Spectral Decomposition

The exponential of a matrix and the spectral decomposition of a matrix can be computed knowing nothing more than the eigenvalues of the matrix and the Cayley-Hamilton theorem. The arrangement of the ideas in this paper is simple enough to be taught to beginning students of ODEs.

Effect of hydrocarbon gas on the seismic frequency attributes was studied and considered for applicability as Direct Hydrocarbon indicator (DHI) in the AN reservoir in the Niger Delta basin. Matching Pursuit algorithm for the spectral decomposition was adopted for frequency attributes analysis at 10Hz to 35Hz, along the interpreted reservoir top. Three frequency surface attributes were co-rendering and color blending to highlight the effect of gas in the reservoir. Gas filled sand exhibits distinctly higher frequency amplitudes at low frequency bands of 15Hz to 25Hz despite a subtle hardness of the sand relative to the overburden thick shale. High frequency amplitude expression in the low frequency (15Hz-25Hz) band observed in the gas reservoir is found to be a consistent character of overpressured gas reservoirs within the Niger Delta basin. It was concluded, therefore based on time-frequency seismic character of the gas sand, that frequency attribute can be used as a direct hydrocarbon indicator for the sandstone gas reservoir in the Niger Delta.

We propose a novel spectral decomposition of a 4th-order covariance tensor, S. Just as the variability of vector (i.e., a 1st-order tensor)-valued random variable is characterized by a covariance matrix (i.e., a 2nd-order tensor), S, the variability of a 2nd-order tensor-valued random variable, D, is characterized by a 4th-order covariance tensor, S. Accordingly, just as the spectral decomposition of S is a linear combination of its eigenvalues and the outer product of its corresponding (1st-order tensors) eigenvectors, the spectral decomposition of S is a linear combination of its eigenvalues and the outer product of its corresponding 2nd-order eigentensors. Analogously, these eigenvalues and 2nd-order eigentensors can be used as features with which to represent and visualize variability in tensor-valued data. Here we suggest a framework to visualize the angular structure of S, and then use it to assess and characterize the variability of synthetic diffusion tensor magnetic resonance imaging (DTI) data. The spectral decomposition suggests a hierarchy of symmetries with which to classify the statistical anisotropy inherent in tensor data. We also present maximum likelihood estimates of the sample mean and covariance tensors associated with D, and derive formulae for the expected value of the mean and variance of the projection of D along a particular direction (i.e., the apparent diffusion coefficient or ADC). These findings would be difficult, if not impossible, to glean if we treated 2nd-order tensor random variables as vector-valued random variables, which is conventionally done in multi-variate statistical analysis. r

Given an operator L acting on a function space, the J-matrix method consists of finding a sequence y_n of functions such that the operator L acts tridiagonally on y_n with respect to n. Once such a tridiagonalization is obtained, a number of characteristics of such an operator L can be obtained. In particular, information on eigenvalues and eigenfunctions, bound states, spectral decompositions, etc. can be obtained in this way. We review the general set-up, and we discuss two examples in detail; the Schrodinger operator with Morse potential and the Lame equation.

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more ...

Rms amplitude and spectral decomposition attribute have been extracted for hydrocarbon potential identification in Amandah area, Talangakar Formation, North West Java Basin. Purpose of rms amplitude extractions is to see the change of lithology which is extreme. Example is like reservoir existence. Spectral decomposition has been used to see reservoir at thin thickness. The seismic attributes has been extracted from seismic data 3D Pre Stack Time Migration (PSTM). Log data has been taken from a well (AMD-01) to interpret and determine reservoir thickness in interest zone. Seismic attribute analysis has been used to see existence and shape of channel's geometry spreading.

By using the finite element (FE) method and experimental modal analysis, including time average holography, natural frequencies and modes of vibration are investigated for the stepwise increase in the water level in a vertical thin-walled steel cylindrical shell. Specifically, rather curious changes are described in some eigenmodes of the shell caused by the rise in the water level. The agreement between the numerical results and the measurement is excellent in most cases studied. Ahmad shell elements with reduced integration for thin shells and quadratic fluid elements for inviscid incompressible fluid are used in the FE representation of the fluid-structure interaction model. A simple method of reduction of large fluid-structural eigenvalue problems to a standard form of reduced order is tested. It is based on the incomplete modal and spectral decomposition in the FE model of the structure in vacuo. The experimentally verified FE analysis can be used in vibration studies of more complicated shell-fluid systems.

We introduce factor circulant matrices: matrices with the structure of circulants, but with the entries below the diagonal multiplied by the same factor. The diagonalization of a circulant matrix and spectral decomposition are conveniently generalized to block matrices with the structure of factor circulants. Differential equations involving factor circulants are considered.

Miano area is one of the distinct major hydrocarbon producing fields of the Lower Indus basin.
Lower Goru is the reservoir strait in this area. The aim of the present study is to exploit the channels
reservoirs and other stratigraphic features in such a terrain where there is always a challenge
for the geoscientist to search and exploit the channeled reservoirs. To resolve this issue we have
utilized attribute analysis on high resolution 3D-seismic data for the detailed comparative studies
for the channels. There are many astonishing features that are identified in the current study,
which could not otherwise be easily enhanced with the help of 2D Seismic Data. Seismic attributes
such as coherency, frequency (are also appropriate for lithological discrimination), which are sensitive
to the channel edges are applied for the channel delineation and their geometrical analysis.
Spectral decomposition techniques are also applied for the delineation of channels and to appropriately
select the best band for channels identification. Three types of channel geometries are
recognized: 1) highly sinuous channel; 2) narrow-broad meandering belts; 3) moderate to high
sinuous channel. NW-SE, N-W trending faults can be helpful to compartmentalize the reservoir. Instantaneous
and dominant frequency are more beneficial for further field development based on
Gamma Ray logs from nearby drilled wells and dimensional perspectives analysis of the channel
reservoir.

Multivariate autoregressive modelling provides a method to analyse the dynamic interactions between heart rate (HR), blood pressure (BP) and respiration (RESP) by means of noise source contributions (NSCs). The conventional approach presumes the modelled noise sources are mutually independent. This presumption is, in general, not satisfied and causes an error in the results. In the present study, the effect of this error is analysed. A method is presented to remove the error by making the noise sources independent. The method is based on the inclusion of immediate transfer paths in the model. To quantify the strength of the interactions, a measure called NSC ratio (NSCR); is calculated; this states the amount of variability of the signal arising from other signals. The method is demonstrated by studying the inter-relationships between HR, BP and RESP in a healthy male subject in supine and standing positions. It is found that the error is marked and that the presented method provides corrected estimates for spectral decomposition and NSC analysis. The results show it is necessary to include the immediate transfer mechanisms in the model, while analysing the cardiopulmonary dynamics by means of HR and BP variability.

The necessity of sustainable development for landscapes has emerged as an important theme in recent decades. Current methods take a holistic approach to landscape heritage and promote an interdisciplinary dialogue to facilitate complementary landscape management strategies. With the socio-economic values of the natural and cultural landscape heritage increasingly recognised worldwide, remote sensing tools are being used more and more to facilitate the recording and management of landscape heritage. Satellite remote sensing technologies have enabled significant improvements in landscape research. The advent of the cloud-based platform of Google Earth Engine has allowed the rapid exploration and processing of satellite imagery such as the Landsat and Copernicus Sentinel datasets. In this paper, the use of Sentinel-2 satellite data in the identification of palaeo-riverscape features has been assessed in the Po Plain, selected because it is characterized by human exploitation since the ...

Plant-wide oscillations are common in many processes. Their effects propagate to many units and may impact the overall process performance. It is important to detect and diagnose the cause of such oscillations in order to rectify the situation. This paper proposes a new procedure to detect and diagnose plant-wide oscillations using routine operating data. A technique called spectral envelope is used to detect oscillations. Then the variables that have common oscillations can be identified and categorized accurately by a statistical hypothesis test. A new index called the oscillation contribution index (OCI) is proposed to isolate the key variables as the root cause candidates of the common oscillation(s). Two successful industrial case studies are presented to demonstrate the applicability of the proposed procedure.

In this paper, spectral decomposition techniques are applied to deepwater seismic data from Gulf of Mexico to examine the gas associated spectral anomalies. In the first case, thick gas sand with nearly constant P-impedance is encased in shale with non-symmetric P-impedance, and gas reservoir are bright at low-frequency iso-frequency sections; Commercial gas sand and low-gas saturated sand also show apparently different spectral characteristics. In the second case, gas reservoir includes two consecutive up-fining sand intervals with gradually changed P-impedance in each sand interval. Spectral anomalies of gas sand occur at highfrequency iso-frequency sections. Detailed forward modeling is analyzed to help understand the underlying physical mechanisms. Reservoir thickness and Pimpedance structure are the first order factors to control the spectral decomposition responses of the above two gas reservoirs. Systematic synthetic model based on reservoir properties is needed to select optimal frequency range to directly detect hydrocarbon for specific reservoir.

The paper presents the spectral stiffness microplane model, which is a general constitutive model for unidirectional composite laminates, able to simulate the orthotropic stiffness, prepeak nonlinearity, failure envelopes, and, in tandem with the material characteristic length, also the post-peak softening and fracture. The framework of the microplane model is adopted. The model exploits the spectral decomposition of the transversely isotropic stiffness matrix of the material to define orthogonal strain modes at the microplane level. This decomposition is a generalization of the volumetric-deviatoric split already used by Bažant and co-workers in microplane models for concrete, steel, rocks, soils, and stiff foams. Linear strain-dependent yield limits (boundaries) are used to provide bounds for the normal and tangential microplane stresses, separately for each mode. A simple version, with an independent boundary for each mode, can capture the salient aspects of the response of a unidirectional laminate, although a version with limited mode coupling can fit the test data slightly better. The calibration of model parameters, verification by test data, and analysis of multidirectional laminates are postponed for the subsequent companion paper.

The computation of the spectral decomposition of a symmetric arrowhead matrix is an important problem in applied mathematics . It is also the kernel of divide and conquer algorithms for computing the Schur decomposition of symmetric tridiagonal matrices and diagonal-plus-semiseparable matrices . The eigenvalues of symmetric arrowhead matrices are the zeros of a secular equation and some iterative algorithms have been proposed for their computation ]. An important issue of these algorithms is the choice of the initial guess. Let α1 ≤ α2 ≤ . . . ≤ αn−1 be the entries of the main diagonal of a symmetric arrowhead matrix of order n. Denoted by λi, i = 1, . . . , n, the corresponding eigenvalues, it is well know that αi ≤ λi+1 ≤ αi+1, i = 1, . . . , n − 2. An algorithm for computing each eigenvalue λi, i = 1, . . . , n, of a symmetric arrowhead matrix with monotonic quadratic convergence, independent of the choice of the initial guess in the interval ]αi−1, αi[ is proposed in this paper. Although the eigenvalues of a symmetric arrowhead matrix can be computed efficiently, a loss of orthogonality can occur in the computed matrix of eigenvectors .In this paper we propose also a simple, stable and efficient way to compute the eigenvectors of arrowhead matrices.

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The following aspects of our code have been validated: the generation of initial data representing perturbed general relativistic polytropic models (both rotating and non-rotating), the long-term evolution of relativistic stellar models, and the coupling of our evolution code to analysis modules providing, for instance, the detection of apparent horizons or the extraction of gravitational waveforms. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. We have carried out evolutions in full general relativity and compared the results to those obtained either with perturbation techniques, or with lower dimensional numerical codes, or in the Cowling approximation (in which all the perturbations of the spacetime are neglected). In all cases an excellent agreement has been found. The numerical evolutions have been carried out using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. In particular, we have found the "monotonized central differencing" (MC) limiter to be particularly effective in evolving the relativistic stellar models considered. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.

This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions (FAS) of the Lax operator L. Then the inverse scattering problem for L reduces to a Riemann-Hilbert problem. Such construction cab be applied to wide class

Based on the Sylvester and Frobenius theorems, we drastically enhance the feasibility of the transfer-matrix approach to deal with problems involving a large number of propagating and interfering modes, which require the solution of coupled differential equations and the evaluation of functions of matrix variables. We report closed formulas for the spectral decomposition of this type of functions. As specific example, besides the calculation of simple and well-known 1D one channel transfer matrices, we derive the multi-channel transfer matrix for an electron gas in the presence of a transverse electric field.

We consider the models Y i,n = i/n 0 σ(s)dW s + τ (i/n) i,n , andỸ i,n = σ(i/n)W i/n + τ (i/n) i,n , i = 1, . . . , n, where W t denotes a standard Brownian motion and i,n are centered i.i.d. random variables with E 2 i,n = 1 and finite fourth moment. Furthermore, σ and τ are unknown deterministic functions and W t and ( 1,n , . . . , n,n ) are assumed to be independent processes. Based on a spectral decomposition of the covariance structures we derive series estimators for σ 2 and τ 2 and investigate their rate of convergence of the MISE in dependence of their smoothness. To this end specific basis functions and their corresponding Sobolev ellipsoids are introduced and we show that our estimators are optimal in minimax sense. Our work is motivated by microstructure noise models. Our major finding is that the microstructure noise i,n introduces an additionally degree of ill-posedness of 1/2; irrespectively of the tail behavior of i,n . The method is illustrated by a small numerical study.

Uncertainty quantification (UQ) in CFD computations is receiving increased interest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent application of Polynomial Chaos (PC) methods for uncertainty representation and propagation in CFD computations. The fundamental concept on which Polynomial Chaos (PC) representations are based is to regard uncertainty as generating a new set of dimensions, and the solution as being dependent on these dimensions. A spectral decomposition in terms of orthogonal basis functions is used, the evolution of the basis coefficients providing quantitative estimates of the effect of random model data. A general overview of PC applications in CFD is provided, focusing exclusively on applications involving the unreduced Navier-Stokes equations. Included in the present review are an exposition of the mechanics of PC decompositions, an illustration of various means of implementing these representation, a perspective on the applicability of the corresponding techniques to propagate and quantify uncertainty in Navier-Stokes computations.

The mechanical constitutive behavior of geomaterials is quite complex, involving pressure-sensitive yielding, differences in strength in triaxial extension vs. compression, the Bauschinger effect, dependence on porosity, and other factors. Capturing these behaviors necessitates the use of fairly complicated and expensive non-linear material models. For elastically isotropic materials, such models usually involve three-invariant plasticity formulations. Spectral decomposition has been used to increase the efficiency of numerical simulation for such models for the isotropically hardening case. We modify the spectral decomposition technique to models that include kinematic hardening. Finally, we perform some numerical simulations to demonstrate quadratic convergence.

Effect of hydrocarbon gas on the seismic frequency attributes was studied and considered for applicability as Direct Hydrocarbon indicator (DHI) in the AN reservoir in the Niger Delta basin. Matching Pursuit algorithm for the spectral decomposition was adopted for frequency attributes analysis at 10Hz to 35Hz, along the interpreted reservoir top. Three frequency surface attributes were co-rendering and color blending to highlight the effect of gas in the reservoir. Gas filled sand exhibits distinctly higher frequency amplitudes at low frequency bands of 15Hz to 25Hz despite a subtle hardness of the sand relative to the overburden thick shale. High frequency amplitude expression in the low frequency (15Hz-25Hz) band observed in the gas reservoir is found to be a consistent character of overpressured gas reservoirs within the Niger Delta basin. It was concluded, therefore based on time-frequency seismic character of the gas sand, that frequency attribute can be used as a direct hydrocarbon indicator for the sandstone gas reservoir in the Niger Delta.

Multiple pitch estimation consists of inferring the fundamental frequencies and the salience of the notes forming a music signal over short time frames. This mid-level representation can be exploited as a front-end for higher-level applications, such as music-to-score transcription or chord detection. One approach is to decompose the short-term magnitude spectrum of the signal into a sum of basis spectra representing individual pitches scaled by time-varying amplitudes, using algorithms such as nonnegative matrix factorization (NMF). Prior training of the basis spectra is often infeasible due to the wide range of possible instruments. Appropriate spectra must then be estimated from the observed data, which may result in limited performance due to inaccurately estimated spectra. In this article, we model each basis spectrum as a weighted sum of narrowband spectra representing a few adjacent harmonic partials, thus enforcing harmonicity and spectral smoothness while adapting the spectral envelope to each instrument. We derive a NMF-like algorithm to estimate the model parameters and evaluate it on a database of piano recordings, considering several choices for the narrowband spectra. Performance appears superior to unconstrained adaptive NMF and competitive with supervised NMF based on pre-trained piano spectra. We also apply our approach to woodwind data.

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Distributed representation of words, or word embeddings, have motivated methods for calculating semantic representations of word sequences such as phrases, sentences and paragraphs. Most of the existing methods to do so either use algorithms to learn such representations, or improve on calculating weighted averages of the word vectors. In this work, we experiment with spectral methods of signal representation and summarization as mechanisms for constructing such word-sequence embeddings in an unsupervised fashion. In particular, we explore an algorithm rooted in fluid-dynamics, known as higher-order Dynamic Mode Decomposition, which is designed to capture the eigenfrequencies, and hence the fundamental transition dynamics, of periodic and quasi-periodic systems. It is empirically observed that this approach, which we call EigenSent, can summarize transitions in a sequence of words and generate an embedding that can represent well the sequence itself. To the best of the authors’ knowledge, this is the first application of a spectral decomposition and signal summarization technique on text, to create sentence embeddings. We test the efficacy of this algorithm in creating sentence embeddings on three public datasets, where it performs appreciably well. Moreover it is also shown that, due to the positive combination of their complementary properties, concatenating the embeddings generated
by EigenSent with simple word vector averaging achieves state-of-the-art results.

historical forward rates are used to calibrate the lognormal forward rate model - as advocated by Hull and White (1999, 2000), Longstaff, Santa Clara and Schwartz (1999), Rebonato (1999a,b,c), Rebonato and Joshi (2001) and many others - a Libor yield curve needs to be fit to the available data on spot libor rates, forward rate agreements (FRAs) or futures, and swap rates. This paper compares the statistical properties of the time series of forward rates that are obtained using three different yield curve fitting techniques. Introduced by McCulloch (1975), Steely (1991) and Svensson (1994), each of the three techniques is well known for its application to the construction of bond yield curves. Our work focuses on the eigenstructure of estimated forward rate correlation matrices. These are shown to be dominated by the semi-parametric or parametric form that is used in the yield curve model. The spectral decomposition of forward rate correlation - and covariance - matrices is considere...

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of

In a motorway network, correlations between parts or, more precisely, between the sections of (different) motorways, are of considerable interest. Knowledge of flows and velocities on individual motorways is not sufficient, rather, their correlations determine or reflect, respectively, the functionality of and the dynamics on the network. These correlations are time-dependent as the dynamics on the network is highly non-stationary. Apart from the conceptual importance, correlations are also indispensable to detect risks of failure in a traffic network. Here, we proceed with revealing a certain hierarchy of correlations in traffic networks that is due to the presence and to the extent of collectivity. In a previous study, we focused on the collectivity motion present in the entire traffic network, i.e. the collectivity of the system as a whole. Here, we manage to subtract this dominant effect from the data and identify the subdominant collectivities which affect different, large parts of the traffic network. To this end, we employ a spectral analysis of the correlation matrix for the whole system. We thereby extract information from the virtual network induced by the correlations and map it on the true topology, i.e. on the real motorway network. The uncovered subdominant collectivities provide a new characterization of the traffic network. We carry out our study for the large motorway network of North Rhine-Westphalia (NRW), Germany.

Let (X_R, 0) be a germ of real analytic subset in (R^N, 0) of pure dimension n+1 with an isolated singularity at 0. Let (f_R,0) : (X_R, 0) --> (R,0) a real analytic germ with an isolated singularity at 0, such that its complexification f_C vanishes on the singular set S of X_C. We also assume that X_R-[0] is orientable.

A thermodynamically consistent macroscopic constitutive model for concrete that incorporates concrete effective stress space plasticity and fracture energy based - continuum damage mechanics is presented. A plasticity yield criterion, with multiple hardening functions and a non-associative plastic flow rule, is used simultaneously with two (tensile and compressive) isotropic damage criteria. The spectral decomposition of the stress tensor into tensile and compressive components is utilized in all criteria in order to simulate different responses of the material under various loading patterns. The damage criteria are based on the hydrostatic- deviatoric sensitive damage energy release rates in tension and compression derived from the Helmholtz free energy function. Three dissipation mechanisms are defined, one for plasticity and two for damage, to control the dissipation process in the material model. The consistent elastic-plastic-damage tangent operator is also derived, which concl...

Oil and gas exploration is the quest for hydrocarbon deposits trapped underneath the earth surface. Seismic is one of the hydrocarbon exploration tools. Recently significant efforts have been directed, in seismic processing and interpretation, to the development of methods such as spectral decomposition used for tuning hydrocarbon reservoirs and delineating it. In addition, statistical techniques are required to analyze variations in seismic traces. This research work is an alternative technique based on singularity spectrum analysis for detecting and delineating hydrocarbon reservoir. Singularity spectrum captures the singularities occurring in a signal. The technique is applied on synthesized seismograms and three attributes of the singularity spectrum namely width, correlation dimension and peak α are determined. Results show that by using these attributes the reservoir fluids are detected and delineated. Singularity spectrum analysis will potentially improve the performance of Oil & Gas industry by reducing drilling uncertainties, producing accurate geological models of 2D seismic data and for correct production estimates of reservoirs.

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.

We show how periodic motions can be represented by a small number of eigenshapes that capture the whole dynamic mechanism of the motion. Spectral decomposition of a silhouette of a moving object serves as a basis for behavior classification by principle component analysis. The boundary contour of the walking dog, for example, is first computed efficiently and accurately. After normalization, the implicit representation of a sequence of silhouette contours given by their corresponding binary images, is used for generating eigenshapes for the given motion. Singular value decomposition produces these eigenshapes that are then used to analyze the sequence. We show examples of object as well as behavior classification based on the eigendecomposition of the binary silhouette sequence.

In this paper, controllability of the linear discrete-time systems (A,B,Ω):x k+1 =Ax k +Bu k , x k ∈X, u k ∈Ω, is studied, where X is a Banach space and the control set Ω is assumed to be a cone in a Banach space U . Some criteria for approximate controllability are given. The case where the operator A is compact is examined in detail by using the spectral decomposition of the state space X. As a result, a criterion for approximate controllability of (A,B,Ω) is obtained without imposing a restrictive condition that the system with no control constraints (A,B,U ) is exactly controllable. The obtained results are then applied to consider the problem of controllability for linear functional differential equations with positive controls. Some necessary and sufficient conditions of approximate controllability to the state space R n ×L p are presented and some illustrating examples are given.

It is shown that HYSCORE spectra of paramagnetic centers having nuclei of spin I=1 with isotropic hfi and arbitrary NQI consist of ridges having zero width. A parametric presentation of these ridges is found which shows the range of possible frequencies in the HYSCORE spectrum and aids in spectral assignments and rapid estimation of spin Hamiltonian parameters. An alternative approach for the spectral density calculation is presented that is based on spectral decomposition of the Hamiltonian. Only the eigenvalues of the Hamiltonian are needed in this approach. An atlas of HYSCORE spectra is given in the Supporting Information. This approach is applied to the estimation of the spin Hamiltonian parameters of the oxovanadium-EDTA complex.

Dissolved organic matter (DOM) plays an important role in many soil ecosystem functions. Multidimensional fluorescence spectroscopy of DOM with parallel factor analysis (PARAFAC) of the resulting spectral landscape has been successful in characterizing DOM from a variety of aquatic sources. This study was conducted to assess the multiway PARAFAC approach for quantitatively characterizing the fluorescent landscapes of DOM from aqueous extracts of soils and soil amendments. The DOM was extracted from plant biomass representative of crop, wetlands, and tree species; animal manures; and soils from controlled studies of cropping systems with known histories of organic amendments. The fluorescence landscape spectra were collected in the excitation range from 240 to 400 nm and emission range from 300 to 500 nm in 3-nm increments. The excitation and emission spectra modeled from the PARAFAC analysis showed that the plant biomass, animal manure, and soil DOM contained five fluorescing components: tryptophan-like (peak location at excitation 270 nm, emission 354 nm), tyrosine-like (273/309 nm), and three humic-substance-like components (.240/465 nm, 306/405 nm, and 315/447 nm). Principal component analysis of the concentration loading showed that the soil-derived DOM was very similar despite the different types and quantities of organic amendments incorporated in the different cropping systems. This study shows that PARAFAC analysis of multidimensional fluorescence spectra can model the chemical profile of terrestrial DOM in a chemically meaningful way. This represents a significant advance over current approaches to interpreting the complex DOM fluorescence spectra.

► Contemporary high-resolution global geopotential models (e.g., EGM2008) improve regional geoid modeling. ► A new version of Matlab-based software for stochastic modifications of Stokes's formula was developed. ► Typical procedures for generating the core quantities of the modifications are explained.

We study correlation functions of parafermionic currents and disorder fields in the Z(N) symmetric conformal field theory perturbed by the first thermal operator. Following the ideas of Al. Zamolodchikov, we develop for the correlation functions the conformal perturbation theory at small scales and the form factors spectral decomposition at large ones. For all N there is an agreement between the data at the intermediate distances. We consider the problems arising in the description of the space of scaling fields in perturbed models, such as null vector relations, equations of motion and a consistent treatment of fields related by a resonance condition.

In this paper, we simulate the effects of eddy currents induced by switched gradient coils in the cylindrical cryostat structures of a high-temperature superconducting (HTS) magnetic resonance imaging magnet. A novel network method was used with spectral decomposition of the current density in the φand z-directions to simulate the effects of X-gradient coils. Two types of active magnetic shielding were simulated, and it was found that one type is able to reduce the power of the eddy currents in the cryostat to a greater extent than the other. These results will inform the design of gradient coils that protect the HTS magnet from eddy-current-induced heating and vibrations.

We have developed a toolbox and graphic user interface, EEGLAB, running under the cross-platform MATLAB environment (The Mathworks, Inc.) for processing collections of single-trial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multi-trial ERP-image plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), Independent Component Analysis (ICA) and time/frequency decompositions including channel and component cross-coherence supported by bootstrap statistical methods based on data resampling. EEGLAB functions are organized into three layers. Top-layer functions allow users to interact with the data through the graphic interface without needing to use MATLAB syntax. Menu options allow users to tune the behavior of EEGLAB to available memory. Middle-layer functions allow users to customize data processing using command history and interactive 'pop' functions. Experienced MATLAB users can use EEGLAB data structures and stand-alone signal processing functions to write custom and/or batch analysis scripts. Extensive function help and tutorial information are included. A 'plug-in' facility allows easy incorporation of new EEG modules into the main menu. EEGLAB is freely available (http://www.sccn.ucsd.edu/eeglab/) under the GNU public license for noncommercial use and open source development, together with sample data, user tutorial and extensive documentation.

We study the central limit theorem and the structure of the corresponding covari- ance operator for the Markov chains generated by successive (overlapping) k-tuples (Xn+1,...,Xn+k), n = 0,1,... formed from the i.i.d.r.v. {Xn}. The potential applica- tion of the theory includes the design of statistical tests. In particular, we present the explicit spectral analysis of the covariance matrices related to