Multihistogram Method Research Articles

Adaptive multi-histogram reversible data hiding with contrast enhancement

Unlike existing reversible data hiding with contrast enhancement (RDHCE) methods, which excessively improve the image contrast for achieving the required capacity, the proposed method improves the image contrast appropriately while providing satisfactory embedding capacity. To this end, an adaptive multi-histogram RDHCE method is proposed in this study to improve the local and global contrast by considering the local properties of the histograms. On the one hand, fuzzy C-means clustering combining multiple features that are deliberately designed for contrast enhancement is employed to generate seven sharply-distributed prediction error histograms (PEHs). Subsequently, the genetic algorithm is utilized to adaptively select the optimal pairs achieving the best embedding performance for each PEH according to the local characteristics of PEH distribution, resulting in improving the local contrast adaptively and embedding significant amount of data. Additionally, two-sided histogram shifting (HS) is utilized to improve the global contrast appropriately while embedding reasonable amount of data. The experimental results demonstrate that the proposed method achieves better local and global contrast while providing a high embedding capacity compared with other existing RDHCE methods.

Statistical mechanical analysis of sparse linear regression as a variable selection problem

An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive the result. The analysis is conducted through evaluation of the entropy, an exponential rate of the number of combinations of variables giving a specific value of fit error to given data which is assumed to be generated from a linear process using the design matrix. This yields the typical achievable limit of the fit error when solving a representative problem and includes the presence of unfavourable phase transitions preventing local search algorithms from reaching the minimum-error configuration. The associated phase diagrams are presented. A noteworthy outcome of the phase diagrams is that there exists a wide parameter region where any phase transition is absent from the high temperature to the lowest temperature at which the minimum-error configuration or the ground state is reached. This implies that certain local search algorithms can find the ground state with moderate computational costs in that region. Another noteworthy result is the presence of the random first-order transition in the strong noise case. The theoretical evaluation of the entropy is confirmed by extensive numerical methods using the exchange Monte Carlo and the multi-histogram methods. Another numerical test based on a metaheuristic optimisation algorithm called simulated annealing is conducted, which well supports the theoretical predictions on the local search algorithms. In the successful region with no phase transition, the computational cost of the simulated annealing to reach the ground state is estimated as the third order polynomial of the model dimensionality.

Optimal Temperature Set for Replica Exchange Sampling

Replica Exchange Monte Carlo method has been introduced to improve sampling of a rugged energy landscape for such systems as polymers, biopolymers and spin glasses. Efficiency of the method however critically depends on the set of replica temperatures used for simulations. A novel method selecting these parameters has been recently proposed1, which numerically evaluates the probability of replica swap between temperatures based on estimated density of states for a system under study. Here we extend this method and prove it provides the optimal set of temperatures i.e. temperatures that guarantee the fastest flow of replicas from the lowest to the highest temperature.During an initial phase of the protocol, energy distributions are collected at different temperatures. Based on these observations, the density of states for the system is computed by the multihistogram method. Knowing the density, improved temperature set is established by minimizing the mean first passage time of replicas in the temperature space. The procedure has been illustrated with a coarse-grained protein folding simulation and all-atom dynamics in AMBER force field. The method has been implemented in BioShell package.2,31 D. Gront and A. Kolinski “Efficient scheme for optimization of parallel tempering Monte Carlo method” Journal of Physics: Condensed Matter 2007 19(3) 036225 http://dx.doi.org/10.1088/0953-8984/19/3/0362252 D. Gront and A. Kolinski “BioShell - a package of tools for structural biology computations” Bioinformatics 2006 22(5):621-6223D. Gront and A. Kolinski “Utility library for structural bioinformatics” Bioinformatics 2008 24(4):584-585

Histogram Equalization: A Strong Technique for Image Enhancement

Generally for improving contrast in digital images, HE is the method that commonly used but in result it gives unnatural artifacts like intensity saturation, over-enhancement and noise amplification. To overcome these problems there was a need to partition the image histogram, at first image histogram was partitioned into two parts and then different transformation functions were applied on each partition. After that image histogram was partitioned into many partitions and same process was applied with some additional features. DHE is the multi histogram method and CLAHE is the extension of AHE. These methods are compared to HE and found that both methods give better result than HE but DHE method also gives better result than CLAHE.

A Counterexample Concerning to the Phase Space Multi-Histogram Method

The phase space multi-histogram method is a new technique to study phase transitions in hard particle systems. The method constrains the phase space using a Monte Carlo approach by smoothly varying a potential between the ideal gas and the hard particle limit. Using a small sphere system, we give an example of computing chemical potential at the liquid state. However, we find that the method fails for a dense sphere system at the coexisting liquid-solid state. We conclude that the method is appropriate for dilute hard particle systems, but it fails when the volume fraction of the system is too high.

Images Enhancement with Brightness Preserving using MRHRBFN

In the image processing, Images Enhancement with Brightness Preserving has many methods likes HE(Histogram Equalization), MHE(Multi-Histogram Equalization), IDBPHE(Image Dependent Brightness Preserving Histogram Equalization). We are proposed a novel methodology for the enhancement of images MRHRBFN (Multi-Resolution Histogram with Radial Bias Function Network). Enhancement process using pixel independent multi histogram method and Radial Bias Function Network. In process of our methodology image are decompose in terms of subbands. The sub band division perform by Curvelet transform. The Curvelet Transform divides two types of bands as higher band and lower band. The separation band of frequency generates a multiple matrix for input of radial bias Function Network. We have radial Bias function network work in low band data, because higher band data preserve brightness of image. The lower frequency matrix calculates bias and proceed weight factor when The lower value of frequency matrix regret reaches the mean value of given image. Finally we get better enhance image in comparison of multi histogram equalization.

Hexatic and Herringbone Orderings in 2D Liquid Crystals

We investigate the universality class of Bruinsma-Aeppli (BA) model in two dimensions. This model is consisting of two coupled XY order parameters, six-fold and two-fold symmetry, and is proposed to describe the Smc-A to Hex-B transition in some Smectic liquid crystal compounds. Using high resolution Monte Carlo simulation technique based on multi-histogram method and cluster algorithm, and also finite size scaling, we compute the critical exponents of this model with high accuracy. We find that for some ranges of coupling constants this model undergoes transition from disordered phase to a symmetry broken phase with both hexaitc and herringbone orderings.

Tricritical transition in the classicalXYmodel on the kagome lattice under local anisotropy

Using mean-field theory and high-resolution Monte Carlo simulation technique based on multihistogram method, we have investigated the critical properties of an antiferromagnetic $XY$ model on the two-dimensional (2D) kagome lattice, with single-ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first-order transition for small values of anisotropy, which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behavior of the system deviates from 2D ${\ensuremath{\phi}}^{6}$ model near the tricritical point. This suggests the possibility for existence of another tricritical universality in two dimensions.

Multi-Histogram Equalization Methods for Contrast Enhancement and Brightness Preserving

Histogram equalization (HE) has proved to be a simple and effective image contrast enhancement technique. However, it tends to change the mean brightness of the image to the middle level of the gray-level range, which is not desirable in the case of images from consumer electronics products. In the latter case, preserving the input brightness of the image is required to avoid the generation of non-existing artifacts in the output image. To surmount this drawback, Bi- HE methods for brightness preserving and contrast enhancement have been proposed. Although these methods preserve the input brightness on the output image with a significant contrast enhancement, they may produce images with do not look as natural as the input ones. In order to overcome this drawback, this work proposes a novel technique called Multi-HE, which consists of decomposing the input image into several sub-images, and then applying the classical HE process to each one. This methodology performs a less intensive image contrast enhancement, in a way that the output image presents a more natural look. We propose two discrepancy functions for image decomposing, conceiving two new Multi-HE methods. A cost function is also used for automatically deciding in how many sub-images the input image will be decomposed on. Experiments show that our methods preserve more the brightness and produce more natural looking images than the other HE methods.

Emergence of hexatic and threefold hidden order in two-dimensional smectic liquid crystals: A Monte Carlo study

Using a high resolution Monte Carlo simulation technique based on a multihistogram method and cluster algorithm, we have investigated the critical properties of a coupled XY model, consisting of a sixfold symmetric hexatic and a hidden order parameter of threefold symmetry in two dimensions. The simulation results demonstrate a series of continuous transitions in which both kinds of orderings are established simultaneously. It is found that the specific-heat anomaly exponents for some regions in coupling constants space are in excellent agreement with the experimentally measured exponents extracted from heat-capacity data near the smectic- A -hexatic- B transition of two-layer free standing films.

Monte Carlo simulation of a strongly coupledXYmodel in three dimensions

Many experimental studies, over the past two decades, have constantly reported a critical behavior for the transition from the smectic- A phase of liquid crystals to the hexatic- B phase with non- XY critical exponents. However, according to symmetry arguments this transition must belong to the XY universality class. Using an optimized Monte Carlo simulation technique based on the multihistogram method, we have investigated the phase diagram of a coupled XY model, proposed by Bruinsma and Aeppli [Phys. Rev. Lett. 48, 1625 (1982)], in three dimensions. The simulation results demonstrate the existence of a tricritical point for this model, in which two different orderings are established simultaneously. This result verifies the accepted idea that the large specific heat anomaly exponent observed for the SmA-HexB transition could be due to the occurrence of this transition in the vicinity of a tricritical point.

Phase behavior of Ising mixtures

We present phase diagrams that were calculated both in mean-field theory and via Monte Carlo (MC) simulations for binary mixtures of a ferromagnetic Ising fluid and a nonmagnetic fluid (Ising mixtures) in the absence of an external field. We look at both the simple ideal Ising mixture, consisting of an ideal Ising fluid and a hard-sphere fluid, as well as at the general case with one component being a nonideal Ising fluid and the other a van der Waals fluid. It is shown that the mean-field phase diagram of the ideal Ising mixture in the limit of infinite pressure is identical to that of the Blume-Capel model for 3He-4He mixtures. The MC phase diagrams were obtained using the Gibbs ensemble, the cumulant intersection technique, and the multi-histogram re-weighting method, adapted to the semi-grand ensemble. The results are qualitatively compared with mean-field theory, and both types of tri-critical lines occurring there are verified in the computer simulations.

A Minimal Physically Realistic Protein-Like Lattice Model: Designing an Energy Landscape that Ensures All-Or-None Folding to a Unique Native State

A simple protein model restricted to the face-centered cubic lattice has been studied. The model interaction scheme includes attractive interactions between hydrophobic (H) residues, repulsive interactions between hydrophobic and polar (P) residues, and orientation-dependent P-P interactions. Additionally, there is a potential that favors extended β-type conformations. A sequence has been designed that adopts a native structure, consisting of an antiparallel, six-member Greek-key β-barrel with protein-like structural degeneracy. It has been shown that the proposed model is a minimal one, i.e., all the above listed types of interactions are necessary for cooperative (all-or-none) type folding to the native state. Simulations were performed via the Replica Exchange Monte Carlo method and the numerical data analyzed via a multihistogram method.

Toward minimalist models of larger proteins: A ubiquitin-like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed α/β content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/Tf ∼ 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces. Proteins 2002;46:368–379. © 2002 Wiley-Liss, Inc.

Toward minimalist models of larger proteins: A ubiquitin‐like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed alpha/beta content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/T(f) approximately 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces.

Study of phase changes of the water octamer using parallel tempering and multihistogram methods

Parallel tempering Monte Carlo and multihistogram methods are combined to study the phase changes of the water octamer. The heat capacity is calculated continuously from very low temperatures up to T=230 K. We find the melting temperature to be 178.5 K. In addition, a solid–solid phase change is found at 12 K. We introduce an order parameter to monitor this low temperature phase change.

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.

Computation of the vortex free energy in SU(2) gauge theory

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.

Miscellaneous results on the electroweak phase transition

We present new 4- D Monte Carlo results characterizing the strength of the finite temperature phase transition for Higgs/W mass ratios 1.0 and 0.6, obtained on isotropic lattices mainly with N, = 16, Nt = 2. We discuss the distribution of an gauge invariant block spin order parameter, estimating the Higgs condensate ¢c at To. We use the Potvin/Rebbi method in order to find the interface tension a/7~. We demonstrate how the multi-histogram method (giving free energy differences) can be used to avoid the limiting procedure 6~ --* 0. From pure-phase histograms at ~, extrapolated with the help of this method, we estimate the latent heat Ac/7~. Actual time series at lower Higgs mass require blocking in order to determine the jump of the lattice observables.

A Monte Carlo Simulation of the Stillinger-Weber Model for Si-Ge Alloys

ABSTRACTThe bulk phase behavior of silicon-germanium alloys is investigated by means of a constant pressure Monte Carlo simulation of the Stillinger-Weber potential in the semi-grand-canonical ensemble. At low temperatures, Si and Ge phase separate into a Si-rich phase and a Ge-rich phase. The two-phase region is terminated by a critical point whose nature is investigated thoroughly by the multihistogram method combined with finite size scaling analysis. These results showed that the critical behavior of the alloy belongs to the mean field universality class, presumably due to the elastic degrees of freedom. We have also studied the structural properties of the mixture and found that the linear thermal expansions of both Si and Ge agree well with experiments. We also verified Végard's law above the critical point and calculated bond length distributions.