Spectral Sets Research Articles

Wave Phase-Sensitive Transformation of 3d-Straining of Mechanical Fields

It is the area of research of oscillatory processes in elastic mechanical systems. Technical result of innovation is creation of spectral set of multidimensional images which reflect time-correlated three-dimensional vector parameters of metrological, and\\or estimated, and\\or design parameters of oscillations in mechanical systems. Reconstructed images of different dimensionality integrated in various combinations depending on their objective function can be used as homeostatic profile or cybernetic image of oscillatory processes in mechanical systems for an objective estimation of current operational conditions in real time. The innovation can be widely used to enhance the efficiency of monitoring and research of oscillation processes in mechanical systems (objects) in construction, mechanical engineering, acoustics, etc. Concept method of vector vibrometry based on application of vector 3D phase- sensitive vibro-transducers permits unique evaluation of real stressed-strained states of power aggregates and loaded constructions and opens fundamental innovation opportunities: conduct of continuous (on-line regime) reliable monitoring of turboagregates of electrical machines, compressor installations, bases, supports, pipe-lines and other objects subjected to damaging effect of vibrations; control of operational safety of technical systems at all the stages of life cycle including design, test production, tuning, testing, operational use, repairs and resource enlargement; creation of vibro-diagnostic systems of authentic non-destructive control of anisotropic characteristics of materials resistance of power aggregates and loaded constructions under outer effects and operational flaws. The described technology is revolutionary, universal and common for all branches of engineering industry and construction building objects.

Set-based similarity learning in subspace for agricultural remote sensing classification

Similarity between spectral lines is key in the field of agricultural sensing classification, however, the measured spectral lines mostly mislead the classification because of unexpected disturbance in application. To enhance the accuracy of classification, similarity learning is introduced into agricultural remote sensing classification. Within the framework of similarity learning, the training set is generated by pairing the labeled spectral lines which means the size of training set for learning similarity is heavily increasing. Noticed this problem, a novel spectrum-set similarity learning algorithm is reported for balancing the gain in classification and the computational burden of learning similarity. Different from traditional point-based similarity, the spectrum-set similarity measures the similarity between two spectral sets which contain some spectral lines. Following the idea, set-based training set is generated by clustering the spectral lines in the point-based training set. Experimental results have shown the effectiveness and efficiency of learning spectrum-set similarity measure for agriculture sensing classification.

Spectrality of Self-Similar Tiles

We call a set $$K \subset {\mathbb {R}}^s$$ with positive Lebesgue measure a spectral set if $$L^2(K)$$ admits an exponential orthonormal basis. It was conjectured that K is a spectral set if and only if K is a tile (Fuglede’s conjecture). Although the conjecture was proved to be false in $${\mathbb {R}}^s$$ , $$s\ge 3$$ (Kolountzakis in Forum Math 18:519–528, 2006; Tao in Math Res Lett 11:251–258, 2004), it still poses challenging questions with additional assumptions. In this paper, our additional assumption is self-similarity. We study the spectral properties of a class of self-similar tiles K in $${\mathbb {R}}$$ that has a product structure on the associated digit sets. We show that strict product-form tiles and the associated modulo product-form tiles are spectral sets. For the converse question, we give a pilot study for the self-similar set K generated by arbitrary digit sets with four elements. We investigate the zeros of its Fourier transform due to the orthogonality and verify Fuglede’s conjecture for this special case. We also make use of this case to illustrate the theorems and discuss some questions that arise in the general situation.

An Independent Filter for Gene Set Testing Based on Spectral Enrichment.

Gene set testing has become an indispensable tool for the analysis of high-dimensional genomic data. An important motivation for testing gene sets, rather than individual genomic variables, is to improve statistical power by reducing the number of tested hypotheses. Given the dramatic growth in common gene set collections, however, testing is often performed with nearly as many gene sets as underlying genomic variables. To address the challenge to statistical power posed by large gene set collections, we have developed spectral gene set filtering (SGSF), a novel technique for independent filtering of gene set collections prior to gene set testing. The SGSF method uses as a filter statistic the p-value measuring the statistical significance of the association between each gene set and the sample principal components (PCs), taking into account the significance of the associated eigenvalues. Because this filter statistic is independent of standard gene set test statistics under the null hypothesis but dependent under the alternative, the proportion of enriched gene sets is increased without impacting the type I error rate. As shown using simulated and real gene expression data, the SGSF algorithm accurately filters gene sets unrelated to the experimental outcome resulting in significantly increased gene set testing power.

The failure of rational dilation on the tetrablock

We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1) . We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model.

The Learning Method of Speech RecognitionBased on HMM

This paper helps to improve the student’s interest towards speech recognition. It implements Automatic Speech Recognition System based on the following: Preprocessing, Feature Extraction Technique (MFCC- Mel Frequency Cepstrum Coefficients) and Hidden Markov Model (used in recognition phase) .Its purpose is that the human voice can be converted to a computer-readable input, Such as buttons, binary-coded, or sequence of characters. Acoustic phonetic approach, Knowledge based approach and Pattern recognition approach are the three approaches used in speech recognition. In this paper Pattern recognition technique is used. This approach requires no explicit knowledge of speech. This approach has two steps – namely, training of speech patterns based on some generic spectral parameter set and recognition of patterns via pattern comparison.

Explicit and Unique Construction of Tetrablock Unitary Dilation in a Certain Case

Consider the domain $E$ in $\mathbb{C}^3$ defined by $$ E=\{(a_{11},a_{22},\text{det}A): A=\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}\text{ with }\lVert A \rVert <1\}. $$ This is called the tetrablock. This paper constructs explicit boundary normal dilation for a triple $(A,B,P)$ of commuting bounded operators which has $\bar{E}$ as a spectral set. We show that the dilation is minimal and unique under a certain natural condition. As is well-known, uniqueness of minimal dilation usually does not hold good in several variables, e.g., Ando's dilation is not known to be unique. However, in the case of the tetrablock, the third component of the dilation can be chosen in such a way as to ensure uniqueness.

Soluble Solids Content and pH Prediction and Maturity Discrimination of Lychee Fruits Using Visible and Near Infrared Hyperspectral Imaging

Hyperspectral imaging (HSI) technique has shown promise as a rapid and nondestructive tool to evaluate various internal quality attributes of fruits and vegetables. The objective of this study was to investigate the nondestructive prediction of soluble solids content (SSC) and pH of lychees and maturity discrimination. Two hyperspectral imaging systems of visible/short-wave near infrared range (600–1000 nm, Spectral Set I) and long-wave near infrared range (1000–2500 nm, Spectral Set II) were employed. Results showed that Spectral Set II (SSC: r p = 0.877, RMSEP = 0.911 °Brix; pH: r p = 0.745, RMSEP = 0.291) performed better than Spectral Set I (SSC: r p = 0.790, RMSEP = 1.279 °Brix; pH: r p = 0.701, RMSEP = 0.308) for the internal quality prediction of litchi and maturity discrimination. The partial least square discriminant analysis (PSL-DA) model had a discrimination rate of 90.63 % for Spectral Set I and 96.88 % for Spectral Set II. β-Coefficients of partial least squares regression (PLSR) models were used to choose optimal wavelengths for quality predictions. The performance of optimized PLSR in both spectral sets were comparable to the models developed using the whole spectral range.

The Value of Nonenhanced Single-Source Dual-Energy CT for Differentiating Metastases From Adenoma in Adrenal Glands

To evaluate the value of the nonenhanced single-source dual-energy computed tomography (ssDECT) in differentiating metastases from adenomas in adrenal glands. This retrospective study was approved by our Institutional Review Board, and written informed consent was waived. One hundred twelve patients (66 men:46 women; mean age, 58 years) with 63 adrenal metastases (AMs) and 64 adrenal adenomas (AAs) underwent a plain dual-energy spectral CT imaging from August 2011 to December 2013 were included. The fat (water) density (DFa [Wa]) from the material decomposition (MD) images and CT number and effective atomic number (eff-Z) from the virtual monochromatic spectral (VMS) image sets were measured for the AMs and AAs. The spectral Hounsfield unit (HU) curve (CT number as a function of photon energy from 40 to 140 keV) was generated, and its slope (K) was calculated. The difference of these parameters between AMs and AAs was statistically compared by the Wilcoxon rank sum test. Receiver operating characteristic curve (ROC) curves were used to compare the diagnostic efficacies of these measures in the identification of AAs and AMs. The distribution of spectral HU curve was analyzed using the chi-square test in terms of its slope K: ascending (K > 0.1), straight (-0.1 ≤ K ≤ 0.1), and descending (K < -0.1). 1) The CT number (medium, range) of metastases (50.47, 29.93 HU at 40 keV and 29.00, 9.36 HU at 140 keV) was significantly higher than that of adenomas (-0.76, 33.04 to 13.73, 18.96 HU) at each energy level from 40 to 140 keV (P < .05). 2) The fat concentration of metastases (-177.37, 296.38 mg/mL) was statistically lower than that of adenomas (126.73, 328.07 mg/mL; P < .05). 3) The eff-Z of metastases (7.76, 0.23) was significantly higher than that of adenomas (7.42, 0.32; P < .05). 4) With CT number of VMS image at 40 keV of 21.78 HU as a threshold, the sensitivity and specificity for differentiating metastases from adenomas was 92.1% and 76.6%, respectively, and the area under the ROC curve was 0.90. 5) The spectral curve types included 3.2% (2 of 63) ascending, 20.6% (13 of 63) straight, and 76.2% (48 of 63) descending for the metastases, whereas the corresponding numbers were 60.9% (39 of 64), 21.9% (14 of 64), and 17.2% (11 of 64) for the adenomas. The difference was statistically significant (X(2) = 56.63; P < .05). The nonenhanced ssDECT enables a multiparametric approach to provide an excellent sensitivity for identifying AMs from AAs.

Tiling properties of spectra of measures

We investigate tiling properties of spectra of measures, i.e., sets \(\Lambda \) in \(\mathbb {R}\) such that \(\{e^{2\pi i \lambda x}{:}\, \lambda \in \Lambda \}\) forms an orthogonal basis in \(L^2(\mu )\), where \(\mu \) is some finite Borel measure on \(\mathbb {R}\). Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprizing tiling properties for spectra of fractal measures, the existence of complementing sets and spectra for finite sets with the Coven–Meyerowitz property, the existence of complementing Hadamard pairs in the case of Hadamard pairs of size 2, 3, 4 or 5. In the context of the Fuglede conjecture, we prove that any spectral set is a tile, if the period of the spectrum is 2, 3, 4 or 5.

Monitoring of the manufacturing process for ambroxol hydrochloride tablet using NIR-chemometric methods: compression effect on content uniformity model and relevant process parameters testing

This study aimed at using near-infrared (NIR) spectroscopy to monitor compaction pressure for simultaneously determining the tensile strength and content uniformity, as well as moisture and mean particle size of ambroxol hydrochloride tablets. The content uniformity, compression force and tensile strength of the laboratory samples were obtained by pressing a mixture of active principle and excipient components into tablets. To reduce the spectral baseline shift of the laboratory samples, the compaction pressure applied to the mixture was assessed by a variable pressure test. Production samples were added to the test and subjected to principal component analysis. The expanded partial least-squares (PLS) calibration model used to quantify the active content was more accurate than the model constructed from laboratory samples using the production tablets included in the calibration set. The model showed good predictability, with correlation coefficient (R) 0.9977. The validation and reliability of the content model were evaluated to determine trueness and reliability for the measurement of individual production tablets and the laboratory tablets with drug content ranging from 24 to 36 mg. The PLS calibration models for compression force and tensile strength were constructed using the same spectral set assuming both were highly related. These models yielded high R values (0.9955 and 0.9910). The R values of the moisture and mean particle size were 0.9994 and 0.9919, respectively. This study demonstrated that NIR spectroscopy combined with chemometric techniques can be successfully used to quantitatively monitor the tablet manufacturing process in the pharmaceutical industry.

Spectral gene set enrichment (SGSE).

BackgroundGene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist for unsupervised gene set testing, they predominantly compute enrichment relative to clusters of the genomic variables with performance strongly dependent on the clustering algorithm and number of clusters.ResultsWe propose a novel method, spectral gene set enrichment (SGSE), for unsupervised competitive testing of the association between gene sets and empirical data sources. SGSE first computes the statistical association between gene sets and principal components (PCs) using our principal component gene set enrichment (PCGSE) method. The overall statistical association between each gene set and the spectral structure of the data is then computed by combining the PC-level p-values using the weighted Z-method with weights set to the PC variance scaled by Tracy-Widom test p-values. Using simulated data, we show that the SGSE algorithm can accurately recover spectral features from noisy data. To illustrate the utility of our method on real data, we demonstrate the superior performance of the SGSE method relative to standard cluster-based techniques for testing the association between MSigDB gene sets and the variance structure of microarray gene expression data.ConclusionsUnsupervised gene set testing can provide important information about the biological signal held in high-dimensional genomic data sets. Because it uses the association between gene sets and samples PCs to generate a measure of unsupervised enrichment, the SGSE method is independent of cluster or network creation algorithms and, most importantly, is able to utilize the statistical significance of PC eigenvalues to ignore elements of the data most likely to represent noise.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0490-7) contains supplementary material, which is available to authorized users.

Unitary groups and spectral sets

We study spectral theory for bounded Borel subsets of R and in particular finite unions of intervals. For Hilbert space, we take L2 of the union of the intervals. This yields a boundary value problem arising from the minimal operator D=12πiddx with domain consisting of C∞ functions vanishing at the endpoints. We offer a detailed interplay between geometric configurations of unions of intervals and a spectral theory for the corresponding self-adjoint extensions of D and for the associated unitary groups of local translations. While motivated by scattering theory and quantum graphs, our present focus is on the Fuglede-spectral pair problem. Stated more generally, this problem asks for a determination of those bounded Borel sets Ω in Rk such that L2(Ω) has an orthogonal basis of Fourier frequencies (spectrum), i.e., a total set of orthogonal complex exponentials restricted to Ω. In the general case, we characterize Borel sets Ω having this spectral property in terms of a unitary representation of (R,+) acting by local translations. The case of k=1 is of special interest, hence the interval-configurations. We give a characterization of those geometric interval-configurations which allow Fourier spectra directly in terms of the self-adjoint extensions of the minimal operator D. This allows for a direct and explicit interplay between geometry and spectra.

Weak spectral synthesis in commutative Banach algebras. III

Let A be a regular and semisimple commutative Banach algebra with structure space Δ(A). Continuing the investigations of [7] and [9], we establish various results on weak spectral sets in Δ(A). To each closed subset of Δ(A) we associate a descending sequence of subsets of Δ(A) which proves to be a powerful tool in the study of weak spectral synthesis. Applications concern injection type properties, unions of weak spectral sets and projective tensor products. A number of interesting examples is discussed: algebras of m-times continuously differentiable functions and of Lipschitz functions, and L1(RN).

An algorithm for identification of substances using a finite set of secondary-emission spectra

A problem of identification of chemical composition in the absence of sampling procedures is considered. A method that allows identification using spectra of a desired substance is proposed. The measure of the difference between spectral sets is determined. The method is employed in the experiments using a visible and near-UV Fourier spectrometer. The secondary emission of samples is excited by UV sources with maximum intensities at wavelengths of 280 and 310 nm. Anthracene, POPOP, PPO, stilbene, and tryptophan are used in experiments. The ROC curves are constructed and compared to specify the parameters that are used in the algorithm for searching for substances in the database of reference spectra. The results will make it possible to improve the reliability and applicability of express analyzers of chemical substances.

Robust Spectral Features for Automatic Speaker Recognition in Mismatch Condition

Abstract The widespread use of automatic speaker recognition technology in real world applications demands for robustness against various realistic conditions. In this paper, a robust spectral feature set, called NDSF (Normalized Dynamic Spectral Features) is proposed for automatic speaker recognition in mismatch condition. Magnitude spectral subtraction is performed on spectral features for compensation against additive noise. A spectral domain modification is further performed using time-difference approach followed by Gaussianization Non-linearity. Histogram normalization is applied to these dynamic spectral features, to compensate the effect of channel mismatch and some non-linear effects introduced due to handset transducers. Feature extraction using proposed features is carried out for a text independent automatic speaker recognition (identification) system. The performance of proposed feature set is compared with conventional cepstral features like (mel-frequency cepstral coefficients and linear prediction cepstral coefficients), for acoustic mismatch condition caused by use of different sensors. Studies are performed on two databases: A multi-variability speaker recognition (MVSR) developed by IIT-Guwahati and Multi-speaker continuous (Hindi) speech database (By Department of Information Technology, Government of India). From experimental analysis, it is observed that, spectral domain dynamic features enhance the robustness by reducing additive noise and channel effects caused by sensor mismatch. The proposed NDSF features are found to be more robust than cepstral features for both datasets.

Maps preserving Fredholm or semi-Fredholm elements relative to some ideal

We consider the Calkin algebra CR(A) and the Fredholm theory in a Banach algebra A, relative to some fixed ideal F of A. Our aim is to study linear maps between unital Banach algebras A and B which are surjective up to the inessential elements relative to F, and preserve Fredholm or semi-Fredholm elements in both directions or equivalently different relatively essential spectral sets such as essential spectrum, left or right essential spectrum, the boundary of essential spectrum or the full essential spectrum. We characterize such mappings when one ofCR(A) orCR(B) is commutative and also investigate similar problems when A is assumed to be a unital C ∗ -algebra of real rank zero and B is an arbitrary Banach algebra.

Operator Theory on Symmetrized Bidisc

A commuting pair of operators (S, P ) on a Hilbert space H is said to be a Γ-contraction if the symmetrized bidisc Γ = {(z1 + z2, z1z2) : |z1|, |z2| ≤ 1} is a spectral set of the tuple (S, P ). In this paper we develop some operator theory inspired by Agler and Young’s results on a model theory for Γ-contractions. We prove a Beurling-Lax-Halmos type theorem for Γ-isometries. Along the way we solve a problem in the classical one-variable operator theory, namely, a non-zero Mz-invariant subspace S of H E∗(D) is invariant under the analytic Toeplitz operator with the operatorvalued polynomial symbol p(z) = A + A∗z if and only if the Beurling-Lax-Halmos inner multiplier Θ of S satisfies (A+A∗z)Θ = Θ(B +B∗z), for some unique operator B. We use a ”pull back” technique to prove that a completely non-unitary Γ-contraction (S, P ) can be dilated to a pair (((A+AMz)⊕ U), (Mz ⊕Meit)), which is the direct sum of a Γ-isometry and a Γ-unitary on the Sz.-Nagy and Foias functional model of P , and that (S, P ) can be realized as a compression of the above pair in the functional model QP of P as (PQP ((A+A Mz)⊕ U)|QP , PQP (Mz ⊕Meit)|QP ). Moreover, we show that this representation is unique. We identify a complete set of unitary invariants for the class of completely non-unitary Γ-contractions. We prove that a commuting tuple (S, P ) with ∥S∥ ≤ 2 and ∥P∥ ≤ 1 is a Γ-contraction if and only if there exists a bounded linear operator X such that S = X +X∗P and both X and X∗ commutes with P and the numerical radius w(X) ≤ 1. In the commutant lifting set up, we obtain a unique and explicit solution to the lifting of S where (S, P ) is a completely non-unitary Γ-contraction. Our results concerning the Beurling-Lax-Halmos theorem of Γ-isometries and the functional model of Γ-contractions answers a pair of questions of J. Agler and N. J. Young.

Distinguishing co‐existing unimolecular and bimolecular structural forms using joint analysis of Raman and UV absorption data

Standard Raman measurements of solutions require relatively high concentration of dissolved species, which supports formation of intermolecular complexes. In case of simultaneous presence of unimolecular and bimolecular structural forms, it is often difficult or even impossible to discriminate between them by using only the Raman data. We present a possible and effective way how to combine temperature dependencies of Raman scattering and UV absorption in a joint thermodynamic analysis. This approach is based on a joint fit of the results of multivariate analysis (singular value decomposition) of individual Raman and UV absorption spectral sets to a thermodynamic model. Our case study on RNA oligonucleotides, which can form imperfect intermolecular duplexes or intramolecular hairpin structures, demonstrates that this approach allows to determine thermodynamic parameters of co‐existing unimolecular and bimolecular structural forms and to isolate their Raman spectra. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Independent component analysis and multivariate curve resolution to improve spectral interpretation of complex spectroscopic data sets: Application to infrared spectra of marine organic matter aggregates

The aim of this study is the identification of the most reliable multivariate technique for an efficient structural characterization of complex IR data sets. Different samples of organic matter (OM) aggregates were chosen as an object of investigation. In fact, the simultaneous presence of different biomolecules such as carbohydrates proteins and lipids makes difficult the interpretation and the comparison of the most significant fractions and structures, which describe the mechanisms of OM aggregation. With this aim, we collected the FTIR spectra of several samples of normal and anomalous size aggregates of organic matter and then submitted them to independent component analysis (ICA) by means of the algorithms fast independent component analysis (FastICA), joint approximate diagonalization of eigenmatrices (JADE), mutual information least dependent component analysis (MILCA) as well as to multivariate curve resolution alternate least squares (MCR-ALS). Among ICA algorithms, the MILCA was the most efficient because it always allowed a good spectra resolution and a higher number of significant and chemically interpretable components than the FastICA and the JADE algorithms, avoiding in addition the presence of some spectral ambiguities often observed when the two last ICA algorithms were applied. For the examined spectral sets, MCR-ALS gave comparable results with MILCA in terms of the number of identified components and for the exclusion of spectral ambiguities, though we observed some differences between MILCA and MCR-ALS. For instance, MCR-ALS spectra generally resulted more resolved than MILCA ones for all spectral sets, supporting the reduction of the spectral noise, but for one specific spectral set, it showed some misleading spectra, not observed in the corresponding MILCA treatment.The different abilities of these multivariate methods were briefly discussed. The influence of different pre-processing techniques (mean-centering, Pareto scaling, derivatives) on the decomposition results was also investigated. ICA and MCR-ALS deconvolution combined with appropriate preprocessing are capable to deal with complex IR data sets regarding separation of meaningful information from noise and its interpretation.