Properties Of Spectrum Research Articles

Threshold for blowup for the supercritical cubic wave equation

We consider the focusing cubic wave equation in the energy supercritical case, i.e. in dimensions . For this model an explicit nontrivial self-similar blowup solution was recently found by the first and third author in Glogić and Schörkhuber (2018 (arXiv:1810.07681)). Furthermore, the solution is proven to be co-dimension one stable in d = 7. In this paper, we study the equation from a numerical point of view. For d = 5 and d = 7 in the radial case, we provide evidence that this solution is at the threshold between generic ODE blowup and dispersion. In addition, we investigate the spectral problem that underlies the stability analysis and compute the spectrum in general supercritical dimensions.

Three dimensional excitation-emission matrix fluorescence spectroscopy of typical Japanese soil powders.

Front face fluorescence spectroscopy of typical Japanese soil powders (soil A: Typic Hapludand; soil H: Typic Hydraquent; soil Y: Typic Paleudult) has been conducted. Three dimensional excitation-emission matrix fluorescence spectra of the 100wt% soils showed similar fluorescence patterns to each other. The fluorescence patterns were similar between the soil samples and their residues after extraction by NaOH solution for 60min. In order to examine fluorescence extinction from a view point of whiteness of the soils, the soil powders were mixed with white and black diluents (Al2O3 and Fe3O4) and fluorescence spectra of the mixtures were measured at 450nm excitation. At low levels of dilution with Al2O3 (2-100wt% of A; 50-100wt% of H and Y), the fluorescence intensities increased with dilution. At high levels of dilution with Al2O3, the fluorescence intensities decreased with dilution. On the other hand, fluorescent intensities decreased by dilution with Fe3O4. These results suggested inner filter effect-like fluorescence extinction by (1) large amount of blackish organic compounds giving high total carbon value and (2) blackish non-fluorescent mineral compounds. In order to correct the fluorescence intensities of the mixtures containing the sample soils and the diluents, we preliminary applied a correction method based on the Kubelka-Munk theory using diffuse reflectance. The corrected fluorescence intensities of samples with white diluents (Al2O3) were described by a simple fluorescence response model having saturation values.

A Second-Quantized Kolmogorov–Chentsov Theorem via the Operator Product Expansion

We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the object of recent progress thanks to Hairer’s theory of regularity structures and the theory of paracontrolled distributions introduced by Gubinelli, Imkeller and Perkowski. The second topic is Wilson’s operator product expansion which is a general property of models of quantum field theory and a cornerstone of the bootstrap approach to conformal field theory. Our main result is a general theorem for the almost sure construction of products of random distributions by mollification and suitable additive as well as multiplicative renormalizations. The hypothesis for this theorem is the operator product expansion with precise bounds for pointwise correlations. We conjecture these bounds to be universal features of quantum field theories with gapped dimension spectrum. Our theorem can accommodate logarithmic corrections, anomalous scaling dimensions and even lack of translation invariance. However, it only applies to fields with short distance singularities that are milder than white noise. As an application, we provide a detailed treatment of a scalar conformal field theory of mean field type, i.e., the fractional massless free field also known as the fractional Gaussian field.

Length Reduction of Singular Spectrum Analysis With Guarantee Exact Perfect Reconstruction via Block Sliding Approach

The conventional singular spectrum analysis is to divide a signal into segments where there is only one non-overlapping point between two consecutive segments. By putting these segments into the columns of a matrix and performing the singular value decomposition on the matrix, various one dimensional singular spectrum analysis vectors are obtained. Since different one dimensional singular spectrum analysis vectors represent different parts of the signal such as the trend part, the oscillation part and the noise part of the signal, the singular spectrum analysis plays a very important role in the nonlinear and adaptive signal analysis. However, as the length of each one dimensional singular spectrum analysis vector is the same as that of the original signal, there is a redundancy among these one dimensional singular spectrum analysis vectors. In order to reduce the required computational power and the required units for the memory storage for performing the singular spectrum analysis, this article proposes a method to reduce the total number of the elements of all the one dimensional singular spectrum analysis vectors. In particular, the length of the shift block for generating the trajectory matrix is increased from one to a positive integer greater than one under a certain criterion. In this case, the total number of the columns of the trajectory matrix is reduced. As a result, the total number of the off-diagonals of all the two dimensional singular spectrum analysis matrices is reduced. Hence, the total number of the elements of all the one dimensional singular spectrum analysis vectors is reduced. In order to guarantee exact perfect reconstruction, this article reformulates the de-Hankelization process. In particular, the first element of the off-diagonals of all the two dimensional singular spectrum analysis matrices is taken as the elements of the one dimensional singular spectrum analysis vectors. Exact perfect reconstruction condition is derived. Simulations show that exact perfect reconstruction can be achieved while the total number of the elements of all the one dimensional singular spectrum analysis vectors is significantly reduced.

Multisource Latent Feature Selective Ensemble Modeling Approach for Small-Sample High-Dimensional Process Data in Applications

Several difficult-to-measure production qualities or environment pollution indices of industrial process must be measured using offline laboratory instruments. Soft measurement method is often used to perform online prediction of such parameters. Only small-sample modeling data with high-dimensional input features can be obtained due to the limitations and complex characteristics of the measurement device and process, respectively. Therefore, a new multisource latent feature selective ensemble (SEN) modeling approach is proposed in this study. First, input features are divided into different subgroups according to the characteristics of the modeling data. Second, the extracted multisource latent features evolve from the multi-layered selection algorithms, which are specified by feature reduction ratio, feature contribution ratio and mutual information value orderly for each subgroup. Finally, in order to construct candidate sub-models, an adaptive hyper-parameter selection algorithm based on the multi-step grid search is employed in terms of the reduced features. Sequentially, the optimized ensemble submodels with their weighting strategies are adaptively determined to build the final SEN model. The proposed method is verified by using benchmark near-infrared data, high dimensional mechanical frequency spectrum data and industrial dioxin emission concentration data.

Photon echoes and two dimensional spectra of the amide I band of proteins measured by femtosecond IR - Raman spectroscopy.

Infrared (IR) and Raman spectroscopy are fundamental techniques in chemistry, allowing the convenient determination of bond specific chemical composition and structure. Over the last decades, ultrafast multidimensional IR approaches using sequences of femtosecond IR pulses have begun to provide a new means of gaining additional information on molecular vibrational couplings, distributions of molecular structures and ultrafast molecular structural dynamics. In this contribution, new approaches to measuring multidimensional spectra involving IR and Raman processes are presented and applied to the study of the amide I band of proteins. Rephasing of the amide I band is observed using dispersed IR-Raman photon echoes and frequency domain 2D-IR-Raman spectra are measured by use of a mid-IR pulse shaper or over a broader spectral range using a tuneable picosecond laser. A simple pulse shaping approach to performing heterodyned time-domain Fourier Transform 2D-IR-Raman spectroscopy is introduced, revealing that the 2D-IR-Raman spectra distinguish homogeneous and inhomogeneous broadening in the same way as the well-established methods of 2D-IR spectroscopy. Across all datasets, the unique dependence of the amide I data on the IR and Raman strengths, vibrational anharmonicities and inhomogeneous broadening provides a fascinating spectroscopic view of the amide I band.

Histogram tomography

In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors tensors and functions. The data can also be higher dimensional and in many cases consists of a one or two dimensional spectrum for each ray. In many such cases the data contain not just integrals along rays but the distribution of values along the ray. If this is discretized into bins we can think of this as a histogram. In this paper we introduce the concept of "histogram tomography". For scalar problems with histogram data this holds the possibility of reconstruction with fewer rays. In vector and tensor problems it holds the promise of reconstruction of images that are in the null space of related integral transforms. For scalar histogram tomography problems we show how bins in the histogram correspond to reconstructing level sets of function, while moments of the distribution are the x-ray transform of powers of the unknown function. In the vector case we give a reconstruction procedure for potential components of the field. We demonstrate how the histogram longitudinal ray transform data can be extracted from Bragg edge neutron spectral data and hence, using moments, a non-linear system of partial differential equations derived for the strain tensor. In x-ray diffraction tomography of strain the transverse ray transform can be deduced from the diffraction pattern the full histogram transverse ray transform cannot. We give an explicit example of distributions of strain along a line that produce the same diffraction pattern, and characterize the null space of the relevant transform.

Model of assessment of the hardness of the iron rollers СПХН-43 and СШХНФ-47

Relevance of the article. The quality criteria of massive metal products is affected by many technological parameters. Changing some of these parameters can lead to a significant change in the quality of the target product. Therefore, various types of models are widely used in materials science to simulate individual processes or predict individual criteria. An analysis of literary sources indicates the prospects of using fractal geometry to model the structure and properties of various materials. It is proposed to apply multifractal analysis to assess the structure of cast-iron rolls. Materials and methods. The influence of the structure of cast irons on their hardness was investigated. The microstructure of cast iron was investigated using quantitative methods of metallography (ГОСТ 3443) and multifractal analysis. The calculation of the spectrum of statistical dimensions of the cast iron microstructure was carried out according to the Renyi formula. The hardness indices of the roll-forming rolls СПХН-43 (520 ´ 1 000 mm) and СШХНФ-47 (680 ´ 1 000 mm) were determined at three points evenly spaced along the length of the roll barrel. Results and its discussion. The influence of the spectrum of statistical dimensions D 0 , D 1 , D 2 , D -100 and D 100 of carbides, lamellar and spherical graphite on the hardness indices of cast iron rolls is studied. It was found that the pair correlation coefficients in the prediction of hardness according to the traditional characteristics of the structure (length, diameter, area) are R 2 = 0,73...0,87. The correlation coefficients in the prediction of hardness by multifractal characteristics for rolls СПХН-43 are 0,78...0,88. For rolls СШХНФ-47, the correlation coefficients are 0,81...0,93. The obtained results confirm the effectiveness of using multifractal analysis in assessing the quality criteria of cast-iron rolls. Scientific novelty. The influence of multifractal dimensions of graphite and carbides on the hardness of cast iron rolls СПХН-43 and СШХНФ-47 is established. The sensitivity of the СПХН-43 roll hardness indices to the information and correlation dimensions of carbides, as well as to the fractal and statistical D -100 dimensions of plate graphite, was revealed. The sensitivity of hardness indices to the fractal and statistical D 100 dimensions of carbides and to the fractal and correlation dimensions of spherical graphite was established for the СШХНФ-47 rolls. Conclusions. Based on the results obtained, an approach has been developed to assess the hardness indices of rolls СПХН-43 and СШХНФ-47, which includes: 1) Determination of the spectrum of statistical dimensions of structural elements of cast irons. 2) Determination of sensitivity coefficients of hardness indicators to the spectrum of dimensions of structural elements. 3) Construction of a mathematical model for forecasting roll hardness. The approach considered can be interpreted as an alternative method for assessing the quality criteria of cast irons based on an analysis of their structure.

Breast Cancer Detection with Low-dimension Ordered Orthogonal Projection in Terahertz Imaging.

This paper proposes a new dimension reduction algorithm based on low-dimension ordered orthogonal projection (LOOP), which is used for cancer detection with terahertz (THz) images of freshly excised human breast cancer tissues. A THz image can be represented by a data cube with each pixel containing a high dimension spectrum vector covering several THz frequencies, where each frequency represents a different dimension in the vector. The proposed algorithm projects the high-dimension spectrum vector of each pixel within the THz image into a low-dimension subspace that contains the majority of the unique features embedded in the image. The low-dimension subspace is constructed by sequentially identifying its orthonormal basis vectors, such that each newly chosen basis vector represents the most unique information not contained by existing basis vectors. A multivariate Gaussian mixture model is used to represent the statistical distributions of the low-dimension feature vectors obtained from the proposed dimension reduction algorithm. The model parameters are iteratively learned by using unsupervised learning methods such as Markov chain Monte Carlo or expectation maximization, and the results are used to classify the various regions within a tumor sample. Experiment results demonstrate that the proposed method achieves apparent performance improvement in human breast cancer tissue over existing approaches such as one-dimension Markov chain Monte Carlo. The results confirm that the dimension reduction algorithm presented in this paper is a promising technique for breast cancer detection with THz images, and the classification results present a good correlation with respect to the histopathology results of the analyzed samples.

A High-Resolution Framework for Range-Doppler Frequency Estimation in Automotive Radar Systems

In this paper, a signal processing framework using high-resolution algorithms is applied to automotive radar systems for target separation purposes. In many critical use cases, targets sharing similar parameters, i.e., range and relative velocity, can hardly be discriminated in a 2-dimensional (2-D) range-Doppler spectrum via conventional radar signal processing techniques. The proposed framework by taking advantage of a 2-D model-based algorithm with high-resolution capability, i.e., modified matrix enhancement and matrix pencil (MMEMP), is able to separate the overlapping targets by jointly estimating their aforementioned target parameters in a precise manner. Additionally, to reduce computational cost, the presented framework could preselect the peaks (local maxima) of interest via a 2-D model order selection algorithm, i.e., 2-D subspace-based automatic model order selection (2-D SAMOS), and apply the MMEMP only in multi-target situations. Finally, simulation and experiments are carried out to evaluate the performance of the proposed high-resolution target separation framework.

Anisotropy of the Spectral Index in Ion Scale Compressible Turbulence: MMS Observations in the Magnetosheath

Turbulence in the Earth’s magnetosheath at ion kinetic scales is investigated with the Magnetospheric MultiScale (MMS) spacecraft. The multi-point measurements allow the three dimensional power spectra in wave-vector space to be determined. Previously the three dimensional structure of fluctuations in the magnetic field and density (using spacecraft potential as a proxy) were possible with Cluster. However, using the excellent time resolution data set provided from both the Fluxgate Magnetometer (FGM) and the Fast Plasma Investigation (FPI) on MMS the spectra can be determined for a number of different parameters such as ion velocity, and ion temperatures parallel and perpencidular to the mean magnetic field directions. The spectra for different fluctuations show similar features to one another such as a strong power anisotropy with respect to the mean magnetic field direction, such that the energy decays faster in the direction parallel to the mean magnetic field than the perpendicular direction. A weak non-gyrotropy is also seen in the direction of the bulk velocity similar to what has been seen in magnetic field fluctuations with Cluster at ion kinetic scales in the solar wind. Velocity fluctuations are shown to be the most anisotropic. The density and temperature fluctuations exhibit similar anisotropies but are much weaker in comparison.

Prediction of terminal velocity of fractal aggregates with IBM-LBM method

The settling of well-characterised fractal aggregates has been investigated numerically. The Immersed Boundary Method coupled with the Lattice Boltzmann Method (IBM-LBM) was developed to fully solve the liquid flow passing through the porous aggregate. Aggregates with prescribed structures covering the large spectrum of fractal dimension were fabricated and the benchmark experimental data have been collected to extensively validate the numerical model. Subsequently, the settling dynamics of fractal aggregates in liquid in terms of orientation evolution, time dependent drag force and terminal orientation was investigated and correlated to their morphological characteristics. Different equations have been developed for predicting the terminal settling velocity of fractal aggregates. A correlation that only requires inputs of primary particle size and fractal dimension is proposed for predicting the terminal velocity of fractal aggregates. Deviations less than 7% were obtained when applying the model for aggregates with the primary particle size ranging between 1.5 mm and 5 mm. The model's applicability to small aggregates comprised of primary particles less than 1 mm has also been demonstrated and discussed.

Synchronization in Interpersonal Speech.

During both positive and negative dyadic exchanges, individuals will often unconsciously imitate their partner. A substantial amount of research has been made on this phenomenon, and such studies have shown that synchronization between communication partners can improve interpersonal relationships. Automatic computational approaches for recognizing synchrony are still in their infancy. In this study, we extend on previous work in which we applied a novel method utilizing hand-crafted low-level acoustic descriptors and autoencoders (AEs) to analyse synchrony in the speech domain. For this purpose, a database consisting of 394 in-the-wild speakers from six different cultures, is used. For each speaker in the dyadic exchange, two AEs are implemented. Post the training phase, the acoustic features for one of the speakers is tested using the AE trained on their dyadic partner. In this same way, we also explore the benefits that deep representations from audio may have, implementing the state-of-the-art Deep Spectrum toolkit. For all speakers at varied time-points during their interaction, the calculation of reconstruction error from the AE trained on their respective dyadic partner is made. The results obtained from this acoustic analysis are then compared with the linguistic experiments based on word counts and word embeddings generated by our word2vec approach. The results demonstrate that there is a degree of synchrony during all interactions. We also find that, this degree varies across the 6 cultures found in the investigated database. These findings are further substantiated through the use of 4,096 dimensional Deep Spectrum features.

On the dimension spectrum of infinite subsystems of continued fractions

In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if E E is any arithmetic progression, the set of primes, or the set of squares { n 2 } n ∈ N \{n^2\}_{n \in \mathbb {N}} , then the continued fractions whose digits lie in E E have full dimension spectrum, which we denote by D S ( C F E ) DS(\mathcal {CF}_E) . Moreover we prove that if E E is an infinite set of consecutive powers, then the dimension spectrum D S ( C F E ) DS(\mathcal {CF}_E) always contains a non-trivial interval. We also show that there exists some E ⊂ N E \subset \mathbb {N} and two non-trivial intervals I 1 , I 2 I_1, I_2 , such that D S ( C F E ) ∩ I 1 = I 1 DS(\mathcal {CF}_E) \cap I_1=I_1 and D S ( C F E ) ∩ I 2 DS(\mathcal {CF}_E) \cap I_2 is a Cantor set. On the way we employ the computational approach of Falk and Nussbaum in order to obtain rigorous effective estimates for the Hausdorff dimension of continued fractions whose entries are restricted to infinite sets.

Multifractal spectra of Moran measures without local dimension

A measure without local dimension is a measure such that local dimension does not exist for any point in its support. In this paper, we construct such a class of Moran measures and study their lower and upper local dimensions. We show that the related ‘free energy’ function (Lq-spectrum) does not exist. Nevertheless, we can obtain the full Hausdroff and packing dimension spectra for level sets defined by lower and upper local dimensions. They can be viewed as a generalized multifractal formalism.

A nitrogen spectral response model and nitrogen estimation of summer maize during the entire growth period

ABSTRACT Timely and effective prediction of nitrogen content in summer maize could provide support data for precise fertilization. In this study, the feasibility and expansibility of predicting the nitrogen mechanism model of summer maize leaves through its entire growth period were investigated on the basis of the theory of leaf radiation transmission mechanism. A complete random test of data from two maize varieties and two nitrogen fertilizer applications in 2017 was conducted. Three versions of the leaf optical PROperties SPECTra (PROSPECT) model, namely, PROSPECT-4, PROSPECT-5, and PROSPECT-D were used to link the established leaf nitrogen density (LND) and chlorophyll-a + b (chl-a + b) models, that is, chl-a + b-LND model. A nitrogen response transfer model (N-RTM) was established by linking the optimal PROSPECT and chl-a + b-LND models. Results were as follows. (1) chl-a + b estimation using the PROSPECT-D model yielded the highest accuracy (the coefficient of determination (R 2) = 0.774, the normalized root mean squared error (nRMSE) = 13.19%) among the three PROSPECT models, it shows that the model considering more factors can better reflect the internal law of blade, and could be used as the basic model of N-RTM; (2) Established chl-a + b-LND models based on the dataset from each growth stage showed differences using the confidence interval method, and the R 2 values of the optimal regression model at V12, VT, and R3 were 0.794, 0.781, and 0.821, respectively. Based on the changes of chl-a + b and LND during the growth period, a piecewise model was constructed; (3) The R 2 and nRMSE values between the measured and estimated LNDs were 0.656% and 22.86%, respectively. The validation results are better than the traditional empirical model. The results showed that the segmented model, which considered the interaction of various factors within the leaves and the change of chl-a + b-LND during the growth period, had better performance in nitrogen monitoring. The constructed nitrogen model in this study preliminarily realized the remote sensing prediction of the nitrogen mechanism model and had a certain mechanism.

Gravitational waves as a probe of the extra dimension

We consider the Einstein-Hilbert action without cosmological constant in 5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For non-zero compactification radius, the 4- dimensional spectrum contains massless and massive KK modes. For the massive KK modes, we retain four KK tensor and one KK scalar modes after a gauge fixing. We treat those massive KK modes as stochastic sources of gravitational wave (GW) with characteristic dependences of the frequencies on the size of the extra dimension. Using the observational bounds on the size of the extra dimension and on the characteristic strain, we make an order estimation on the frequencies and amplitudes of the massive KK modes that can contribute to the GW.

Price, Cultural Dimensions, and the Cross-Section of Expected Stock Returns

We document a nominal stock price effect that is (like momentum) associated with (national) culture. Using the full spectrum of cultural dimensions proposed by Hofstede et al. and the cross-section of stock returns of 41 countries, we not only show a robust predictive and explanatory power of price in conjunction with several cultural dimensions, but of cultural differences in general. Although momentum and price are related investment strategies, we find a broad (escalating) European high-price effect, but a material low-price effect in Asia as well as the most significant and robust low-price effect for the US. Most consistent around the world, high-priced stocks show lower return volatility and market betas than low-priced stocks and lower values for skewness of returns.

Mathcal{N} = 2 Liouville SCFT in four dimensions

We construct a Liouville superconformal field theory with eight real supercharges in four dimensions. The Liouville superfield is an mathcal{N} = 2 chiral superfield with sixteen bosonic and sixteen fermionic component fields. Its lowest component is a logcorrelated complex scalar field whose real part carries a background charge. The theory is non-unitary with a continuous spectrum of scaling dimensions. We study its quantum dynamics on the supersymmetric 4-sphere and show that the classical background charge is not corrected quantum mechanically. We calculate the super-Weyl anomaly coefficients and find that c vanishes, while a is negative and depends on the background charge. We derive an integral expression for the correlation functions of superfield vertex operators in mathcal{N} = 2 superspace and analyze them in the semiclassical approximation by using a quaternionic formalism for the mathcal{N} = 2 superconformal algebra.

Multifractal analysis and evolution rules of micro-fractures in brittle tectonically deformed coals of Yangquan mining area

Micro-fractures act as a bridge between pores and macro-fractures and directly affect the permeability of coal reservoirs. Understanding the micro-fracture heterogeneity and its relationships with deformation can enrich our knowledge on the gas transportation behavior of tectonically deformed coals. The multifractal theory was applied to characterize the variations and heterogeneity of micro-fractures in high-rank brittle tectonically deformed coals. The results indicated that the micro-fractures exhibit multifractal behavior at e = 1–1/16 (e being the size of the boxes considered), and that the obtained generalized dimension spectra Dq-q, multifractal singularity spectrum f(α)-α, and characteristic parameters, including the capacity dimension D0, information dimension D1, correlation dimension D2, D1/D0, the width of multifractal spectrum Δα, and the difference of the fractal dimensions Δf(α), can be applied to accurately describe the differences and variations of the micro-fracture distributions and scales. Moreover, the deformation has a significant influence on the variation and heterogeneity of micro-fracture distributions and scales, as demonstrated by the change rules of the characteristic parameters. The D1, D2, and D1/D0 increased with the increase of deformation degree, while Δα and Δf(α) decreased. Consequently, the deformation leads to higher density, more uniform distributions, and more dispersed and complex scales in the micro-fractures of brittle tectonically deformed coals, and controls the permeability of coal reservoirs.