Danny Barash

Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation

In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connection between adaptive smoothing and bilateral filtering. Previously, adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation.

A common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift

Abstract In this paper, a common framework is outlined for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift procedure. Previously, the relationship between bilateral filtering and the nonlinear diffusion equation was explored by using a consistent adaptive smoothing formulation. However, both nonlinear diffusion and adaptive smoothing were treated as local processes applying a 3×3 window at each iteration. Here, these two approaches are extended to an arbitrary window, showing their equivalence and stressing the importance of using large windows for edge-preserving smoothing. Subsequently, it follows that bilateral filtering is a particular choice of weights in the extended diffusion process that is obtained from geometrical considerations. We then show that kernel density estimation applied in the joint spatial–range domain yields a powerful processing paradigm—the mean shift procedure, related to bilateral filtering but having additional flexibility. This establishes an attractive relationship between the theory of statistics and that of diffusion and energy minimization. We experimentally compare the discussed methods and give insights on their performance.

Nucleosome DNA Bendability Matrix (C. elegans)

Abstract An original signal extraction procedure is applied to database of 146 base nucleosome core DNA sequences from C. elegans (S. M. Johnson et al. Genome Research 16, 1505–1516, 2006). The positional preferences of various dinucleotides within the 10.4 base nucleosome DNA repeat are calculated, resulting in derivation of the nucleosome DNA bendability matrix of 16x10 elements. A simplified one-line presentation of the matrix (“consensus” repeat) is…A(TTTCCGGAAA)T…. All 6 chromosomes of C. elegans conform to the bendability pattern. The strongest affinity to their respective positions is displayed by dinucleotides AT and CG, separated within the repeat by 5 bases. The derived pattern makes a basis for sequence-directed mapping of nucleosome positions in the genome of C. elegans. As the first complete matrix of bendability available the pattern may serve for iterative calculations of the species-specific matrices of bendability applicable to other genomic sequences.

Bilateral Filtering and Anisotropic Diffusion: Towards a Unified Viewpoint

Bilateral filtering has recently been proposed as a noniterative alternative to anisotropic diffusion. In both these approaches, images are smoothed while edges are preserved. Unlike anisotropic diffusion, bilateral filtering does not involve the solution of partial differential equations and can be implemented in a single iteration. Despite the difference in implementation, both methods are designed to prevent averaging across edges while smoothing an image. Their similarity suggests they can somehow be linked. Using a generalized representation for the intensity, we show that both can be related to adaptive smoothing. As a consequence, bilateral filtering can be applied to denoise and coherence-enhance degraded images with approaches similar to anisotropic diffusion.

Single-base resolution nucleosome mapping on DNA sequences.

Abstract Nucleosome DNA bendability pattern extracted from large nucleosome DNA database of C. elegans is used for construction of full length (116 dinucleotide positions) nucleosome DNA bendability matrix. The matrix can be used for sequence-directed mapping of the nucleosomes on the sequences. Several alternative positions for a given nucleosome are typically predicted, separated by multiples of nucleosome DNA period. The corresponding computer program is successfully tested on best known experimental examples of accurately positioned nucleosomes. The uncertainty of the computational mapping is ±1 base. The procedure is placed on publicly accessible server and can be applied to any DNA sequence of interest.

FineStr: a web server for single-base-resolution nucleosome positioning

SUMMARY The DNA in eukaryotic cells is packed into the chromatin that is composed of nucleosomes. Positioning of the nucleosome core particles on the sequence is a problem of great interest because of the role nucleosomes play in different cellular processes including gene regulation. Using the sequence structure of 10.4 base DNA repeat presented in our previous works and nucleosome core DNA sequences database, we have derived the complete nucleosome DNA bendability matrix of Caenorhabditis elegans. We have developed a web server named FineStr that allows users to upload genomic sequences in FASTA format and to perform a single-base-resolution nucleosome mapping on them. AVAILABILITY FineStr server is freely available for use on the web at http:/www.cs.bgu.ac.il/ approximately nucleom. The site contains a help file with explanation regarding the exact usage. CONTACT gabdank@cs.bgu.ac.il.

RNAmute: RNA secondary structure mutation analysis tool

BackgroundRNAMute is an interactive Java application that calculates the secondary structure of all single point mutations, given an RNA sequence, and organizes them into categories according to their similarity with respect to the wild type predicted structure. The secondary structure predictions are performed using the Vienna RNA package. Several alternatives are used for the categorization of single point mutations: Viennas RNAdistance based on dot-bracket representation, as well as tree edit distance and second eigenvalue of the Laplacian matrix based on Shapiros coarse grain tree graph representation.ResultsSelecting a category in each one of the processed tables lists all single point mutations belonging to that category. Selecting a mutation displays a graphical drawing of the single point mutation and the wild type, and includes basic information such as associated energies, representations and distances. RNAMute can be used successfully with very little previous experience and without choosing any parameter value alongside the initial RNA sequence. The package runs under LINUX operating system.ConclusionRNAMute is a user friendly tool that can be used to predict single point mutations leading to conformational rearrangements in the secondary structure of RNAs. In several cases of substantial interest, notably in virology, a point mutation may lead to a loss of important functionality such as the RNA virus replication and translation initiation because of a conformational rearrangement in the secondary structure.

Second eigenvalue of the Laplacian matrix for predicting RNA conformational switch by mutation

MOTIVATION Conformational switching in RNAs is thought to be of fundamental importance in several biological processes, including translational regulation, regulation of self-cleavage in viruses, protein biosynthesis and mRNA splicing. Current methods for detecting bi-stable RNAs that can lead to structural switching when triggered by an outside event rely on kinetics, energetics and properties of the combinatorial structure space of RNAs. Based on these properties, tools have been developed to predict whether a given sequence folds to a structure characterized by a bi-stable conformation, or to design multi-stable RNAs by an iterative algorithm. A useful addition is in developing a local procedure to prescribe, given an initial sequence, the least amount of mutations needed to drive the system into an optimal bi-stable conformation. RESULTS We introduce a local procedure for predicting mutations, by generating and analyzing eigenvalue tables, that are capable of transforming the wild-type sequence into a bi-stable conformation. The method is independent of the folding algorithms but relies on their success. It can be used in conjunction with existing tools, as well as being incorporated into more general RNA prediction packages. We apply this procedure on three well-studied structures. First, the method is validated on the mutation leading to a conformational switch in the spliced leader RNA from Leptomonas collosoma, a mutation that has already been confirmed by an experiment. Second, the method is used to predict a mutation that can lead to a novel conformational switch in the P5abc subdomain of the group I intron ribozyme in Tetrahymena thermophila. Third, the method is applied on Hepatitis delta virus to predict mutations that transform the wild-type into a bi-stable conformation, a configuration assessed by calculating the free energies using folding prediction algorithms. The predictions in the final examples need to be verified experimentally, whereas the mutation predicted in the first example complies with the experiment. This supports the use of our proposed method on other known structures, as well as genetically engineered ones. AVAILABILITY An eigenvalue application will be available in the near future attached to one of the existing tools.

Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.

RNAexinv: An extended inverse RNA folding from shape and physical attributes to sequences

BackgroundRNAexinv is an interactive java application that performs RNA sequence design, constrained to yield a specific RNA shape and physical attributes. It is an extended inverse RNA folding program with the rationale behind that the generated sequences should not only fold into a desired structure, but they should also exhibit favorable attributes such as thermodynamic stability and mutational robustness. RNAexinv considers not only the secondary structure in order to design sequences, but also the mutational robustness and the minimum free energy. The sequences that are generated may not fully conform with the given RNA secondary structure, but they will strictly conform with the RNA shape of the given secondary structure and thereby take into consideration the recommended values of thermodynamic stability and mutational robustness that are provided.ResultsThe output consists of designed sequences that are generated by the proposed method. Selecting a sequence displays the secondary structure drawings of the target and the predicted fold of the sequence, including some basic information about the desired and achieved thermodynamic stability and mutational robustness. RNAexinv can be used successfully without prior experience, simply specifying an initial RNA secondary structure in dot-bracket notation and numerical values for the desired neutrality and minimum free energy. The package runs under LINUX operating system. Secondary structure predictions are performed using the Vienna RNA package.ConclusionsRNAexinv is a user friendly tool that can be used for RNA sequence design. It is especially useful in cases where a functional stem-loop structure of a natural sequence should be strictly kept in the designed sequences but a distant motif in the rest of the structure may contain one more or less nucleotide at the expense of another, as long as the global shape is preserved. This allows the insertion of physical observables as constraints. RNAexinv is available at http://www.cs.bgu.ac.il/~RNAexinv.