Performance Analysis of Spectral Clustering on Compressed, Incomplete and Inaccurate Measurements

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals respectively. We combine the distance preserving measurements of compressed sensing and matrix completion with the power of robust spectral clustering. Our analysis provides rigorous bounds on how small errors in the affinity matrix can affect the spectral coordinates and clusterability. This work generalizes the current perturbation results of two-class spectral clustering to incorporate multi-class clustering with k eigenvectors. We thoroughly track how small perturbation from using compressed sensing and matrix completion affect the affinity matrix and in succession the spectral coordinates. These perturbation results for multi-class clustering require an eigengap between the kth and (k+1)th eigenvalues of the affinity matrix, which naturally occurs in data with k well-defined clusters. Our theoretical guarantees are complemented with numerical results along with a number of examples of the unsupervised organization and clustering of image data

Organism-sediment interactions govern post-hypoxia recovery of ecosystem functioning

Hypoxia represents one of the major causes of biodiversity and ecosystem functioning loss for coastal waters. Since eutrophication-induced hypoxic events are becoming increasingly frequent and intense, understanding the response of ecosystems to hypoxia is of primary importance to understand and predict the stability of ecosystem functioning. Such ecological stability may greatly depend on the recovery patterns of communities and the return time of the system properties associated to these patterns. Here, we have examined how the reassembly of a benthic community contributed to the recovery of ecosystem functioning following experimentally-induced hypoxia in a tidal flat. We demonstrate that organism-sediment interactions that depend on organism size and relate to mobility traits and sediment reworking capacities are generally more important than recovering species richness to set the return time of the measured sediment processes and properties. Specifically, increasing macrofauna bioturbation potential during community reassembly significantly contributed to the recovery of sediment processes and properties such as denitrification, bedload sediment transport, primary production and deep pore water ammonium concentration. Such bioturbation potential was due to the replacement of the small-sized organisms that recolonised at early stages by large-sized bioturbating organisms, which had a disproportionately stronger influence on sediment. This study suggests that the complete recovery of organism-sediment interactions is a necessary condition for ecosystem functioning recovery, and that such process requires long periods after disturbance due to the slow growth of juveniles into adult stages involved in these interactions. Consequently, repeated episodes of disturbance at intervals smaller than the time needed for the system to fully recover organism-sediment interactions may greatly impair the resilience of ecosystem functioning.

Design and Analysis of SMA-Based Tendon for Marine Structures

A tension-leg platform (TLP), as an offshore structure, is a vertically moored floating structure, connecting to tendon groups, fixed to subsea by foundations, to eliminate its vertical movements. TLPs are subjected to various non-deterministic loadings, including winds, currents, and ground motions, keeping the tendons under ongoing cyclic tensions. The powerful loads can affect the characteristics of tendons and cause permanent deformation. As a result of exceeding the strain beyond the elastic phase of the tendons, it makes unbalancing on the floated TLPs. Shape memory alloy (SMA)-based tendons due to their superelasticity properties may potentially resolve such problem in TLP structures. In the present work, performance and functionality of SMA wire, as the main component of SMA-based tendon under cyclic loading, have been experimentally investigated. It shows a significant enhancement in recovering large deformation and reduces the amount of permanent deformation

The Tongue as an Excitable Medium

Geographic tongue (GT) is a benign condition affecting approximately 2% of the population, whereby the papillae covering the upper part of the tongue are lost due to a slowly expanding inflammation. The resultant dynamical appearance of the tongue has striking similarities with well known phenomena observed in excitable media, such as forest fires, cardiac dynamics and chemically-driven reaction-diffusion systems. Here we explore the dynamics associated with GT from a dynamical systems perspective, utilizing cellular automata simulations. We emphasize similarities with other excitable systems as well as unique features observed in GT. Our results shed light on the evolution of the inflammation and contribute to the classification of the severity of the condition, based on the characteristic patterns observed in GT patients

The inverse solution of the atomic mixing equations by an operator-splitting method

The quantification problem of recovering the original material distribution from secondary ion mass spectrometry (SIMS) data is considered in this paper. It is an inverse problem, is ill-posed and hence it requires a special technique for its solution. The quantification problem is essentially an inverse diffusion or (classically) a backward heat conduction problem. In this paper an operator-splitting method (that is proposed in a previous paper by the first author for the solution of inverse diffusion problems) is developed for the solution of the problem of recovering the original structure from the SIMS data. A detailed development of the quantification method is given and it is applied to typical data to demonstrate its effectiveness

Recovering 3D structural properties of galaxies from SDSS-like photometry

Because of the 3D nature of galaxies, an algorithm for constructing spatial density distribution models of galaxies on the basis of galaxy images has many advantages over surface density distribution approximations. We present a method for deriving spatial structure and overall parameters of galaxies from images and estimate its accuracy and derived parameter degeneracies on a sample of idealised model galaxies. The test galaxies consist of a disc-like component and a spheroidal component with varying proportions and properties. Both components are assumed to be axially symmetric and coplanar. We simulate these test galaxies as if observed in the SDSS project through ugriz filters, thus gaining a set of realistically imperfect images of galaxies with known intrinsic properties. These artificial SDSS galaxies were thereafter remodelled by approximating the surface brightness distribution with a 2D projection of a bulge+disc spatial distribution model and the restored parameters were compared to the initial ones. Down to the r-band limiting magnitude 18, errors of the restored integral luminosities and colour indices remain within 0.05 mag and errors of the luminosities of individual components within 0.2 mag. Accuracy of the restored bulge-to-disc ratios (B/D) is within 40% in most cases, and becomes worse for galaxies with low B/D, but the general balance between bulges and discs is not shifted systematically. Assuming that the intrinsic disc axial ratio is < 0.3, the inclination angles can be estimated with errors < 5deg for most of the galaxies with B/D < 2 and with errors < 15deg up to B/D = 6. Errors of the recovered sizes of the galactic components are below 10% in most cases. In general, models of disc components are more accurate than models of spheroidal components for geometrical reasons.Comment: 15 pages, 13 figures, accepted for publication in RA

Family of Origin History, Psychological Distress, Quality of Childhood Memory, and Content of First and Recovered Childhood Memories

Objective: Individual differences in quality of childhood memory and recovered memories from childhood remain poorly understood. Therefore, this study tested several hypotheses which may help account for the large amount of variation that individuals report in the general quality of their childhood memory and the valence of the memories that many individuals report recovering from their childhoods. It was hypothesized that family of origin dysfunction would be associated with poorer childhood memory, that current depressed mood would be associated with impaired childhood recall and the recall of negative memories, and that the content of recovered childhood memories would be disproportionately negative because they include a significant number of memories which had been repressed or dissociated. Method: Questionnaires were administered to 553 college students, 27% of whom reported a history of child abuse. Results: The participants reported substantial variation in the general quality of their childhood memories and also a wide variety of different types of experiences for both their first childhood memories and the recovered memories that most of them had from their childhoods. Weak associations were found between family of origin dysfunction and poorer general quality of childhood memory, but the study as a whole resulted in few significant findings. Conclusions: Only weak support was found for some of the factors that have been hypothesized to distort autobiographical memory. The substantial individual variation in childhood memory that has been reported by college student samples remains poorly understood