High-resolution cryo-electron microscopy structure of the Trypanosoma brucei ribosome.

Ribosomes, the protein factories of living cells, translate genetic information carried by messenger RNAs into proteins, and are thus involved in virtually all aspects of cellular development and maintenance. The few available structures of the eukaryotic ribosome reveal that it is more complex than its prokaryotic counterpart, owing mainly to the presence of eukaryote-specific ribosomal proteins and additional ribosomal RNA insertions, called expansion segments. The structures also differ among species, partly in the size and arrangement of these expansion segments. Such differences are extreme in kinetoplastids, unicellular eukaryotic parasites often infectious to humans. Here we present a high-resolution cryo-electron microscopy structure of the ribosome of Trypanosoma brucei, the parasite that is transmitted by the tsetse fly and that causes African sleeping sickness. The atomic model reveals the unique features of this ribosome, characterized mainly by the presence of unusually large expansion segments and ribosomal-protein extensions leading to the formation of four additional inter-subunit bridges. We also find additional rRNA insertions, including one large rRNA domain that is not found in other eukaryotes. Furthermore, the structure reveals the five cleavage sites of the kinetoplastid large ribosomal subunit (LSU) rRNA chain, which is known to be cleaved uniquely into six pieces, and suggests that the cleavage is important for the maintenance of the T. brucei ribosome in the observed structure. We discuss several possible implications of the large rRNA expansion segments for the translation-regulation process. The structure could serve as a basis for future experiments aimed at understanding the functional importance of these kinetoplastid-specific ribosomal features in protein-translation regulation, an essential step towards finding effective and safe kinetoplastid-specific drugs.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n-sided polygon, the quadratic serendipity elements have 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n(n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L2-optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

SHAPE BASED IMAGE RECONSTRUCTION USING LINEARIZED DEFORMATIONS.

We introduce a reconstruction framework that can account for shape related a priori information in ill-posed linear inverse problems in imaging. It is a variational scheme that uses a shape functional defined using deformable templates machinery from shape theory. As proof of concept, we apply the proposed shape based reconstruction to 2D tomography with very sparse measurements, and demonstrate strong empirical results.

PF2fit: Polar Fast Fourier Matched Alignment of Atomistic Structures with 3D Electron Microscopy Maps.

There continue to be increasing occurrences of both atomistic structure models in the PDB (possibly reconstructed from X-ray diffraction or NMR data), and 3D reconstructed cryo-electron microscopy (3D EM) maps (albeit at coarser resolution) of the same or homologous molecule or molecular assembly, deposited in the EMDB. To obtain the best possible structural model of the molecule at the best achievable resolution, and without any missing gaps, one typically aligns (match and fits) the atomistic structure model with the 3D EM map. We discuss a new algorithm and generalized framework, named PF(2) fit (Polar Fast Fourier Fitting) for the best possible structural alignment of atomistic structures with 3D EM. While PF(2) fit enables only a rigid, six dimensional (6D) alignment method, it augments prior work on 6D X-ray structure and 3D EM alignment in multiple ways: Scoring. PF(2) fit includes a new scoring scheme that, in addition to rewarding overlaps between the volumes occupied by the atomistic structure and 3D EM map, rewards overlaps between the volumes complementary to them. We quantitatively demonstrate how this new complementary scoring scheme improves upon existing approaches. PF(2) fit also includes two scoring functions, the non-uniform exterior penalty and the skeleton-secondary structure score, and implements the scattering potential score as an alternative to traditional Gaussian blurring. Search. PF(2) fit utilizes a fast polar Fourier search scheme, whose main advantage is the ability to search over uniformly and adaptively sampled subsets of the space of rigid-body motions. PF(2) fit also implements a new reranking search and scoring methodology that considerably improves alignment metrics in results obtained from the initial search.

On the construction of general cubature formula by flat extensions.

We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyze the algebraic properties associated to flat extensions and show how to recover the cubature points and weights from the truncated Hankel operator. We next present an algorithm to test the flat extension property and to additionally compute the decomposition. To generate cubature formulae with a minimal number of points, we propose a new relaxation hierarchy of convex optimization problems minimizing the nuclear norm of the Hankel operators. For a suitably high order of convex relaxation, the minimizer of the optimization problem corresponds to a cubature formula. Furthermore cubature formulae with a minimal number of points are associated to faces of the convex sets. We illustrate our method on some examples, and for each we obtain a new minimal cubature formula.

Recipes for when physics fails: recovering robust learning of physics informed neural networks.

Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers' equations.

Detection of secondary and supersecondary structures of proteins from cryo-electron microscopy.

Recent advances in three-dimensional electron microscopy (3D EM) have enabled the quantitative visualization of the structural building blocks of proteins at improved resolutions. We provide algorithms to detect the secondary structures (α-helices and ß-sheets) from proteins for which the volumetric maps are reconstructed at 6-10Å resolution. Additionally, we show that when the resolution is coarser than 10Å, some of the supersecondary structures can be detected from 3D EM maps. For both these algorithms, we employ tools from computational geometry and differential topology, specifically the computation of stable/unstable manifolds of certain critical points of the distance function induced by the molecular surface. Our results connect mathematically well-defined constructions with bio-chemically induced structures observed in proteins.

A dynamic data structure for flexible molecular maintenance and informatics.

MOTIVATION: We present the 'Dynamic Packing Grid' (DPG), a neighborhood data structure for maintaining and manipulating flexible molecules and assemblies, for efficient computation of binding affinities in drug design or in molecular dynamics calculations. RESULTS: DPG can efficiently maintain the molecular surface using only linear space and supports quasi-constant time insertion, deletion and movement (i.e. updates) of atoms or groups of atoms. DPG also supports constant time neighborhood queries from arbitrary points. Our results for maintenance of molecular surface and polarization energy computations using DPG exhibit marked improvement in time and space requirements. AVAILABILITY: http://www.cs.utexas.edu/~bajaj/cvc/software/DPG.shtml.

Exploring the Study of miR-1301 Inhibiting the Proliferation and Migration of Squamous Cell Carcinoma YD-38 Cells through PI3K/AKT Pathway under Deep Learning Medical Images.

With the rapid development and application of deep learning medical image recognition, natural language processing, and other fields, at the same time, deep learning has become the most popular research direction in the field of image processing and recognition. Through deep learning medical image recognition technology, it is of great significance to explore the research of miR-1301. The purpose of this article is to use an improved CNN neural network model algorithm combined to contrast the experimental groups and use deep learning medical imaging technology to study the mechanism by which miR-1301 inhibits the proliferation of carcinoma YD-38 cells through the PI3K/AKT pathway. This paper studies the method of image recognition of squamous cell carcinoma YD-38 cells using a convolutional neural network (CNN). First, a CNN classification model for the characteristics of YD-38 cell images is constructed. Then, pretraining and dropout technology are used to improve and optimize the proposed CNN model to improve the robustness of the model. In this paper, the miR mimic group and the miR blank group and the PI3K/AKT pathway inhibitor Wortmannin were selected to jointly treat YD-38 cells. The expression of mRNA in miR-1301 in HGF-1 was determined using RT-PCR (real and real-time fluorescence and YD-38 cells). The blank plasmids and the miR-1301 mimic (miR-1301 mimic) were transfected into YD-38 cells. The experiments were divided into two groups in the miR-1301 blank group and the miR-1301 simulation groups, respectively. The proliferation capacity of YD-38 cells was prepared in 1.5 ml sterile EP tubes and then diluted with medium for the proliferation of the cells. The scratch test and Transwell test were used to detect the effect of miR-1-3p on the migration and invasion of liver cancer cells. In this paper, CCK-8 experiment, clone formation experiment, flow cytometry, scratch experiment, and Transwell chamber experiment are used to analyze the effects of target gene CAAP1 on the proliferation, apoptosis, migration, and invasion of liver cancer cells. This paper uses CCK-8 to detect five kinds of the effect of miRNA on the proliferation ability of liver cancer cells and the effect of miR-1-3p on the proliferation ability of liver cancer cells. Experimental studies have shown that, compared with the miR blank group, the expression of PI3K and p-AKT was significantly downregulated in the miR mimic group after 24, 48, and 72 hours and the phosphorylation level of AKT was also significantly reduced (P < 0.05).

Single-particle reconstruction using L(2)-gradient flow.

In this paper, we present an iterative algorithm for reconstructing a three-dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L(2)-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Our method compares favorably with those of the weighted back projection, Fourier method, algebraic reconstruction technique and simultaneous iterative reconstruction technique.

Regularization of B-Spline Objects.

By a d-dimensional B-spline object (denoted as ), we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object we mean the process of relocating the control points of such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for , d = 1, 2, 3 based on solving weak form L(2)-gradient flows constructed from the minimization of certain regularizing energy functionals. These flows are integrated via the finite element method using B-spline basis functions. Our experimental results demonstrate that our new regularization method is very effective.

Computational Inversion of Electron Tomography Images Using L2-Gradient Flows.

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electric tomographic images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L2-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

Materials for emergent silicon-integrated optical computing.

Progress in computing architectures is approaching a paradigm shift: traditional computing based on digital complementary metal-oxide semiconductor technology is nearing physical limits in terms of miniaturization, speed, and, especially, power consumption. Consequently, alternative approaches are under investigation. One of the most promising is based on a "brain-like" or neuromorphic computation scheme. Another approach is quantum computing using photons. Both of these approaches can be realized using silicon photonics, and at the heart of both technologies is an efficient, ultra-low power broad band optical modulator. As silicon modulators suffer from relatively high power consumption, materials other than silicon itself have to be considered for the modulator. In this Perspective, we present our view on such materials. We focus on oxides showing a strong linear electro-optic effect that can also be integrated with Si, thus capitalizing on new materials to enable the devices and circuit architectures that exploit shifting computational machine learning paradigms, while leveraging current manufacturing infrastructure. This is expected to result in a new generation of computers that consume less power and possess a larger bandwidth.

An Automatic 3D Mesh Generation Method for Domains with Multiple Materials.

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.

Weighted Random Forests to Improve Arrhythmia Classification.

Construction of an ensemble model is a process of combining many diverse base predictive learners. It arises questions of how to weight each model and how to tune the parameters of the weighting process. The most straightforward approach is simply to average the base models. However, numerous studies have shown that a weighted ensemble can provide superior prediction results to a simple average of models. The main goals of this article are to propose a new weighting algorithm applicable for each tree in the Random Forest model and the comprehensive examination of the optimal parameter tuning. Importantly, the approach is motivated by its flexibility, good performance, stability, and resistance to overfitting. The proposed scheme is examined and evaluated on the Physionet/Computing in Cardiology Challenge 2015 data set. It consists of signals (electrocardiograms and pulsatory waveforms) from intensive care patients which triggered an alarm for five cardiac arrhythmia types (Asystole, Bradycardia, Tachycardia, Ventricular Tachycardia, and Ventricular Fultter/Fibrillation). The classification problem regards whether the alarm should or should not have been generated. It was proved that the proposed weighting approach improved classification accuracy for the three most challenging out of the five investigated arrhythmias comparing to the standard Random Forest model.

VoroCrust: Voronoi Meshing Without Clipping.

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrary curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably correct algorithm for conforming Voronoi meshing for non-convex and possibly non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while all sharp features are preserved in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.

A Fast Variational Method for the Construction of Resolution Adaptive C-Smooth Molecular Surfaces.

We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic-acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C(2) interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C(2) smooth and resolution adaptive molecular surfaces.

A Streaming model for Generalized Rayleigh with extension to Minimum Noise Fraction.

The Rayleigh quotient optimization is the maximization of a rational function, or a max-min problem, with simultaneous maximization of the numerator function and minimization of the denominator function. Here, we describe a low-rank, streaming solution for Rayleigh quotient optimization applicable for big-data scenarios where the data matrix is too large to be fully loaded into main memory. We apply this for a maximization of the Signal to Noise ratio of big-data, of very large static and dynamic data. Our implementation is shown to achieve faster processing time compared to a standard data read into memory. We demonstrate the trade-offs with synthetic and real data, on different scales to validate the approach in terms of accuracy, speed and storage.

SketchyCoreSVD: SketchySVD from Random Subsampling of the Data Matrix.

We present a method called SketchyCoreSVD to compute the near-optimal rank r SVD of a data matrix by building random sketches only from its subsampled columns and rows. We provide theoretical guarantees under incoherence assumptions, and validate the performance of our SketchyCoreSVD method on various large static and time-varying datasets.

Tensor Maps for Synchronizing Heterogeneous Shape Collections.

Establishing high-quality correspondence maps between geometric shapes has been shown to be the fundamental problem in managing geometric shape collections. Prior work has focused on computing efficient maps between pairs of shapes, and has shown a quantifiable benefit of joint map synchronization, where a collection of shapes are used to improve (denoise) the pairwise maps for consistency and correctness. However, these existing map synchronization techniques place very strong assumptions on the input shapes collection such as all the input shapes fall into the same category and/or the majority of the input pairwise maps are correct. In this paper, we present a multiple map synchronization approach that takes a heterogeneous shape collection as input and simultaneously outputs consistent dense pairwise shape maps. We achieve our goal by using a novel tensor-based representation for map synchronization, which is efficient and robust than all prior matrix-based representations. We demonstrate the usefulness of this approach across a wide range of geometric shape datasets and the applications in shape clustering and shape co-segmentation.