Geometric Clustering Research Articles

Combination of geometric clustering and nonlocal means for SAR image despeckling

Recently, nonlocal filtering methods for synthetic aperture radar (SAR) despeckling have attracted a lot of attention. In general, a suitable similarity measure well suited to SAR images is derived by incorporating the noise statistics. One important nonlocal framework is the probabilistic patch-based (PPB) filter, which derives the similarity measure in a data-driven way and provides promising results. A drawback of this filter is the suppression of thin and dark details since the PPB method takes into account the photometrically similar patches, yet it ignores the geometric structure of image patches. To overcome these disadvantages, a new patch-based despeckling method is presented which exploits both geometrical and photometrical similarities. Numerical experiments suggest that the proposed method is on a par with or exceeds the state-of-the-art PPB method, both visually and quantitatively.

Multilevel mesh simplification

The goal of a multilevel simplification method is to produce different levels of refinement of a mesh, reducing the resolution (total number of faces), while preserving the original topology and a good approximation to the original geometry. A new approach to simplification based on the evolution of surfaces under p-Laplacian flow is presented. Such an evolution provides a natural geometric clustering process where the spatial effect of the p-Laplacian allows for identifying suitable regions that need to be simplified. The concrete scheme is a multiresolution framework composed, at each simplification level, of a spatial clustering diffusion flow to determine the potential candidates for deletion, followed by an incremental decimation process to update the mesh vertex locations in order to decrease the overall resolution. Numerical results show the effectiveness of our strategy in multilevel simplification of different models with different complexities, in particular for models characterized by sharp features and flat parts.

Learning Kinetic Distance Metrics for Markov State Models of Protein Conformational Dynamics.

Statistical modeling of long timescale dynamics with Markov state models (MSMs) has been shown to be an effective strategy for building quantitative and qualitative insight into protein folding processes. Existing methodologies, however, rely on geometric clustering using distance metrics such as root mean square deviation (RMSD), assuming that geometric similarity provides an adequate basis for the kinetic partitioning of phase space. Here, inspired by advances in the machine learning community, we introduce a new approach for learning a distance metric explicitly constructed to model kinetic similarity. This approach enables the construction of models, especially in the regime of high anisotropy in the diffusion constant, with fewer states than was previously possible. Application of this technique to the analysis of two ultralong molecular dynamics simulations of the FiP35 WW domain identifies discrete near-native relaxation dynamics in the millisecond regime that were not resolved in previous analyses.

Monte Carlo tests of nucleation concepts in the lattice gas model

The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier ΔF(*), constructed in terms of a balance of surface and bulk term of a critical droplet of radius R(*), implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius R=R(*). For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ℓ(*) where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate ΔF(*) also for nonspherical cluster shapes.

Exotic cluster structure in light nuclei

We discuss the appearance of various cluster structures in light nuclei. One of the examples is the appearance of geometric cluster configurations; gas-like α cluster states found in 12C and 16O could be stabilized with geometric shapes by adding neutrons or giving large angular momentum. We show in 16O that four α particles can have linear configurations with large angular momentum, which is very stable with respect to the bending motion using Skyrme cranked Hartree-Fock method. There exists a region of angular momentum (13-18 ℏ) where the linear chain configuration is stabilized. The calculated moment of inertia (ℏ2/2(-_ ~ 0.06-0.08 MeV) agrees well with conventional cluster model calculations. Another example of exotic cluster structure is the gas-like state of α clusters. The most famous example is the second 0+ state in 12C, the so called Hoyle state, which plays a dominant role in the synthesis of 12C and the heavier elements in the stars. We go one step further that such a dilute state of α particles exists around a strongly bound core in heavier systems. This study is performed by introducing a Monte Carlo technique for the description of the THSR (Tohsaki Horiuchi Schuck Röpke) wave function, and first we apply such method to three α state around a 40Ca core. Furthermore, coupling effect to other low-lying cluster states is taken into account; a large isoscalar monopole (E0) transition strength from the ground to the gas-like state is discussed in 24Mg. The gas-like state of two α clusters in 24Mg around the 16O core appears slightly below the 2α-thresliold energy.

On the similarity of equilibrium and critical clusters in atomic vapors

In a previous paper [I. Napari, J. Julin, and H. Vehkamäki, J. Chem. Phys. 131, 244511 (2009)] we compared sizes of critical and equilibrium clusters in Lennard-Jones vapors using various geometrical clusters definitions. In particular, we found that the critical and equilibrium clusters were of the same size if each constituent atom in the cluster was required to have at least five neighboring atoms (ten Wolde-Frenkel cluster) but the critical clusters were much larger if only one neighboring atom was sufficient to fulfill the cluster definition (Stillinger cluster). The conclusion was that the critical clusters at high vapor densities have more ramified structure than the corresponding equilibrium clusters. In this study we have performed new molecular dynamics simulations to enlighten this matter. It is found that the surprising conclusion of the earlier work can be traced to the mean first passage time method which was used to obtain critical cluster sizes from simulations. When a certain sized Stillinger cluster first appears in the simulation, the cluster tends to have a more ramified structure than Stillinger clusters of that size observed later in the simulation. However, for the latter clusters the ratio of Stillinger and ten Wolde-Frenkel sizes in the vapor is the same as in the equilibrium simulations, implying similar structure of critical and equilibrium clusters.

Building Markov state models with solvent dynamics

BackgroundMarkov state models have been widely used to study conformational changes of biological macromolecules. These models are built from short timescale simulations and then propagated to extract long timescale dynamics. However, the solvent information in molecular simulations are often ignored in current methods, because of the large number of solvent molecules in a system and the indistinguishability of solvent molecules upon their exchange.MethodsWe present a solvent signature that compactly summarizes the solvent distribution in the high-dimensional data, and then define a distance metric between different configurations using this signature. We next incorporate the solvent information into the construction of Markov state models and present a fast geometric clustering algorithm which combines both the solute-based and solvent-based distances.ResultsWe have tested our method on several different molecular dynamical systems, including alanine dipeptide, carbon nanotube, and benzene rings. With the new solvent-based signatures, we are able to identify different solvent distributions near the solute. Furthermore, when the solute has a concave shape, we can also capture the water number inside the solute structure. Finally we have compared the performances of different Markov state models. The experiment results show that our approach improves the existing methods both in the computational running time and the metastability.ConclusionsIn this paper we have initiated an study to build Markov state models for molecular dynamical systems with solvent degrees of freedom. The methods we described should also be broadly applicable to a wide range of biomolecular simulation analyses.

Scalable Symmetry Detection for Urban Scenes

AbstractIn this paper, we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which has only been demonstrated on data sets of a few hundred megabytes maximum, our method scales to very large scenes: We map the detection problem to a nearest‐neighbour problem in a low‐dimensional feature space, and follow this with a cascade of tests for geometric clustering of potential matches. Our algorithm robustly handles noisy real‐world scanner data, obtaining a recognition performance comparable to that of state‐of‐the‐art methods. In practice, it scales linearly with scene size and achieves a high absolute throughput, processing half a terabyte of scanner data overnight on a dual socket commodity PC.

Classifying bases for 6D F-theory models

Abstract We classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors (“clusters”) that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f4, e6, e8, e8, (g2 ⊕ su(2)); and su(2) ⊕ so(7) ⊕ su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.

Hydrogen bonding of ethanol in supercritical mixtures with CO2 by 1H NMR spectroscopy and molecular simulation

Abstract High pressure 1 H NMR spectroscopic studies of mixtures of CO 2 and ethanol (EtOH) were conducted at a wide range of temperatures (293.15, 308.15, 323.15, and 338.15 K), pressures (5–25.5 MPa) and concentrations ( x EtOH = 0.0017–1.0 mol/mol). The relative chemical shift of the protons in the hydroxyl group was used to describe the degree of hydrogen bonding in ethanol. The dependence of the results on pressure is only weak. The quantification of hydrogen bonding was based on the assumption that the observed shift results from a superposition of the shifts of ethanol molecules differing in the way they are hydrogen bonded. Three different types were distinguished: monomer, donor and acceptor. The monomer shift was found from an extrapolation of the NMR data. Molecular dynamics simulations based on force fields from the literature were carried out for the same mixtures at the same conditions and were used to determine the distribution of differently hydrogen bonded ethanol species. Geometric cluster criteria from the literature were used for identifying the hydrogen bonding and the different types of ethanol species. Using the species distribution from the molecular simulations together with the NMR spectroscopic data, the two state independent numbers for the shifts of the hydrogen bond donor and hydrogen bond acceptor molecules were found. Even though only these two parameters are fitted the large set of experimental data is very well described. This confirms our earlier observations on the CO 2 –methanol system that molecular models of the simple Lennard–Jones plus point charge type as they are used here can describe both thermodynamic properties and the structural effects of hydrogen bonding in solutions.

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.

Percolation in a kinetic opinion exchange model

We study the percolation transition of the geometrical clusters in the square-lattice LCCC model [a kinetic opinion exchange model introduced by Lallouache, Chakrabarti, Chakraborti, and Chakrabarti, Phys. Rev. E 82, 056112 (2010)] with the change in conviction and influencing parameter. The cluster is comprised of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion (Ω). The transition point is different from that obtained for the transition of the order parameter (average opinion value) found by Lallouache et al. Although the transition point varies with the change in the threshold value of the opinion, the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size, the cluster size distribution, and the Binder cumulant remain the same. The exponents are also independent of the values of conviction and influencing parameters, indicating the robustness of this transition. The exponents do not match any other known percolation exponents (e.g., the static Ising, dynamic Ising, and standard percolation). This means that the LCCC model belongs to a separate universality class.

Critical behavior of the geometrical spin clusters and interfaces in the two-dimensionalthermalized bond Ising model

The fractal dimensions and the percolation exponents of geometrical spin clusters of likesign at criticality are obtained numerically for an Ising model with temperaturedependent annealed bond dilution, also known as the thermalized bond Ising model(TBIM), in two dimensions. For this purpose, a modified Wolff single-clusterMonte Carlo simulation is used to generate equilibrium spin configurations onsquare lattices in the critical region. A tie-breaking rule is employed to identifynonintersecting spin cluster boundaries along the edges of the dual lattice. Thevalues obtained for the fractal dimensions of the spanning geometrical clustersDc, and theirinterfaces DI, are in perfect agreement with those reported for the standard two-dimensional ferromagneticIsing model. Furthermore, the variance of the winding angles results in a diffusivityκ = 3 for the two-dimensional thermalized bond Ising model, thus placing it in the universalityclass of the regular Ising model. A finite-size scaling analysis of the largest geometricalclusters results in a reliable estimation of the critical percolation exponents forthe geometrical clusters in the limit of an infinite lattice size. The percolationexponents thus obtained are also found to be consistent with those reported for theregular Ising model. These consistencies are explained in terms of the Fisherrenormalization relations, which express the thermodynamic critical exponentsof systems with annealed bond dilution in terms of those of the regular modelsystem.

A new geometric shape-based genetic clustering algorithm for the multi-depot vehicle routing problem

In this paper, a new type of geometric shape based genetic clustering algorithm is proposed. A genetic algorithm based on this clustering technique is developed for the solution process of the multi-depot vehicle routing problem. A set of problems obtained from the literature is used to compare the efficiency of the proposed algorithm with the nearest neighbor algorithm so as to solve the multi-depot vehicle routing problem. The experimental results show that the proposed algorithm provides a better clustering performance in terms of the distance of each customer to each depot in clusters. This result in a considerably less computation time required, when compared with the nearest neighbor algorithm.

Dynamical percolation transition in the Ising model studied using a pulsed magnetic field

We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.

Atomic-scale lateral heterogeneity and dynamics of two-component lipid bilayers composed of saturated and unsaturated phosphatidylcholines

Studies of lateral heterogeneity in cell membranes are important since they help to understand the physical origin of lipid domains and rafts. The simplest membrane mimics are hydrated bilayers composed of saturated and unsaturated lipids. While their atomic structural details resist easy experimental characterization, important insight can be gained via computer modeling. We present the results of all-atom molecular dynamics simulations for a series of fluid dioleoylphosphatidylcholine (DOPC) and dipalmitoylphosphatidylcholine (DPPC) bilayers. Lateral arrangement of lipids in these systems is not random and reveals small geometrical and hydrophobic clusters on the surface. Being “sharp” inside the bilayer, lateral heterogeneity is very “fuzzy” on the surface. This picture is highly dynamic – lifetimes of clusters are ∼1 ns. In the binary system, DPPC acts as an “order-preferring” agent, which efficiently modulates behavior of DOPC. Bilayer properties are tuned in a wide range by the chemical nature and relative content of lipids. The impact that the micro-heterogeneity may have on formation of lateral domains in response to external signals is discussed. Understanding of such effects creates a basis for rational design of artificial membranes with predefined properties.

Feature-Space-Based fMRI Analysis Using the Optimal Linear Transformation

The optimal linear transformation (OLT), an image analysis technique of feature space, was first presented in the field of MRI. This paper proposes a method of extending OLT from MRI to functional MRI (fMRI) to improve the activation-detection performance over conventional approaches of fMRI analysis. In this method, first, ideal hemodynamic response time series for different stimuli were generated by convolving the theoretical hemodynamic response model with the stimulus timing. Second, constructing hypothetical signature vectors for different activity patterns of interest by virtue of the ideal hemodynamic responses, OLT was used to extract features of fMRI data. The resultant feature space had particular geometric clustering properties. It was then classified into different groups, each pertaining to an activity pattern of interest; the applied signature vector for each group was obtained by averaging. Third, using the applied signature vectors, OLT was applied again to generate fMRI composite images with high SNRs for the desired activity patterns. Simulations and a blocked fMRI experiment were employed for the method to be verified and compared with the general linear model (GLM)-based analysis. The simulation studies and the experimental results indicated the superiority of the proposed method over the GLM-based analysis in detecting brain activities.

Codificación geométrica y análisis de conglomerados para evaluar el control metabólico de pacientes con diabetes mellitus tipo 2

Determine the frequency of combinations of higher-than-normal metabolic control parameters, using geometric coding and hierarchical cluster analysis, in patients with type 2 diabetes (DM2) A descriptive cross-sectional study was conducted in Mexico to assess a group of 1 051 patients with DM2. The inclusion criteria were to have one or more of the following values: fasting glucose of 130 mg/dL, total cholesterol of 240 mg/dL, total triglycerides of 200 mg/dL, Body Mass Index of 27 kg/m(2), and systolic blood pressure higher than 130 mmHg or diastolic blood pressure higher than 85 mmHg. Through geometric coding, the frequencies of all combinations were obtained. Cluster analysis was used to determine similarities among the combinations. Using the proposed instrument, it was observed that the paired combinations with the highest number of subjects were hyperglycemia-hypertriglyceridemia (7.3%) and hyperglycemia-hypercholesterolemia (3.6%). The most frequent polycombinations were hyperglycemia-hypercholesterolemia-hypertriglyceridemia (13.2%) and hyperglycemia-hypertriglyceridemia-hypercholesterolemia-hypertension (10.5%). Geometric coding and cluster analysis could become a suitable instrument for assessing the metabolic control of patients with DM2, as well as for identifying parameters that will help improve their monitoring and treatment.

Comparing geometric and kinetic cluster algorithms for molecular simulation data

The identification of metastable states of a molecule plays an important role in the interpretation of molecular simulation data because the free-energy surface, the relative populations in this landscape, and ultimately also the dynamics of the molecule under study can be described in terms of these states. We compare the results of three different geometric cluster algorithms (neighbor algorithm, K-medoids algorithm, and common-nearest-neighbor algorithm) among each other and to the results of a kinetic cluster algorithm. First, we demonstrate the characteristics of each of the geometric cluster algorithms using five two-dimensional data sets. Second, we analyze the molecular dynamics data of a beta-heptapeptide in methanol--a molecule that exhibits a distinct folded state, a structurally diverse unfolded state, and a fast folding/unfolding equilibrium--using both geometric and kinetic cluster algorithms. We find that geometric clustering strongly depends on the algorithm used and that the density based common-nearest-neighbor algorithm is the most robust of the three geometric cluster algorithms with respect to variations in the input parameters and the distance metric. When comparing the geometric cluster results to the metastable states of the beta-heptapeptide as identified by kinetic clustering, we find that in most cases the folded state is identified correctly but the overlap of geometric clusters with further metastable states is often at best approximate.

Physics-based virtual reality for task learning and intelligent disassembly planning

Physics-based simulation is increasingly important in virtual manufacturing for product assembly and disassembly operations. This work explores potential benefits of physics-based modeling for automatic learning of assembly tasks and for intelligent disassembly planning in desktop virtual reality. The paper shows how realistic physical animation of manipulation tasks can be exploited for learning sequential constraints from user demonstrations. In particular, a method is proposed where information about physical interaction is used to discover task precedences and to reason about task similarities. A second contribution of the paper is the application of physics-based modeling to the problem of disassembly sequence planning. A novel approach is described to find all physically admissible subassemblies in which a set of rigid objects can be disassembled. Moreover, efficient strategies are presented aimed at reducing the computational time required for automatic disassembly planning. The proposed strategies take into account precedence relations arising from user assembly demonstrations as well as geometrical clustering. A motion planning technique has also been developed to generate non-destructive disassembly paths in a query-based approach. Experiments have been performed in an interactive virtual environment including a dataglove and motion tracker that allows realistic object manipulation and grasping.