Symmetry-based Algorithm Research Articles

Using Symmetry to Enhance the Performance of Agent-Based Epidemic Models.

Symmetries express the invariance of a system towards sets of mathematical transformations. In more practical terms, symmetries greatly reduce or simplify the computational efforts required to evaluate relevant properties of a system. In this paper, two methods are proposed to implement spin symmetries which simplify the analysis of the spreading of diseases in an agent-based epidemic model. We perform a set of simulations to measure the efficiency gains compared to traditional methods. Our findings show symmetry-based algorithms improve the performance of the Monte Carlo simulation and the exact Markov process.

Symmetry-Based Algorithms for Invertible Mappings of Polynomially Nonlinear PDE to Linear PDE

This paper is a sequel to our previous work where we introduced the MapDE algorithm to determine the existence of analytic invertible mappings of an input (source) differential polynomial system (DPS) to a specific target DPS, and sometimes by heuristic integration an explicit form of the mapping. A particular feature was to exploit the Lie symmetry invariance algebra of the source without integrating its equations, to facilitate MapDE, making algorithmic an approach initiated by Bluman and Kumei. In applications, however, the explicit form of a target DPS is not available, and a more important question is, can the source be mapped to a more tractable class? We extend MapDE to determine if a source nonlinear DPS can be mapped to a linear differential system. MapDE applies differential-elimination completion algorithms to the various over-determined DPS by applying a finite number of differentiations and eliminations to complete them to a form for which an existence-uniqueness theorem is available, enabling the existence of the linearization to be determined among other applications. The methods combine aspects of the Bluman–Kumei mapping approach with techniques introduced by Lyakhov, Gerdt and Michels for the determination of exact linearizations of ODE. The Bluman–Kumei approach for PDE focuses on the fact that such linearizable systems must admit a usually infinite Lie sub-pseudogroup corresponding to the linear superposition of solutions in the target. In contrast, Lyakhov et al. focus on ODE and properties of the so-called derived sub-algebra of the (finite) dimensional Lie algebra of symmetries of the ODE. Examples are given to illustrate the approach, and a heuristic integration method sometimes gives explicit forms of the maps. We also illustrate the powerful maximal symmetry groups facility as a natural tool to be used in conjunction with MapDE.

Spherical indexing of overlap EBSD patterns for orientation-related phases – Application to titanium

We propose a new electron backscatter diffraction (EBSD) indexing approach that can handle overlapping patterns arising from fine-scale mixtures of two crystallographically distinct but related phases. The approach relies on a combination of spherical indexing (SI) with an overlap master pattern (OMP) in which the two phases have the proper orientation relation. We illustrate the approach using a Ti-10-2-3 sample and compare results from traditional Hough-based indexing of the α and β-phases with SI maps. We show that the SI approach produces superior orientation maps, and we present a symmetry-based algorithm for the determination of the α-phase variant when experimental patterns are indexed with respect to the OMP. We illustrate the use of the OMP to determine the parent β-phase volume fraction and obtain excellent agreement with Thermo-Calc phase fraction predictions.

基于对称性投影的大视场小目标三维定位算法

基于对称性投影的大视场小目标三维定位算法

Symmetry-Independent Stability Analysis of Synchronization Patterns

The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks. However, to make further progress we must overcome the limitations of this celebrated formalism, which focuses on global synchronization and requires both the oscillators and their interaction functions to be identical, while many systems of interest are inherently heterogeneous and exhibit complex synchronization patterns. Here, we establish a generalization of the MSF formalism that can characterize the stability of any cluster synchronization pattern, even when the oscillators and/or their interaction functions are nonidentical. The new framework is based on finding the finest simultaneous block diagonalization of matrices in the variational equation and does not rely on information about network symmetry. This leads to an algorithm that is error-tolerant and orders of magnitude faster than existing symmetry-based algorithms. As an application, we rigorously characterize the stability of chimera states in networks with multiple types of interactions.

Brain Midline Shift Measurement and Its Automation: A Review of Techniques and Algorithms.

Midline shift (MLS) of the brain is an important feature that can be measured using various imaging modalities including X-ray, ultrasound, computed tomography, and magnetic resonance imaging. Shift of midline intracranial structures helps diagnosing intracranial lesions, especially traumatic brain injury, stroke, brain tumor, and abscess. Being a sign of increased intracranial pressure, MLS is also an indicator of reduced brain perfusion caused by an intracranial mass or mass effect. We review studies that used the MLS to predict outcomes of patients with intracranial mass. In some studies, the MLS was also correlated to clinical features. Automated MLS measurement algorithms have significant potentials for assisting human experts in evaluating brain images. In symmetry-based algorithms, the deformed midline is detected and its distance from the ideal midline taken as the MLS. In landmark-based ones, MLS was measured following identification of specific anatomical landmarks. To validate these algorithms, measurements using these algorithms were compared to MLS measurements made by human experts. In addition to measuring the MLS on a given imaging study, there were newer applications of MLS that included comparing multiple MLS measurement before and after treatment and developing additional features to indicate mass effect. Suggestions for future research are provided.

ParSymG: a parallel clustering approach for unsupervised classification of remotely sensed imagery

ABSTRACTSymmetry is a common feature in the real world. It may be used to improve a classification by using the point symmetry-based distance as a measure of clustering. However, it is time consuming to calculate the point symmetry-based distance. Although an efficient parallel point symmetry-based K-means algorithm (ParSym) has been propsed to overcome this limitation, ParSym may get stuck in sub-optimal solutions due to the K-means technique it used. In this study, we proposed a novel parallel point symmetry-based genetic clustering (ParSymG) algorithm for unsupervised classification. The genetic algorithm was introduced to overcome the sub-optimization problem caused by inappropriate selection of initial centroids in ParSym. A message passing interface (MPI) was used to implement the distributed master–slave paradigm. To make the algorithm more time-efficient, a three-phase speedup strategy was adopted for population initialization, image partition, and kd-tree structure-based nearest neighbor searching. The advantages of ParSymG over existing ParSym and parallel K-means (PKM) alogithms were demonstrated through case studies using three different types of remotely sensed images. Results in speedup and time gain proved the excellent scalability of the ParSymG algorithm.

Generation of isomers for icosahedral clusters A12−xBx (x = 0–12) from a symmetry-based algorithm

All isomers of (quasi-)icosahedral, binary A12−xBx clusters were constructed based on a simple symmetry-based algorithm. This algorithm can also be applied to other starting geometries, but it is advantageous to restrict to high starting symmetries and high degeneracies of atom sites. Also, the (relative) degeneracies of the isomers are calculated. Chiral isomers are identified, showing that chirality in binary, (quasi-)icosahedral clusters may play an important role in A8B4, A7B5, A6B6, A5B7, and A4B8. Chirality is of importance in nonlinear optics and asymmetric catalysis. The results provided may stimulate further research in these areas using binary metal clusters.

Rough Based Symmetrical Clustering for Gene Expression Profile Analysis.

Identification of coexpressed genes is the central goal in microarray gene expression data analysis. Point symmetry-based clustering is an important unsupervised learning technique for recognizing symmetrical convex or non-convex shaped clusters. To enable fast automatic clustering of large microarray data, in this article, a distributed time-efficient scalable parallel rough set based hybrid approach for point symmetry-based clustering algorithm has been proposed. A natural basis for analyzing gene expression data using the symmetry-based algorithm, is to group together genes with similar symmetrical patterns of expression. Rough-set theory helps in faster convergence and initial automatic optimal classification, thereby solving the problem of unknown knowledge of number of clusters in microarray data. This new parallel implementation with K-means algorithm also satisfies the linear speedup in timing on large microarray datasets. This proposed algorithm is compared with another parallel symmetry-based K-means and parallel version of existing K-means over four artificial and benchmark microarray datasets. We also have experimented over three skewed cancer gene expression datasets. The statistical analysis are also performed to establish the significance of this new implementation. The biological relevance of the clustering solutions are also analyzed.

GPR evaluation of the Damaoshan highway tunnel: A case study

Ground-penetrating radar (GPR) is widely used in the field of civil engineering; it can locate anomalies and record detailed information on the possible presence of damage within a tunnel. However, because of the complexity of tunnel structures and a long data interpretation period, the analysis and interpretation of field data is a relatively difficult and time-consuming task. In this paper, a case study of the Damaoshan Tunnel located in Fujian province, China is executed to perform a condition assessment combining GPR and finite-difference time-domain (FDTD) techniques based on prior information regarding the designed tunnel structure. This combination is used to assist and improve the interpretation of field data. The aims of this survey are to locate the rebar, estimate the thickness of the second lining, and determine the presence and distribution of any damage for an annual inspection. Additionally, a symmetry-based algorithm and a hyperbola match method are combined to achieve these goals and determine the wave velocity inversion. The interpreted results, based on both measured and simulated data, reveal that the combination of FDTD and GPR techniques is a quick and efficient survey methodology for tunnel evaluation. The survey shows that the rebar number is 367 (which is less than the standard 492), the average qualified rate of lining thickness is 79.87% of the design parameters, and there are 81 damages spanning the entire tunnel.

Stereoselective Cycloaddition of 1,3-Cyclohexadiene on Si(100): A Simple Algorithm for Product Identification Based on Secondary Orbital Interactions

We consider the reaction of 1,3-cyclohexadiene (1,3-CHD) on Si(100) and show that the observed reactivity and stereoselectivity cannot be explained on the basis of thermodynamics. We postulate the existence of secondary orbital interactions (SOIs) and introduce a simple algorithm that examines all possible secondary interactions between the frontier orbitals of the molecule and the surface. We demonstrate using an orbital symmetry-based algorithm supported by DFT calculations that SOIs favor a particular molecular configuration, consistent with the experimental observations. The potential role of SOIs in controlling surface chemical reactions is discussed.

Aircraft type recognition in satellite images

This paper proposes a hierarchical classification algorithm to accurately recognise aircrafts in satellite images. Since each aircraft in satellite images is captured far from the ground, it has a very small size and often includes various textures, orientations, dazzle paints, and even noise. All of these will present many challenges in extracting useful features and result in unstableness and inaccuracy of aircraft type recognition. Therefore, before recognition, a novel symmetry-based algorithm is proposed to estimate an aircraft's optimal orientation for rotation correction. In addition, several image preprocessing techniques such as noise removal, binarisation, and geometrical adjustments are also applied to removing the above variations. Then, distinguishable features are derived from each aircraft for aircraft recognition. However, different features have different discrimination abilities to recognise the types of aircrafts. Therefore, a novel booting algorithm is proposed to learn a set of proper weights from training samples for feature integration. Owing to this integration, significant improvements in terms of recognition accuracy and robustness can be achieved. Last, a hierarchical recognition scheme is proposed to recognise the types of aircrafts by using the area feature first for a rough categorisation on which detailed classifications are then achieved using several suggested features. Experiments were conducted on a wide variety of satellite images. Experimental results reveal the feasibility and validity of the proposed approach in recognising aircrafts in satellite images.

Determination of Stereoisomers of Heteronuclear Clusters by a Symmetry-Based Algorithm

A general methodology for the determination of all possible stereoisomers of heteronuclear clusters is reported. The paper is divided into three parts: (1) nomenclature—wherein a systematic numbering system for multi-component clusters under which each and every stereoisomer of a given cluster can be uniquely identified is presented; (2) methodology—wherein the general principles for the determination of symmetry analogs are discussed; and (3) computer algorithm—wherein the implementation of the symmetry principles is described. These principles and algorithms are applied to binary (two-component) systems using octahedral and icosahedral clusters as examples.

Symmetry-based algorithms to relate partial differential equations: I. Local symmetries

Simple and systematic algorithms for relating differential equations are given. They are based on comparing the local symmetries admitted by the equations. Comparisons of the infinitesimal generators and their Lie algebras of given and target equations lead to necessary conditions for the existence of mappings which relate them. Necessary and sufficient conditions are presented for the existence of invertible mappings from a given nonlinear system of partial differential equations to some linear system of equations with examples including the hodograph and Legendre transformations, and the linearizations of a nonlinear telegraph equation, a nonlinear diffusion equation, and nonlinear fluid flow equations. Necessary and sufficient conditions are also given for the existence of an invertible point transformation which maps a linear partial differential equation with variable coefficients to a linear equation with constant coefficients. Other types of mappings are also considered including the Miura transformation and the invertible mapping which relates the cylindrical KdV and the KdV equations.

Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are realized as appropriate local symmetries of a related auxiliary system. Examples include the Hopf-Cole transformation and the linearizations of a nonlinear heat conduction equation, a nonlinear telegraph equation, and the Thomas equations.