Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train

Simulation of underground gravity gradients from stochastic seismic fields

We present results obtained from a finite-element simulation of seismic displacement fields and of gravity gradients generated by those fields. The displacement field is constructed by a plane wave model with a 3D isotropic stochastic field and a 2D fundamental Rayleigh field. The plane wave model provides an accurate representation of stationary fields from distant sources. Underground gravity gradients are calculated as acceleration of a free test mass inside a cavity. The results are discussed in the context of gravity-gradient noise subtraction in third generation gravitational-wave detectors. Error analysis with respect to the density of the simulated grid leads to a derivation of an improved seismometer placement inside a 3D array which would be used in practice to monitor the seismic field.Comment: 24 pages, 12 figure

Antioxidant and cytotoxic potential of selected plant species of the boraginaceae family

Antioxidant activity is one of the most important properties of plant extracts. Antioxidants from natural sources have been intensively studied in the last few decades. The antioxidant contents of medicinal plants may contribute to the protection of diseases. Bioactive components of plants have a potential role in chemoprevention and inhibition of different phases of the malignant transformation process. Therefore, plant extracts and essential oils are in the focus of research, and in recent decades have been tested on a large number of malignant cell lines. The aim of this study was to examine antioxidant and cytotoxic potential of selected plant species from the Boraginaceae family. Determination of antioxidant activity was performed by ammonium-thiocyanate method. Testing citotoxic activity was performed by MTT test on cancer cell lines: HEP 2c (human larynx carcinoma), RD (human cell line-rhabdomyosarcoma) and L2OB (mouse tumor fibroblast line). The best antioxidant activity showed ethanol, acetone and chloroform extracts of Anchusa officinalis, Echium vulgare and Echium italicum. The tested extracts showed an inhibitory effect on cancer cells, but chloroform and acetone extracts of all three plant had the most effective effect on L2OB cells. Isolation of individual active components from this plants and their testing for cancer cells would be of great importance for this field of research

Effect of different fertilizers on the microbial activity and productivity of soil under potato cultivation

This study was conducted to evaluate the effect of the application of different rates of mineral nitrogen, well rotten farmyard manure and Klebsiella planticola SL09- based microbial biofertilizer (enteroplantin) on the count of soil microorganisms (total microbial count, counts of Azotobacter, oligonitrophilic bacteria, fungi and actinomycetes), stem height and yield of potato. The experiment was set up as a randomized block design in four replications at the experimental field of the Biotechnical Faculty, Podgorica in 2008. Potato cultivar Kennebec was used as the test plant. The trial involved six treatments: non-fertilized control; N1 treatment with 100 kg/ha CAN (calcium ammonium nitrate, 27% N); N2 treatment with 200 kg/ha CAN; N3 treatment with 300 kg/ha CAN; treatment with Enteroplantin– K. planticola SL09-based biofertilizer; and treatment with 30 t/ha solid well rotten farmyard manure. The results obtained suggested that well rotten farmyard manure induced the highest increase in microbial counts, potato yield and stem height. A similar effect on all microorganisms, except actinomycetes and fungi was seen with the use of K. planticola SL09-based biofertilizer. The potato yield and stem height obtained with the use of 300 kg/ha CAN was non-significantly higher than that of 200 kg/ha CAN treatment, with the count of the soil microorganisms tested been significantly reduced.Key words: Biofertilization, microorganisms, soil, manure, mineral nitrogen, potato, yield

Accessibility of the Pre-Big-Bang Models to LIGO

The recent search for a stochastic background of gravitational waves with LIGO interferometers has produced a new upper bound on the amplitude of this background in the 100 Hz region. We investigate the implications of the current and future LIGO results on pre-Big-Bang models of the early Universe, determining the exclusion regions in the parameter space of the minimal pre-Big Bang scenario. Although the current LIGO reach is still weaker than the indirect bound from Big-Bang nucleosynthesis, future runs by LIGO, in the coming year, and by Advanced LIGO (~2009) should further constrain the parameter space, and in some parts surpass the Big-Bang nucleosynthesis bound. It will be more diffcult to constrain the parameter space in non-minimal pre-Big-Bang models, which are characterized by multiple cosmological phases in the yet not well understood stringy phase, and where the higher-order curvature and/or quantum-loop corrections in the string effective action should be included.Comment: 8 pages, 8 figure

Structure-Based Model of RNA Pseudoknot Captures Magnesium-Dependent Folding Thermodynamics

We develop a simple, coarse-grained approach for simulating the folding of the Beet Western Yellow Virus (BWYV) pseudoknot toward the goal of creating a transferable model that can be used to study other small RNA molecules. This approach combines a structure-based model (SBM) of RNA with an electrostatic scheme that has previously been shown to correctly reproduce ionic condensation in the native basin. Mg2+ ions are represented explicitly, directly incorporating ion-ion correlations into the system, and K+ is represented implicitly, through the mean-field generalized Manning counterion condensation theory. Combining the electrostatic scheme with a SBM enables the electrostatic scheme to be tested beyond the native basin. We calibrate the SBM to reproduce experimental BWYV unfolding data by eliminating overstabilizing backbone interactions from the molecular contact map and by strengthening base pairing and stacking contacts relative to other native contacts, consistent with the experimental observation that relative helical stabilities are central determinants of the RNA unfolding sequence. We find that this approach quantitatively captures the Mg2+ dependence of the folding temperature and generates intermediate states that better approximate those revealed by experiment. Finally, we examine how our model captures Mg2+ condensation about the BWYV pseudoknot and a U-tail variant, for which the nine 3' end nucleotides are replaced with uracils, and find our results to be consistent with experimental condensation measurements. This approach can be easily transferred to other RNA molecules by eliminating and strengthening the same classes of contacts in the SBM and including generalized Manning counterion condensation

Long gravitational-wave transients and associated detection strategies for a network of terrestrial interferometers

Searches for gravitational waves (GWs) traditionally focus on persistent sources (e.g., pulsars or the stochastic background) or on transients sources (e.g., compact binary inspirals or core-collapse supernovae), which last for time scales of milliseconds to seconds. We explore the possibility of long GW transients with unknown waveforms lasting from many seconds to weeks. We propose a novel analysis technique to bridge the gap between short O(s) “burst” analyses and persistent stochastic analyses. Our technique utilizes frequency-time maps of GW strain cross power between two spatially separated terrestrial GW detectors. The application of our cross power statistic to searches for GW transients is framed as a pattern recognition problem, and we discuss several pattern-recognition techniques. We demonstrate these techniques by recovering simulated GW signals in simulated detector noise. We also recover environmental noise artifacts, thereby demonstrating a novel technique for the identification of such artifacts in GW interferometers. We compare the efficiency of this framework to other techniques such as matched filtering