Tensor LRR and sparse coding-based subspace clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data, and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established state-of-the-art methods.

Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Remarks on the classification of a pair of commuting semilinear operators

Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators. (C) 2011 Elsevier Inc. All rights reserved.

Spectral fluctuation and 1/f(alpha) noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f(alpha) noise with 1 <= alpha <= 2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f(alpha) noise is ubiquitous in nature.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Two-dimensional grayscale ultrasound and spectral Doppler waveform evaluation of dogs with chronic enteropathies

Sonography is an important diagnostic tool to examine the gastrointestinal tract of dogs with chronic diarrhea. Two-dimensional grayscale ultrasound parameters to assess for various enteropathies primarily focus on wall thickness and layering. Mild, generalized thickening of the intestinal wall with maintenance of the wall layering is common in inflammatory bowel disease. Quantitative and semi-quantitative spectral Doppler arterial waveform analysis can be utilized for various enteropathies, including inflammatory bowel disease and food allergies. Dogs with inflammatory bowel disease have inadequate hemodynamic responses during digestion of food. Dogs with food allergies have prolonged vasodilation and lower resistive and pulsatility indices after eating allergen-inducing foods.

Early autonomic dysfunction in patients with diabetes mellitus assessed by spectral analysis of heart rate and blood pressure variability

Patients with diabetes mellitus (DM) often have alterations of the autonomic nervous system (ANS), even early in their disease course. Previous research has not evaluated whether these changes may have consequences on adaptation mechanisms in DM, e.g. to mental stress. We therefore evaluated whether patients with DM who already had early alterations of the ANS reacted with an abnormal regulatory pattern to mental stress. We used the spectral analysis technique, known to be valuable and reliable in the investigation of disturbances of the ANS. We investigated 34 patients with DM without clinical evidence of ANS dysfunction (e.g. orthostatic hypotension) and 44 normal control subjects (NC group). No patients on medication known to alter ANS responses were accepted. The investigation consisted of a resting state evaluation and a mental stress task (BonnDet). In basal values, only the 21 patients with type 2 DM were different in respect to body mass index and systolic blood pressure. In the study parameters we found significantly lower values in resting and mental stress spectral power of mid-frequency band (known to represent predominantly sympathetic influences) and of high-frequency and respiration bands (known to represent parasympathetic influences) in patients with DM (types 1 and 2) compared with NC group (5.3 +/- 1.2 ms2 vs. 6.1 +/- 1.3 ms2, and 5.5 +/- 1.6 ms2 vs. 6.2 +/- 1.5 ms2, and 4.6 +/- 1.7 ms2 vs. 6.2 +/- 1.5 ms2, for resting values respectively; 4.7 +/- 1.4 ms2 vs. 5.9 +/- 1.2 ms2, and 4.6 +/- 1.9 ms2 vs. 5.6 +/- 1.7 ms2, and 3.7 +/- 2.1 ms2 vs. 5.6 +/- 1.7 ms2, for stress values respectively; M/F ratio 6/26 vs. 30/14). These differences remained significant even when controlled for age, sex, and body weight. However, patients with DM type 2 (and significantly higher body weight) showed only significant values in mental stress modulus values. There were no specific group effects in the patients with DM in adaptation mechanisms to mental stress compared with the NC group. These findings demonstrate that power spectral examinations at rest are sufficiently reliable to diagnose early alterations in ANS in patients with DM. The spectral analysis technique is sensitive and reliable in investigation of ANS in patients with DM without clinically symptomatic autonomic dysfunction.

Sea-suface microlayer (SML) and underlying water (ULW) samples focusing on CDOM spectral characteristics during METEOR cruise M91

The coastal upwelling system off the coast of Peru is characterized by high biological activity and a pronounced subsurface oxygen minimum zone, as well as associated emissions of atmospheric trace gases such as N2O, CH4 and CO2. From 3 to 23 December 2012, R/V Meteor (M91) cruise took place in the Peruvian upwelling system between 4.59 and 15.4°S, and 82.0 to 77.5°W. During M91 we investigated the composition of the sea-surface microlayer (SML), the oceanic uppermost boundary directly subject to high solar radiation, often enriched in specific organic compounds of biological origin like chromophoric dissolved organic matter (CDOM) and marine gels. In the SML, the continuous photochemical and microbial recycling of organic matter may strongly influence gas exchange between marine systems and the atmosphere. We analyzed SML and underlying water (ULW) samples at 38 stations focusing on CDOM spectral characteristics as indicator of photochemical and microbial alteration processes. CDOM composition was characterized by spectral slope (S) values and excitation-emission matrix fluorescence (EEMs), which allow us to track changes in molecular weight (MW) of DOM, and to determine potential DOM sources and sinks. Spectral slope S varied between 0.012 to 0.043 1 nm-1 and was quite similar between SML and ULW, with no significant differences between the two compartments. Higher S values were observed in the ULW of the southern stations below 15°S. By EEMs, we identified five fluorescent components (F1-5) of the CDOM pool, of which two had excitation/emission characteristics of amino-acid-like fluorophores (F1, F4) and were highly enriched in the SML, with a median ratio SML : ULW of 1.5 for both fluorophores. In the study region, values for CDOM absorption ranged from 0.07 to 1.47 m-1. CDOM was generally highly concentrated in the SML, with a median enrichment with respect to the ULW of 1.2. CDOM composition and changes in spectral slope properties suggested a local microbial release of DOM directly in the SML as a response to light exposure in this extreme environment. In a conceptual model of the sources and modifications of optically active DOM in the SML and underlying seawater (ULW), we describe processes we think may take place (Fig. 1); the production of CDOM of higher MW by microbial release through growth, exudation and lysis in the euphotic zone, includes the identified fluorophores (F1, F2, F3, F4, F5). Specific amino-acid-like fluorophores (F1, F4) accumulate in the SML with respect to the ULW, as photochemistry may enhance microbial CDOM release by (a) photoprotection mechanisms and (b) cell-lysis processes. Microbial and photochemical degradation are potential sinks of the amino-acid-like fluorophores (F1, F4), and potential sources of reworked and more refractory humic-like components (F2, F3, F5). In the highly productive upwelling region along the Peruvian coast, the interplay of microbial and photochemical processes controls the enrichment of amino-acid-like CDOM in the SML. We discuss potential implications for air-sea gas exchange in this area.

Low-resolution spectroscopy and spectral energy distributions of selected sources towards σ Orionis

Aims. We study in detail nine sources in the direction of the young σ Orionis cluster, which is considered to be a unique site for studying stellar and substellar formation. The nine sources were selected because of their peculiar properties, such as extremely-red infrared colours or excessively strong Hα emission for their blue optical colours. Methods. We acquired high-quality, low-resolution spectroscopy (R ∼ 500) of the nine targets with ALFOSC at the Nordic Optical Telescope. We also re-analysed [24]-band photometry from MIPS/Spitzer and compiled the highest quality photometric dataset available at the ViJHK_s passbands and the four IRAC/Spitzer channels, for constructing accurate spectral energy distributions between 0.55 and 24 μm. Results. The nine targets were classified into: one Herbig Ae/Be star with a scattering edge-on disc; two G-type stars; one X-ray flaring, early-M, young star with chromospheric Hα emission; one very low-mass, accreting, young spectroscopic binary; two young objects at the brown-dwarf boundary with the characteristics of classical T Tauri stars; and two emission-line galaxies, one undergoing star formation, and another whose spectral energy distribution is dominated by an active galactic nucleus. We also discovered three infrared sources associated with overdensities in a cold cloud of the cluster centre. Conclusions. Low-resolution spectroscopy and spectral energy distributions are a vital tool for measuring the physical properties and evolution of young stars and candidates in the σ Orionis cluster.

SPECTRAL DOMAIN-OPTICAL COHERENCE TOMOGRAPHY IMAGE CONTRAST AND BACKGROUND COLOR SETTINGS INFLUENCE IDENTIFICATION OF RETINAL STRUCTURES.

PURPOSE To evaluate image contrast and color setting on assessment of retinal structures and morphology in spectral-domain optical coherence tomography. METHODS Two hundred and forty-eight Spectralis spectral-domain optical coherence tomography B-scans of 62 patients were analyzed by 4 readers. B-scans were extracted in 4 settings: W + N = white background with black image at normal contrast 9; W + H = white background with black image at maximum contrast 16; B + N = black background with white image at normal contrast 12; B + H = black background with white image at maximum contrast 16. Readers analyzed the images to identify morphologic features. Interreader correlation was calculated. Differences between Fleiss-kappa correlation coefficients were examined using bootstrap method. Any setting with significantly higher correlation coefficient was deemed superior for evaluating specific features. RESULTS Correlation coefficients differed among settings. No single setting was superior for all respective spectral-domain optical coherence tomography parameters (P = 0.3773). Some variables showed no differences among settings. Hard exudates and subretinal fluid were best seen with B + H (κ = 0.46, P = 0.0237 and κ = 0.78, P = 0.002). Microaneurysms were best seen with W + N (κ = 0.56, P = 0.025). Vitreomacular interface, enhanced transmission signal, and epiretinal membrane were best identified using all color/contrast settings together (κ = 0.44, P = 0.042, κ = 0.57, P = 0.01, and κ = 0.62, P ≤ 0.0001). CONCLUSION Contrast and background affect the evaluation of retinal structures on spectral-domain optical coherence tomography images. No single setting was superior for all features, though certain changes were best seen with specific settings.

Radical Language, Radical Identity: Korean Writers in Japanese Spaces and the Burden to "Represent"

Thesis (Ph.D.)--University of Washington, 2016-06

Modeling of spectral and statistical properties of a random distributed feedback fiber laser

For the first time we report full numerical NLSE-based modeling of generation properties of random distributed feedback fiber laser based on Rayleigh scattering. The model which takes into account the random backscattering via its average strength only describes well power and spectral properties of random DFB fiber lasers. The influence of dispersion and nonlinearity on spectral and statistical properties is investigated. The evidence of non-gaussian intensity statistics is found. © 2013 Optical Society of America.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.