Properties Of Spectrum Research Articles

Dimension spectrum of infinite self-affine iterated function systems

Given an infinite iterated function system (IFS) {mathcal {F}}, we define its dimension spectrum D({mathcal {F}}) to be the set of real numbers which can be realised as the dimension of some subsystem of {mathcal {F}}. In the case where {mathcal {F}} is a conformal IFS, the properties of the dimension spectrum have been studied by several authors. In this paper we investigate for the first time the properties of the dimension spectrum when {mathcal {F}} is a non-conformal IFS. In particular, unlike dimension spectra of conformal IFS which are always compact and perfect (by a result of Chousionis, Leykekhman and Urbański, Selecta 2019), we construct examples to show that D({mathcal {F}}) need not be compact and may contain isolated points.

Three-loop off-forward evolution kernel for axial-vector operators in Larin’s scheme

Evolution equations for leading-twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at noninteger $d=4\ensuremath{-}2ϵ$ space-time dimensions. In this work, we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin's scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional modified minimal subtraction scheme. The results are directly applicable to deeply virtual Compton scattering and the transition form factor ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\pi}$.

Multifractal Characteristics Analysis Based on Slope Distribution Probability in the Yellow River Basin, China

Multifractal theory provides a reliable method for the scientific quantification of the geomorphological features of basins. However, most of the existing research has investigated small and medium-sized basins rather than complex and large basins. In this study, the Yellow River Basin and its sub-basins were selected as the research areas, and the generalized fractal dimension and multifractal spectrum were computed and analyzed with a multifractal technique based on the slope distribution probability. The results showed that the Yellow River Basin and its sub-basins exhibit clear multifractal characteristics, which indicates that the multifractal theory can be applied well to the analysis of large-scale basin geomorphological features. We also concluded that the region with the most uneven terrain is the Yellow River Downstream Basin with the “overhanging river”, followed by the Weihe River Basin, the Yellow River Mainstream Basin, and the Fenhe River Basin. Multifractal analysis can reflect the geomorphological feature information of the basins comprehensively with the generalized fractal dimension and the multifractal spectrum. There is a strong correlation between some common topographic parameters and multifractal parameters, and the correlation coefficients between them are greater than 0.8. The results provide a scientific basis for analyzing the geomorphic characteristics of large-scale basins and for the further research of the morphogenesis of the forms.

The Hausdorff dimension spectrum of Renyi-like continued fractions

In this paper, we look at a family of Renyi-like continued fraction expansions and the associated conformal iterated function systems. We show that for every k≥2, every such associated system has full Hausdorff dimension spectrum. We construct two examples of iterated function systems that do not have full Hausdorff dimension spectrum. One is a subsystem of any given Renyi-like system, while the second consists of similarities.

Ionization in intense laser fields beyond the electric dipole approximation: concepts, methods, achievements and future directions

The electric dipole approximation is widely used in atomic, molecular and optical physics and is typically related to a regime for which the wavelength is much larger than the atomic structure. However, studies have shown that in strong laser fields another regime exists where the dipole approximation breaks down. During the ionization process in intense laser fields and at long wavelengths the photoelectrons can reach higher velocities such that the magnetic field component of the laser field becomes significant. The ionization dynamics and the final momentum of the electron is therefore modified by the entire Lorentz force. In contrast the magnetic field interaction is neglected in the dipole approximation. Rapid developments in laser technology and advancements in the accuracy of the measurements techniques have enabled the observation of the influence of such non-dipole effects on the final angular photoelectron momentum distributions. More recently the number of studies on ionization beyond the dipole approximation has increased significantly, providing more important insight into fundamental properties of ionization processes. For example we have shown that the final three dimensional photoelectron momentum spectra is significantly affected by the non-dipole drift with the parent–ion interaction, the linear multiphoton momentum transfer on a sub-cycle time scale and the sharing of the transferred linear photon momenta between the electron and the ion. In this article we present an overview of the underlying mechanisms and we review the experimental techniques and the achievements in this field. We focus on ionization in strong laser fields in the regime where the dipole approximation is not valid but a fully relativistic description is not required.

Assouad dimension influences the box and packing dimensions of orthogonal projections

We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the (quasi-)Assouad dimension of F \subseteq\mathbb{R}^n is no greater than m , then the box and packing dimensions of F are preserved under orthogonal projections onto almost all m -dimensional subspaces. We also show that the threshold m for the (quasi-)Assouad dimension is sharp, and bound the dimension of the exceptional set of projections strictly away from the dimension of the Grassmannian.

Geographical discrimination of Boletus edulis using two dimensional correlation spectral or integrative two dimensional correlation spectral image with ResNet

Boletus edulis (B. edulis) is a well-known edible mushroom species in the world due to its high nutritional values. However, its nutritional value varies greatly depending on geographical origins. This study aimed to discriminate the geographical regions of B. edulis by using a novel digital image method based on two dimensional correlation spectra (2DCOS) or integrative two dimensional correlation spectra (i2DCOS). In our research, 106 fruiting bodies of wild-grown B. edulis mushrooms were collected from 2011 to 2014 in 6 geographical regions. We intercepted 1750-400 cm−1 fingerprint regions from their mid-infrared (MIR) spectra, and converted them into 2DCOS or i2DCOS spectra with matlab2017b. Then, a residual convolutional neural network (ResNet) was established with 95 (90%) spectral images. In our model, the discrimination of geographical regions of the Boletus was using directly synchronous 2DCOS, asynchronous 2DCOS or i2DCOS spectral images instead of data matric from these spectra. In the synchronous 2DCOS spectra model, these 95 samples could be correctly classified as their respective regions with 100% accuracy in the train set and 100% accuracy in the test set, and all 11 (10%) samples of external validation set were discriminated correctly. The results indicated that the synchronous 2DCOS spectra model has good discrimination performance, and the new analytical method in this paper can be used for quality control of food, herb and agricultural products.

The incandescent light bulb phase-out: exploring patterns of framing the governance of discontinuing a socio-technical regime

Research interestThis paper aims at a better understanding of the governance of the abandonment of socio-technical regimes through the example of the incandescent light bulb phase-out in the European Union and in the Netherlands as one specific case where the EU discontinuation policy has been implemented. In particular, with this paper we focus on the active and intended discontinuation of a socio-technical regime through dedicated governance.MethodsWe approached the phase-out of the incandescent light bulb from a qualitative perspective and analysed about 230 documents from the EU and Dutch level. The study has an explorative character, for we cannot claim to describe the entire policy process, but bring to surface some key issues in order to outline both governance foci and technicalities of governing the phase-out. We looked into how governance makers were actually structuring the ILB phase-out as a governance task. The specific framings we found were grouped into the (a) spectrum of governance dimensions, (b) the more detailed problem-types raised, and (c) the array of discontinuation issues addressed in policy discourse dedicated to negotiating, drafting and implementing the phase-out measures.ResultsA set of frames apparent in the discontinuation discourses in the EU and the Netherlands has been reconstructed, which entails the five governance dimensions ‘policy instruments’, ‘implementation’, ‘strictness’, ‘monitoring’, and ‘policy level’. Technical details of both the socio-technical products to be banned and the replacing products have been the subject of meticulous negotiations in order to be able to implement the big picture, the lightbulb ban, appropriately and appropriately for both industry and environmental associations. The design of discontinuation governance at national and EU level are closely intertwined, but not identical in all aspects. The complexity of the governance task is therefore high.ConclusionsDiscontinuation has to cope with some resistance to dedicated, forced change that takes place in a technically as well as socially highly complex context. Governing the phase-out of a technical device, a production infrastructure, and industry support policy once supposed to support the EU and Dutch ILB industry was a major techno-political challenge, where policymakers needed to grasp key technical and technological problems. These were related to ILBs as objects, to subjects such as engineers and scientists, lobbyists and disinterested experts, to civil society organisations and mass media, along with all sorts of political and administrative issues and discourses. The challenges are threefold: first, translating for each other what cannot be known from one’s own background, second, shutting down governance which so far fostered lighting industry and, third, helping to change parts of this industry from an old, incumbent one to a new, emerging socio-technical regime with a regime providing a political and regulatory framework for it.

Deep learning can accelerate and quantify simulated localized correlated spectroscopy

Nuclear magnetic resonance spectroscopy (MRS) allows for the determination of atomic structures and concentrations of different chemicals in a biochemical sample of interest. MRS is used in vivo clinically to aid in the diagnosis of several pathologies that affect metabolic pathways in the body. Typically, this experiment produces a one dimensional (1D) 1H spectrum containing several peaks that are well associated with biochemicals, or metabolites. However, since many of these peaks overlap, distinguishing chemicals with similar atomic structures becomes much more challenging. One technique capable of overcoming this issue is the localized correlated spectroscopy (L-COSY) experiment, which acquires a second spectral dimension and spreads overlapping signal across this second dimension. Unfortunately, the acquisition of a two dimensional (2D) spectroscopy experiment is extremely time consuming. Furthermore, quantitation of a 2D spectrum is more complex. Recently, artificial intelligence has emerged in the field of medicine as a powerful force capable of diagnosing disease, aiding in treatment, and even predicting treatment outcome. In this study, we utilize deep learning to: (1) accelerate the L-COSY experiment and (2) quantify L-COSY spectra. All training and testing samples were produced using simulated metabolite spectra for chemicals found in the human body. We demonstrate that our deep learning model greatly outperforms compressed sensing based reconstruction of L-COSY spectra at higher acceleration factors. Specifically, at four-fold acceleration, our method has less than 5% normalized mean squared error, whereas compressed sensing yields 20% normalized mean squared error. We also show that at low SNR (25% noise compared to maximum signal), our deep learning model has less than 8% normalized mean squared error for quantitation of L-COSY spectra. These pilot simulation results appear promising and may help improve the efficiency and accuracy of L-COSY experiments in the future.

Spectrum Sensing Based On Deep Learning To Increase Spectrum Utilization

This paper proposes a new spectrum sensing technique for cognitive radio systems. To determine vacancy of the spectrum, the proposed method employs the recurrent neural network (RNN), one of the popular deep learning techniques. The proposed technique determines the spectrum occupancy of the primary user (PU) by observing the received signal’s energy and any information on the PU signal characteristic is not used. To this end, the received signal’s spectrum is obtained by fast Fourier transform (FFT). This process is performed on consecutive received signals and the resulting spectrums are stacked. Finally, a 2-dimensional spectrum (or spectrogram) is made. This 2-D spectrum is cut into sensing channel bandwidths and inputted to the deep learning model to decide the channel’s occupancy. While the recently published spectrum sensing technique based on convolutional neural network (CNN) relies on an empty channel, the proposed technique does not require any empty channel. Only the channel signal of interest to sense is needed. Since spectrum sensing results is two (busy or idle), binary classification deep learning model is developed. According to the computer simulation results, the proposed method has similar performance with the conventional CNN-based method while the spectral efficiency of the proposed method is much higher than that of the existing scheme. In addition, the overall learnable parameters of the proposed deep learning model is only 2/3 of the existing method

Application and Evolution for Neural Network and Signal Processing in Large-Scale Systems

Low frequency oscillation is an important attribute of human brain activity, and the amplitude of low frequency fluctuation (ALFF) is an effective method to reflect the characteristics of low frequency oscillation, which has been widely used in the treatment of brain diseases and other fields. However, due to the low accuracy of the current analysis methods for low frequency signal extraction of ALFF, we propose the Fourier-based synchrosqueezing transform (FSST), which is often used in the field of signal processing to extract the ALFF of the low frequency power spectrum of the whole-time dimension. The low frequency characteristics of the extracted signal are compared with those of FSST and fast Fourier transform (FFT) through the resting-state data. It is clear that the signal extracted by FSST has more low frequency characteristics, which is significantly different from FFT.

Involving FCGR images in studying fractality and multifractality in human chromosome 22 and bacteria complete genome

The frequency chaos game representation (FCGR) is a simple yet powerful visualization method of DNA sequences. It provides the possibility of representing genomes by images, revealing in such a way different fractal structures. In this paper, we perform a fractal and multifractal analysis of Human chromosome 22 and some complete genomes based on the FGCR image. We used the fractal dimension (FD) and the multifractality degree (ΔDq) to characterize and distinguish genomes. First, we construct the FCGR image with different orders of human chromosome 22. Next, we calculate the fractal dimension, the general dimension spectrum and the multifractal spectrum of each FCGR image using the box-counting method. Then, we examine the FCGR image fractal and multifractal characteristics impact on highlighting the existence of repetitive DNA sequences in human chromosome 22. We also observe the relationship between fractality and multifractality. After that, we apply this study to bacteria completes genomes and C.elegans chromosome I. The obtained results show that the multifractal spectra of all organisms studied are multifractal-like and chromosome 22 strong multifractality proves its richness of repetitive sequences. Also, we observed that with the increasing the FCGR order value, the multifractality grows and the fractal dimension lessens. Finally, by assigning to each sequence a point in two-dimensional space (FD, ΔDq), we obtained three classes of genomes. We can easily distinguish the human chromosome 22 from other genomes and Bacteria are almost close in the spaces (FD, ΔDq).

Personalized Image-Guided Therapies for Local Malignencies: Interdisciplinary Options for Interventional Radiology and Interventional Radiotherapy.

Minimal-invasive interventions considerably extend the therapeutic spectrum in oncology and open new dimensions in terms of survival, tolerability and patient-friendliness. Through the influence of image-guided interventions, many interdisciplinary therapy concepts have significantly evolved, and this process is by far not yet over. The rapid progression of minimal-invasive technologies offers hope for new therapeutic concepts in the short, medium and long term. Image-guided hybrid-technologies complement and even replace in selected cases classic surgery. In this newly begun era of immune-oncology, interdisciplinary collaboration and the focus on individualized and patient-friendly therapies are crucial.

The concept of motivation and its implication in additive disorders

IntroductionThe word motivation derives from the Latin movere, which means to move. In psychiatry, it is an isolated phenomenon found in the substrate of several pathologies, and may be part of an heterogeneous dimensional spectrum. However, there is no unique definition for it, nor a targeted approach. In addictive disorders motivation gains a fundamental role, both as a precipitant of abuse as in its withdrawal.ObjectivesTo review the literature about the concept of motivation and its implications on the psychopathology, especially on addictive disorders.MethodsNarrative review on PubMed/MEDLINE, using the keywords “motivation” AND “psychopatology” AND “addiction”. Articles in English and Portuguese were included.ResultsThree main perspectives were found addressing the concept of motivation in psychopathological terms: psychological, neurobiological and phenomenological. The first describes motivation as the energizing of behaviour in pursuit of a goal. Neurobiology says motivational drive is dependent on the concentration of extrasynaptic dopamine. In phenomenological terms, the concept stands for the web of solicitations that make a certain situation feel in a certain way for the subject. In addictive disorders, learning about what leads to reward, exaggeration in representing those values, and dominance in being guided by those representations lead to alterations on motivation mechanisms.ConclusionsMotivation is described from different perspectives. Although it is recognized as a fundamental piece in addictive disorders, besides motivational interview model, there are no pharmacological approaches aimed to improving motivation. The recognition of motivation as a concrete psychopathological alteration, and its measure through psychopathological instruments, could optimize the patient’s approach.

A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders

Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.

Improved NMR Detection of Phospho-Metabolites in a Complex Mixture.

Phosphorylated metabolites are omnipresent in cells, but their analytical characterization faces several technical hurdles. Here, we detail an improved NMR workflow aimed at assigning the high-resolution subspectrum of the phospho-metabolites in a complex mixture. Combining a pure absorption J-resolved spectrum (Pell, A. J.; J. Magn. Reson. 2007, 189 (2), 293-299) with alternate on- and off-switching of the 31P coupling interaction during the t1 evolution with a pure in-phase (PIP) HSQMBC experiment (Castañar, L.; Angew. Chem., Int. Ed. 2014, 53 (32), 8379-8382) without or with total correlation spectroscopy (TOCSY) transfer during the insensitive nuclei enhancement by polarization transfer (INEPT) gives access to selective identification of the individual subspectra of the phosphorylated metabolites. Returning to the initial J-res spectra, we can extract with optimal resolution the full trace for the individual phospho-metabolites, which can then be transposed on the high-resolution quantitative one dimensional spectrum.

Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged SL(2, ℝ) WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.

Typical and atypical multifractal systems of urban spaces—using construction land in Zhengzhou from 1988 to 2015 as an example

Abstract Urban spatial system is a pre-fractal system, which has a sensitive reaction zone similar to the self-organized critical state (SOC) of complex systems on different spatial scales. In this paper, theoretical analysis includes the interpretation of multifractal dimension spectrum (f(a)-a(q) fitted curve) and its parameters. According to q-value distribution area, the fitted curve is divided into interval A (typical multifractal system distribution), interval B (atypical multifractal system distribution) and interval C (mediocre distribution). Furthermore, this paper launches a case study of the four-year period of construction land in Zhengzhou since the reform and opening up to reveal the spatial-temporal evolution features and operational mechanism of this region from a broader dimension. Analysis shows that Zhengzhou's development has long been in a spatial development trend dominated by chaos (interval B) and mediocrity (interval C), and the influence of q-level with spatial multifractal feature (interval A) on each spatial scale is relatively weak. Until the 2010s, multifractal feature tends to be strengthened, and there is a tendency to dominate regional spatial evolution. The significance of this study is that the combination and evolution of three intervals of the f(a)-a(q) fitting curve can be used to reflect the trend and regularity of regional spatial multifractal system and spatial-temporal succession relationship between them, so as to deeply understand the inherent and complete development and evolution of the geographical objects.

Multifractal scaling analyses of urban street network structure: The cases of twelve megacities in China

Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifractal parameters. The results showed multifractal structure of urban street networks. The global multifractal dimension spectrums are inverse S-shaped curves, while the local singularity spectrums are asymmetric unimodal curves. If the moment order q approaches negative infinity, the generalized correlation dimension will seriously exceed the embedding space dimension 2, and the local fractal dimension curve displays an abnormal decrease for most cities. The scaling relation of local fractal dimension gradually breaks if the q value is too high, but the different levels of the network always keep the scaling reflecting singularity exponent. The main conclusions are as follows. First, urban street networks follow multifractal scaling law, and scaling precedes local fractal structure. Second, the patterns of traffic networks take on characteristics of spatial concentration, but they also show the implied trend of spatial deconcentration. Third, the development space of central area and network intensive areas is limited, while the fringe zone and network sparse areas show the phenomenon of disordered evolution. This work may be revealing for understanding and further research on complex spatial networks by using multifractal theory.

Experimental Study on Monitoring of Dike Piping Process Based on Acoustic Emission Technology

Acoustic emission (AE) is employed in this study to monitor piping failure process in the dike subjected to varied head action. Piping is the main reason for the seepage failure of dikes and dams, and the AE characterization of piping process is investigated. The laboratory experiments and data analyses were carried out using specially designed physical model and data acquisition systems. The monitored data were analyzed using four methods, namely, AE ringing count, fractal dimension, frequency domain analyses and b value. The analysis results showed that the piping failure process can be divided into 3 phases: seepage erosion, piping generation, and piping development. In different stage, the activity of the AE signals is related to seepage flow and seepage pressure. Based on the fractal dimension and waveform energy spectrum distribution analysis in the entire process of piping failure, the measured acoustic signals in the test can reflect both a seepage-induced and a soil-seepage induced AE. The AE ringing count fractal dimension and waveform energy spectrum can be used as new index monitoring the occurrence and development of piping. The abrupt change of AE fractal dimension and AE energy spectrums curve with time can be considered as the precursor to piping occurrence and piping development. What’s more the b value of the AE signal can be used to describe the piping state.