Multiple points on the boundaries of Brownian loop-soup clusters

In the eigenvalue problem for a perturbed two-dimensional oscillator, we suggest a method for constructing asymptotic solutions near the boundaries of spectral clusters by means of a new integral representation and study the issue of calculating the average values of differential operators on the solutions near the boundaries of the clusters.

SLEs as boundaries of clusters of Brownian loops

The splashback radius was proposed as a physically motivated boundary of clusters as it sets the limit between the infalling and the orbitally dominated regions. However, galaxy clusters are complex objects connected to filaments of the cosmic web from which they accrete matter that disturbs them and modifies their morphology. In this context, estimating the splashback radius and the cluster boundary becomes challenging. In this work, we use a constrained hydrodynamical simulation replicating the Virgo cluster embedded in its large-scale structure to investigate the impact of its local environment on the splashback radius estimate. We identify the splashback radius from 3D radial profiles of dark matter density, gas density, and pressure in three regions representative of different dynamical states: accretion from spherical collapse, filaments, and matter outflow. We also identify the splashback radius from 2D-projected radial profiles of observation-like quantities: mass surface density, emission measure, and Compton-y. We show that the splashback radius mainly depends on the dynamics in each region and the physical processes traced by the different probes. We find multiple values for the splashback radius ranging from 3.3 ± 0.2 to 5.5 ± 0.3 Mpc. In particular, in the regions of collapsing and outflowing materials, the splashback radii estimated from gas density and pressure radial profiles overestimate that of the dark matter density profiles, which is considered the reference value given that the splashback radius was originally defined from dark matter simulations in pioneering works. Consequently, caution is required when using the splashback radius as a boundary of clusters, particularly in the case of highly disturbed clusters like Virgo. We conclude with a discussion of the detection of the splashback radius from pressure radial profiles, which could be more related to an accretion shock, and its detection from stacked radial profiles.

Rutherford back-scattering measurements of antimony diffusion in nanocrystalline copper

Manifestations of point and extensive defects of bulk-metallic glasses

We have identified block structure in the Pacific Northwest (west of 116°W between 38°N and 49°N) by clustering GPS stations so that the same Euler vector approximates the velocity of each station in a cluster. Given the total number k of clusters desired, the clustering procedure finds the best assignment of stations to clusters. Clustering is calculated for k = 2–14. In geographic space, cluster boundaries that remain relatively stable as k is increased are tentatively identified as block boundaries. That identification is reinforced if the cluster boundary coincides with a geologic feature. Boundaries identified in Northern California and Nevada are the Central Nevada Seismic Belt, the west side of the Northern Walker Lane Belt, and the Bartlett Springs Fault. Three blocks cover all of Oregon and Washington. The principal block boundary there extends west‐northwest along the Brothers Fault Zone, then north and northwest along the eastern boundary of Siletzia, the accreted oceanic basement of the forearc. East of this boundary is the Intermountain block; its eastern boundary undefined. A cluster boundary at Cape Blanco subdivides the forearc along the faulted southern margin of Siletzia. South of Cape Blanco, the Klamath Mountains‐Basin and Range block, extends east to the Central Nevada Seismic Belt and south to the Sierra Nevada‐Great Valley block. The Siletzia block, north of Cape Blanco, coincides almost exactly with the accreted Siletz terrane. The cluster boundary in the eastern Olympic Peninsula may mark permanent shortening of Siletzia against the Intermountain block.

Knowledge-assisted recognition of cluster boundaries in gene expression data

We investigate the second-order Zeeman effect in a magnetic field using irreducible representations of an algebra with the Karasev - Novikova quadratic commutation relations. To each such representation there corresponds a spectral cluster near the energy level of the unperturbed hydrogen atom. Using this model as an example, we describe a general method for constructing asymptotic solutions near the boundaries of spectral clusters based on a new integral representation. We also study the problem of computing quantum averages near the lower boundaries of clusters.

Imposing structure on a Corsi-type task: Evidence for hierarchical organisation based on spatial proximity in serial-spatial memory

Unsupervised machine learning methods were applied on multivariate geophysical and geochemical datasets of ocean floor sediment cores collected from the South China Sea. The well-preserved and continuous core samples comprising high resolution Cenozoic sediment records enable scientists to carry out paleoenvironment studies in detail. Bayesian age-depth chronological models constructed from biostratigraphic control points for the drilling sites are applied on cluster boundaries generated from two popular unsupervised learning methods: K-means and random forest. The unsupervised learning methods experimented have produced compact and unambiguous clusters from the datasets, indicating that previously unknown data patterns can be revealed when all variables from the datasets are taken into account simultaneously. A study of synchroneity of past events represented by the cluster boundaries across geographically separated ocean drilling sites is achieved through converting the fixed depths of cluster boundaries into chronological ranges represented by Gaussian density plots which are then compared with known past events in the region. A Gaussian density peak at around 7.2 Ma has been identified from results of all three sites and it is suggested to coincide with the initiation of the East Asian monsoon. Contrary to traditional statistical approach, a priori assumptions are not required for unsupervised learning, and the clustering results serve as a novel data-driven proxy for studying the complex and dynamic processes of the paleoenvironment surrounding the ocean sediment. This work serves as a pioneering approach to extract valuable information of regional events and opens up a systematic and objective way to study the vast global ocean sediment datasets.

Interpretability and usability of clustering results are of fundamental importance. A linear time method for transforming point clusters into polygons is explored. This method automatically translates a point data layer into a space filling layer where clusters are identified as some of the resulting regions. The method is based on robustly identifying cluster boundaries in point data. The cluster polygonization process analyses the distribution of intra-cluster edges and the distribution of inter-cluster edges in Delaunay Triangulations. It approximates shapes of clusters and suggests polygons of clusters. The method can then be applied to display choropleth maps of point data without a reference map or to identify associations in the spatial dimension for geographical data mining. Keywords: clustering, Delaunay triangulation, geographical data mining, cluster boundaries, cluster polygonization

By introducing the methods of machine learning into the density functional theory, we made a detour for the construction of the most probable density function, which can be estimated by learning relevant features from the system of interest. Using the properties of universal functional, the vital core of density functional theory, the most probable cluster numbers and the corresponding cluster boundaries in a studying system can be simultaneously and automatically determined and the plausibility is erected on the Hohenberg-Kohn theorems. For the method validation and pragmatic applications, interdisciplinary problems from physical to biological systems were enumerated. The amalgamation of uncharged atomic clusters validated the unsupervised searching process of the cluster numbers and the corresponding cluster boundaries were exhibited likewise. High accurate clustering results of the Fisher’s iris dataset showed the feasibility and the flexibility of the proposed scheme. Brain tumor detections from low-dimensional magnetic resonance imaging datasets and segmentations of high-dimensional neural network imageries in the Brainbow system were also used to inspect the method practicality. The experimental results exhibit the successful connection between the physical theory and the machine learning methods and will benefit the clinical diagnoses.

To plan for the habitat needs of forest songbirds of conservation concern, managers need to understand how spatial heterogeneity in forest conditions influences habitat quality. I used difference boundary detection (wombling) and spatially constrained clustering to delineate boundaries in various combinations of four forest vegetation variables (understory height, understory density, percent deciduous vs. conifer understory, and percent canopy closure) in two Michigan northern hardwood forests. My goal was to identify vegetation boundaries that corresponded with boundaries in an understory-dependent songbird’s distribution, and with boundaries in demographic measures for this songbird that indicate habitat quality (e.g., occupancy by older vs. yearling males, reproductive success). Both forests were actively-managed, mature stands: The first site (78 ha) was heavily deer-browsed (HB), with many browse-resistant conifers in the understory, and the second (62 ha) was less-browsed (LB), with deciduous-dominated understory. I compared the vegetation difference and cluster boundaries to difference boundaries based on 6 years of distribution and demographic data for black-throated blue warblers (Dendroica caerulescens). At the HB site, warbler boundaries overlapped strongly with vegetation boundaries that included all four variables, and clustering effectively divided the habitat into areas with different warbler occupancy and demographic characteristics. At the LB site, warbler distribution showed high overlap with difference and cluster boundaries based on just the height and density of understory vegetation, and cluster boundaries again effectively partitioned the study area into sites that varied in habitat quality. Thus, geographic boundary analysis is likely to be a useful tool for identifying key vegetation variables for management, and for delineating clusters (habitat patches) within sites that capture differences in habitat quality.

Hartree-Fock perturbed-cluster treatment of defects in crystals V. The overlap correction in relaxation studies

With the wide application of categorical-attribute dataset,the demand of obtaining the cluster boundary of categorical-attribute dataset becomes more and more urgent.In order to get cluster boundaries,a categorical-attribute data boundary detection algorithm: CBORDER(Categorical dataset BORDER detection algorithm) was proposed.In this algorithm,firstly,this paper initialized the center of cluster by using random allocation and utilizing boundary-degree to partition clusters;at the same time,the evidence of captured boundary records was got.Then,based on the evidence accumulation,the above procedure was executed repeatedly to acquire the boundaries of clusters at the end.The experimental results demonstrate that CBORDER can effectively detect the boundaries of the high-dimensional categorical data.