Show more Item An approximate inverse to the extended Born modeling operator(Society of Exploration Geophysicists, 2015) Hou, Jie; Symes, William W.; The Rice Inversion ProjectShow more Given a correct (data-consistent) velocity model, reverse time migration (RTM) correctly positions reflectors but generally with incorrect amplitudes and wavelets. Iterative least-squares migration (LSM) corrects the amplitude and wavelet by fitting data in the sense of Born modeling, that is, replacing migration by Born inversion. However, LSM also requires a correct velocity model, and it may require many migration/demigration cycles. We modified RTM in the subsurface offset domain to create an asymptotic (high-frequency) approximation to extended LSM. This extended Born inversion operator outputs extended reflectors (depending on the subsurface offset and position in the earth) with correct amplitude and phase, in the sense that similarly extended Born modeling reproduces the data to good accuracy. Although the theoretical justification of the inversion property relies on ray tracing and stationary phase, application of the weight operators does not require any computational ray tracing. The computational expense of the extended Born inversion operator is roughly the same as that of extended RTM, and the inversion (data-fit) property holds even when the velocity is substantially incorrect. The approximate inverse operator differes from extended RTM only in the application of data- and model-domain weight operators, and takes the form of an adjoint in the sense of weighted inner products in data and model space. Because the Born modeling operator is approximately unitary with respect to the weighted inner products, a weighted version of conjugate gradient iteration dramatically accelerates the convergence of extended LSM. An approximate LSM may be extracted from the approximate extended LSM by averaging over subsurface offset.Show more Item Chromatin architecture transitions from zebrafish sperm through early embryogenesis(Cold Spring Harbor Laboratory Press, 2021) Wike, Candice L.; Guo, Yixuan; Tan, Mengyao; Nakamura, Ryohei; Shaw, Dana Klatt; Díaz, Noelia; Whittaker-Tademy, Aneasha F.; Durand, Neva C.; Aiden, Erez Lieberman; Vaquerizas, Juan M.; Grunwald, David; Takeda, Hiroyuki; Cairns, Bradley R.; Center for Theoretical Biological PhysicsShow more Chromatin architecture mapping in 3D formats has increased our understanding of how regulatory sequences and gene expression are connected and regulated in a genome. The 3D chromatin genome shows extensive remodeling during embryonic development, and although the cleavage-stage embryos of most species lack structure before zygotic genome activation (pre-ZGA), zebrafish has been reported to have structure. Here, we aimed to determine the chromosomal architecture in paternal/sperm zebrafish gamete cells to discern whether it either resembles or informs early pre-ZGA zebrafish embryo chromatin architecture. First, we assessed the higher-order architecture through advanced low-cell in situ Hi-C. The structure of zebrafish sperm, packaged by histones, lacks topological associated domains and instead displays “hinge-like” domains of ∼150 kb that repeat every 1–2 Mbs, suggesting a condensed repeating structure resembling mitotic chromosomes. The pre-ZGA embryos lacked chromosomal structure, in contrast to prior work, and only developed structure post-ZGA. During post-ZGA, we find chromatin architecture beginning to form at small contact domains of a median length of ∼90 kb. These small contact domains are established at enhancers, including super-enhancers, and chemical inhibition of Ep300a (p300) and Crebbpa (CBP) activity, lowering histone H3K27ac, but not transcription inhibition, diminishes these contacts. Together, this study reveals hinge-like domains in histone-packaged zebrafish sperm chromatin and determines that the initial formation of high-order chromatin architecture in zebrafish embryos occurs after ZGA primarily at enhancers bearing high H3K27ac.Show more Item Chromosome size affects sequence divergence between species through the interplay of recombination and selection(Wiley, 2022) Tigano, Anna; Khan, Ruqayya; Omer, Arina D.; Weisz, David; Dudchenko, Olga; Multani, Asha S.; Pathak, Sen; Behringer, Richard R.; Aiden, Erez L.; Fisher, Heidi; MacManes, Matthew D.; Center for Theoretical and Biological PhysicsShow more The structure of the genome shapes the distribution of genetic diversity and sequence divergence. To investigate how the relationship between chromosome size and recombination rate affects sequence divergence between species, we combined empirical analyses and evolutionary simulations. We estimated pairwise sequence divergence among 15 species from three different mammalian clades—Peromyscus rodents, Mus mice, and great apes—from chromosome-level genome assemblies. We found a strong significant negative correlation between chromosome size and sequence divergence in all species comparisons within the Peromyscus and great apes clades but not the Mus clade, suggesting that the dramatic chromosomal rearrangements among Mus species may have masked the ancestral genomic landscape of divergence in many comparisons. Our evolutionary simulations showed that the main factor determining differences in divergence among chromosomes of different sizes is the interplay of recombination rate and selection, with greater variation in larger populations than in smaller ones. In ancestral populations, shorter chromosomes harbor greater nucleotide diversity. As ancestral populations diverge, diversity present at the onset of the split contributes to greater sequence divergence in shorter chromosomes among daughter species. The combination of empirical data and evolutionary simulations revealed that chromosomal rearrangements, demography, and divergence times may also affect the relationship between chromosome size and divergence, thus deepening our understanding of the role of genome structure in the evolution of species divergence.Show more Item Clustering earthquake signals and background noises in continuous seismic data with unsupervised deep learning(Springer Nature, 2020) Seydoux, Léonard; Balestriero, Randall; Poli, Piero; de Hoop, Maarten; Campillo, Michel; Baraniuk, RichardShow more The continuously growing amount of seismic data collected worldwide is outpacing our abilities for analysis, since to date, such datasets have been analyzed in a human-expert-intensive, supervised fashion. Moreover, analyses that are conducted can be strongly biased by the standard models employed by seismologists. In response to both of these challenges, we develop a new unsupervised machine learning framework for detecting and clustering seismic signals in continuous seismic records. Our approach combines a deep scattering network and a Gaussian mixture model to cluster seismic signal segments and detect novel structures. To illustrate the power of the framework, we analyze seismic data acquired during the June 2017 Nuugaatsiaq, Greenland landslide. We demonstrate the blind detection and recovery of the repeating precursory seismicity that was recorded before the main landslide rupture, which suggests that our approach could lead to more informative forecasting of the seismic activity in seismogenic areas.Show more Item A Comparison of High Order Interpolation Nodes for the Pyramid(Society for Industrial and Applied Mathematics, 2015) Chan, Jesse; Warburton, T.Show more The use of pyramid elements is crucial to the construction of efficient hex-dominant meshes [M. Bergot, G. Cohen, and M. Duruflé, J. Sci. Comput., 42 (2010), pp. 345--381]. For conforming nodal finite element methods with mixed element types, it is advantageous for nodal distributions on the faces of the pyramid to match those on the faces and edges of hexahedra and tetrahedra. We adapt existing procedures for constructing optimized tetrahedral nodal sets for high order interpolation to the pyramid with constrained face nodes, including two generalizations of the explicit warp and blend construction of nodes on the tetrahedron [T. Warburton, J. Engrg. Math., 56 (2006), pp. 247--262]. Comparisons between nodal sets show that the lowest Lebesgue constants are given by warp and blend nodes for order $N\leq 7$ and Fekete nodes for $N>7$, though numerical experiments show little variation in the conditioning and accuracy of all surveyed nonequidistant points.Show more Item Compositional heterogeneity near the base of the mantle transition zone beneath Hawaii(Springer Nature, 2018) Yu, Chunquan; Day, Elizabeth A.; de Hoop, Maarten V.; Campillo, Michel; Goes, Saskia; Blythe, Rachel A.; van der Hilst, Robert D.Show more Global seismic discontinuities near 410 and 660 km depth in Earth’s mantle are expressions of solid-state phase transitions. These transitions modulate thermal and material fluxes across the mantle and variations in their depth are often attributed to temperature anomalies. Here we use novel seismic array analysis of SSwaves reflecting off the 410 and 660 below the Hawaiian hotspot. We find amplitude–distance trends in reflectivity that imply lateral variations in wavespeed and density contrasts across 660 for which thermodynamic modeling precludes a thermal origin. No such variations are found along the 410. The inferred 660 contrasts can be explained by mantle composition varying from average (pyrolitic) mantle beneath Hawaii to a mixture with more melt-depleted harzburgite southeast of the hotspot. Such compositional segregation was predicted, from petrological and numerical convection studies, to occur near hot deep mantle upwellings like the one often invoked to cause volcanic activity on Hawaii.Show more Item Conditional Injective Flows for Bayesian Imaging(IEEE, 2023) Khorashadizadeh, AmirEhsan; Kothari, Konik; Salsi, Leonardo; Harandi, Ali Aghababaei; de Hoop, Maarten; Dokmanić, IvanShow more Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspire to make such point estimates misleading or insufficient. The Bayesian approach models images and (noisy) measurements as jointly distributed random vectors and aims to approximate the posterior distribution of unknowns. Recent variational inference methods based on conditional normalizing flows are a promising alternative to traditional MCMC methods, but they come with drawbacks: excessive memory and compute demands for moderate to high resolution images and underwhelming performance on hard nonlinear problems. In this work, we propose C-Trumpets—conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges. Injectivity reduces memory footprint and training time while low-dimensional latent space together with architectural innovations like fixed-volume-change layers and skip-connection revnet layers, C-Trumpets outperform regular conditional flow models on a variety of imaging and image restoration tasks, including limited-view CT and nonlinear inverse scattering, with a lower compute and memory budget. C-Trumpets enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantification.Show more Item Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems(Springer, 2019) Zhang, YinShow more A unified convergence theory is derived for a class of stationary iterative methods for solving linear equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all possible splittings of the submatrix residing in the (1,1)-block of the augmented saddle point matrix that would produce non-expansive iterations. The classic augmented Lagrangian method and alternating direction method of multipliers are two special members of this class.Show more Item Convergence of a high order method in time and space for the miscible displacement equations(EDP Sciences, 2015) Li, Jizhou; Riviere, Beatrice; Walkington, NoelShow more A numerical method is formulated and analyzed for solving the miscible displacement problem under low regularity assumptions. The scheme employs discontinuous Galerkin time stepping with mixed and interior penalty discontinuous Galerkin finite elements in space. The numerical approximations of the pressure, velocity, and concentration converge to the weak solution as the mesh size and time step tend to zero. To pass to the limit a compactness theorem is developed which generalizes the Aubin-Lions theorem to accommodate discontinuous functions both in space and in time.Show more Item Cytoplasmic sphingosine-1-phosphate pathway modulates neuronal autophagy(Springer Nature, 2015) Manchon, Jose Felix Moruno; Uzor, Ndidi-Ese; Dabaghian, Yuri; Furr-Stimming, Erin E.; Finkbeiner, Steven; Tsvetkov, Andrey S.Show more Autophagy is an important homeostatic mechanism that eliminates long-lived proteins, protein aggregates and damaged organelles. Its dysregulation is involved in many neurodegenerative disorders. Autophagy is therefore a promising target for blunting neurodegeneration. We searched for novel autophagic pathways in primary neurons and identified the cytosolic sphingosine-1-phosphate (S1P) pathway as a regulator of neuronal autophagy. S1P, a bioactive lipid generated by sphingosine kinase 1 (SK1) in the cytoplasm, is implicated in cell survival. We found that SK1 enhances flux through autophagy and that S1P-metabolizing enzymes decrease this flux. When autophagy is stimulated, SK1 relocalizes to endosomes/autophagosomes in neurons. Expression of a dominant-negative form of SK1 inhibits autophagosome synthesis. In a neuron model of Huntington's disease, pharmacologically inhibiting S1P-lyase protected neurons from mutant huntingtin-induced neurotoxicity. These results identify the S1P pathway as a novel regulator of neuronal autophagy and provide a new target for developing therapies for neurodegenerative disorders.Show more