Parallels plane projection and its geometric features

A new equivalent map projection called the parallels plane projection is proposed in this paper. The transverse axis of the parallels plane projection is the expansion of the equator and its vertical axis equals half the length of the central meridian. On the parallels plane projection, meridians are projected as sine curves and parallels are a series of straight, parallel lines. No distortion of length occurs along the central meridian or on any parallels of this projection. Angular distortion and the proportion of length along meridians (except the central meridian) introduced by the projection transformation increase with increasing longitude and latitude. A potential application of the parallels plane projection is that it can provide an efficient projection transformation for global discrete grid systems.

Local histogram based geometric invariant image watermarking

Compared with other existing methods, the feature point-based image watermarking schemes can resist to global geometric attacks and local geometric attacks, especially cropping and random bending attacks (RBAs), by binding watermark synchronization with salient image characteristics. However, the watermark detection rate remains low in the current feature point-based watermarking schemes. The main reason is that both of feature point extraction and watermark embedding are more or less related to the pixel position, which is seriously distorted by the interpolation error and the shift problem during geometric attacks. In view of these facts, this paper proposes a geometrically robust image watermarking scheme based on local histogram. Our scheme mainly consists of three components: (1) feature points extraction and local circular regions (LCRs) construction are conducted by using Harris-Laplace detector; (2) a mechanism of grapy theoretical clustering-based feature selection is used to choose a set of non-overlapped LCRs, then geometrically invariant LCRs are completely formed through dominant orientation normalization; and (3) the histogram and mean statistically independent of the pixel position are calculated over the selected LCRs and utilized to embed watermarks. Experimental results demonstrate that the proposed scheme can provide sufficient robustness against geometric attacks as well as common image processing operations. (C) 2010 Elsevier B.V. All rights reserved.

Geometric Distortion Insensitive Image Watermarking in Affine Covariant Regions

Feature-based image watermarking schemes, which aim to survive various geometric distortions, have attracted great attention in recent years. Existing schemes have shown robustness against rotation, scaling, and translation, but few are resistant to cropping, nonisotropic scaling, random bending attacks (RBAs), and affine transformations. Seo and Yoo present a geometrically invariant image watermarking based on affine covariant regions (ACRs) that provide a certain degree of robustness. To further enhance the robustness, we propose a new image watermarking scheme on the basis of Seo's work, which is insensitive to geometric distortions as well as common image processing operations. Our scheme is mainly composed of three components: 1) feature selection procedure based on graph theoretical clustering algorithm is applied to obtain a set of stable and nonoverlapped ACRs; 2) for each chosen ACR, local normalization, and orientation alignment are performed to generate a geometrically invariant region, which can obviously improve the robustness of the proposed watermarking scheme; and 3) in order to prevent the degradation in image quality caused by the normalization and inverse normalization, indirect inverse normalization is adopted to achieve a good compromise between the imperceptibility and robustness. Experiments are carried out on an image set of 100 images collected from Internet, and the preliminary results demonstrate that the developed method improves the performance over some representative image watermarking approaches in terms of robustness.

Local Feature Based Geometric-Resistant Image Information Hiding

Watermarking aims to hide particular information into some carrier but does not change the visual cognition of the carrier itself. Local features are good candidates to address the watermark synchronization error caused by geometric distortions and have attracted great attention for content-based image watermarking. This paper presents a novel feature point-based image watermarking scheme against geometric distortions. Scale invariant feature transform (SIFT) is first adopted to extract feature points and to generate a disk for each feature point that is invariant to translation and scaling. For each disk, orientation alignment is then performed to achieve rotation invariance. Finally, watermark is embedded in middle-frequency discrete Fourier transform (DFT) coefficients of each disk to improve the robustness against common image processing operations. Extensive experimental results and comparisons with some representative image watermarking methods confirm the excellent performance of the proposed method in robustness against various geometric distortions as well as common image processing operations.

Consensus scoring for enriching near-native structures from protein-protein docking decoys

The identification of near native protein-protein complexes among a set of decoys remains highly challenging. A stategy for improving the success rate of near native detection is to enrich near native docking decoys in a small number of top ranked decoys. Recently, we found that a combination of three scoring functions (energy, conservation, and interface propensity) can predict the location of binding interface regions with reasonable accuracy. Here, these three scoring functions are modified and combined into a consensus scoring function called ENDES for enriching near native docking decoys. We found that all individual scores result in enrichment for the majority of 28 targets in ZDOCK2.3 decoy set and the 22 targets in Benchmark 2.0. Among the three scores, the interface propensity score yields the highest enrichment in both sets of protein complexes. When these scores are combined into the ENDES consensus score, a significant increase in enrichment of near-native structures is found. For example, when 2000 dock decoys are reduced to 200 decoys by ENDES, the fraction of near-native structures in docking decoys increases by a factor of about six in average. ENDES was implemented into a computer program that is available for download at http://sparks.informatics.iupui.edu.

Refining near-native protein-protein docking decoys by local resampling and energy minimization

How to refine a near-native structure to make it closer to its native conformation is an unsolved problem in protein-structure and protein-protein complex-structure prediction. In this article, we first test several scoring functions for selecting locally resampled near-native protein-protein docking conformations and then propose a computationally efficient protocol for structure refinement via local resampling and energy minimization. The proposed method employs a statistical energy function based on a Distance-scaled Ideal-gas REference state (DFIRE) as an initial filter and an empirical energy function EMPIRE (EMpirical Protein-InteRaction Energy) for optimization and re-ranking. Significant improvement of final top-1 ranked structures over initial near-native structures is observed in the ZDOCK 2.3 decoy set for Benchmark 1.0 (74% whose global rmsd reduced by 0.5 angstrom or more and only 7% increased by 0.5 angstrom or more). Less significant improvement is observed for Benchmark 2.0 (38% versus 33%). Possible reasons are discussed.

Docking and molecular dynamics study on the inhibitory activity of coumarins on aldose reductase

In order to explore the inhibitory mechanism of coumarins toward aldose reductase (ALR2), AutoDock and Gromacs software were used for docking and molecular dynamics studies on 14 coumarins (CM) and ALR2 protease. The docking results indicate that residues TYR48, HIS110, and TRP111 construct the active pocket of ALR2 and, besides van der Waals and hydrophobic interaction, CM mainly interact with ALR2 by forming hydrogen bonds to cause inhibitory behavior. Except for CM1, all the other coumarins take the lactone part as acceptor to build up the hydrogen bond network with active-pocket residues. Unlike CM3, which has two comparable binding modes with ALR2, most coumarins only have one dominant orientation in their binding sites. The molecular dynamics calculation, based on the docking results, implies that the orientations of CM in the active pocket show different stabilities. Orientation of CM1 and CM3a take an unstable binding mode with ALR2; their conformations and RMSDs relative to ALR2 change a lot with the dynamic process. While the remaining CM are always hydrogen-bonded with residues TYR48 and HIS110 through the carbonyl O atom of the lactone group during the whole process, they retain the original binding mode and gradually reach dynamic equilibrium.

Docking and molecular dynamics studies toward the binding of new natural phenolic marine inhibitors and aldose reductase

Phenolic marine natural product is a kind of new potential aldose reductase inhibitors (ARIs). In order to investigate the binding mode and inhibition mechanism, molecular docking and dynamics studies were performed to explore the interactions of six phenolic inhibitors with human aldose reductase (hALR2). Considering physiological environment, all the neutral and other two ionized states of each phenolic inhibitor were adopted in the simulation. The calculations indicate that all the inhibitors are able to form stable hydrogen bonds with the hALR2 active pocket which is mainly constructed by residues TYR48, HIS110 and TRP111, and they impose the inhibition effect by occupying the active space. In all inhibitors, only La and its two ionized derivatives La_ion1 and La_ion2, in which neither of the ortho-hydrogens of 3-hydroxyl is substituted by Br, bind with hALR2 active residues using the terminal 3-hydroxyl. While, all the other inhibitors, at least one of whose ortho-sites of 3- and 6-hydroxyls are substituted by Br substituent which take much electron-withdrawing effect and steric hindrance, bind with hALR2 through the lactone group. This means that the Br substituent can effectively regulate the binding modes of phenolic inhibitors. Although the lactone bound inhibitors have relatively high RMSD values, our dynamics study shows that both binding modes are of high stability. For each inhibitor molecule, the ionization does not change its original binding mode, but it does gradually increase the binding free energy, which reveals that besides hydrogen bonds, the electrostatic effect is also important to the inhibitor–hALR2 interaction.

Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

A Modern Differential Geometric Approach to Shape from Shading

How the visual system extracts shape information from a single grey-level image can be approached by examining how the information about shape is contained in the image. This technical report considers the characteristic equations derived by Horn as a dynamical system. Certain image critical points generate dynamical system critical points. The stable and unstable manifolds of these critical points correspond to convex and concave solution surfaces, giving more general existence and uniqueness results. A new kind of highly parallel, robust shape from shading algorithm is suggested on neighborhoods of these critical points. The information at bounding contours in the image is also analyzed.

A Study of Qualitative and Geometric Knowledge in Reasoning about Motion

Reasoning about motion is an important part of our commonsense knowledge, involving fluent spatial reasoning. This work studies the qualitative and geometric knowledge required to reason in a world that consists of balls moving through space constrained by collisions with surfaces, including dissipative forces and multiple moving objects. An analog geometry representation serves the program as a diagram, allowing many spatial questions to be answered by numeric calculation. It also provides the foundation for the construction and use of place vocabulary, the symbolic descriptions of space required to do qualitative reasoning about motion in the domain. The actual motion of a ball is described as a network consisting of descriptions of qualitatively distinct types of motion. Implementing the elements of these networks in a constraint language allows the same elements to be used for both analysis and simulation of motion. A qualitative description of the actual motion is also used to check the consistency of assumptions about motion. A process of qualitative simulation is used to describe the kinds of motion possible from some state. The ambiguity inherent in such a description can be reduced by assumptions about physical properties of the ball or assumptions about its motion. Each assumption directly rules out some kinds of motion, but other knowledge is required to determine the indirect consequences of making these assumptions. Some of this knowledge is domain dependent and relies heavily on spatial descriptions.

Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.

Geometric Generalizations of the Power of Two Choices

A well-known paradigm for load balancing in distributed systems is the``power of two choices,''whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings for distributed computing where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is in fact the backdrop for distributed hash tables such as Chord, where the geometric space is determined by clockwise distance on a one-dimensional ring. Theoretically, we consider the following load balancing problem. Suppose that servers are initially hashed uniformly at random to points in the space. Sequentially, each item then considers d candidate insertion points also chosen uniformly at random from the space,and selects the insertion point whose associated server has the least load. For the one-dimensional ring, and for Euclidean distance on the two-dimensional torus, we demonstrate that when n data items are hashed to n servers,the maximum load at any server is log log n / log d + O(1) with high probability. While our results match the well-known bounds in the standard setting in which each server is selected equiprobably, our applications do not have this feature, since the sizes of the nearest-neighbor regions around servers are non-uniform. Therefore, the novelty in our methods lies in developing appropriate tail bounds on the distribution of nearest-neighbor region sizes and in adapting previous arguments to this more general setting. In addition, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.