Invariance Properties Research Articles

GFBLS: Graph-regularized fuzzy broad learning system for detection of interictal epileptic discharges

Epilepsy as the most common neurological disorder globally has drawn more and more attention. However, it is time-consuming and labor-intensive for manual detection of interictal epileptic discharges (IEDs). Thus, there is an urgent need to develop an efficient and automated detection approach as a more accurate diagnostic alternative for epilepsy detection. Recently, fuzzy broad learning system (FBLS) has been recognized as an alternative to deep learning and utilized in various fields. Nevertheless, FBLS ignores the locally invariant property of data. To effectively address this issue and further improve the performance of FBLS, a novel graph-regularized fuzzy broad learning system (GFBLS) is first proposed based on graph regularization. Moreover, an automated GFBLS-based approach is proposed for IEDs detection from EEG recordings. In the proposed method, graph convolutional neural networks (GCN) is firstly utilized to extract features from line graphs with undirected connections, which are constructed by EEG recordings, then extracted features by GCN are fed into GFBLS for IEDs detection. The experimental results demonstrated that GFBLS can achieve accuracy of 92.20%, specificity of 90.90% and precision of 91.13% with the training time of only 31.6 s, which is superior or comparable performance compared with other state-of-the-art approaches.

Automatic selfadjoint-ideal semigroups for finite matrices

The notion of automatic selfadjointness of all ideals in a multiplicative semigroup of the bounded linear operators on a separable Hilbert space B(H) arose in a 2015 discussion with Heydar Radjavi who pointed out that B(H) and the finite rank operators F(H) possessed this unitary invariant property which category we named SI semigroups (for automatic selfadjoint ideal semigroups). Equivalent to the SI property is the solvability, for each A in the semigroup, of the bilinear operator equation A⁎=XAY which we believe is a new connection relating the semigroup theory with the theory of operator equations.We found in our earlier works in the subject that even at the basic level of singly generated semigroups, the investigation of SI semigroups led to interesting algebraic and analytic phenomena when generated by rank one operators, normal operators, partial and power partial isometries, subnormal-hyponormal-essentially normal operators, and weighted shift operators; and generated by commuting families of normal operators.In this paper, we focus on a separate Mn(C) treatment for singly generated SI semigroups that requires studying the solvability of the bilinear matrix equation A⁎=XAY in a multiplicative semigroup of finite matrices. This separate focus is needed because the techniques employed in our earlier works we could not adapt to finite matrices. In this paper we find that for certain classes of generators, being a partial isometry is equivalent to generating an SI semigroup. Such classes are: degree 2 nilpotent matrices, weighted shifts, and non-normal Jordan matrices. For the key tools used to establish these equivalences, we developed a number of necessary conditions for singly generated semigroups to be SI for the very general classes: nonselfadjoint matrices, nonzero nilpotent matrices, nonselfadjoint invertible matrices, and Jordan blocks. We also show, for a nonselfadjoint matrix generator in an SI semigroup, the matrix being a partial isometry is equivalent to having norm one. And as an aside, we also prove necessary generator conditions for the SI property when generated by matrices with nonnegative entries.

Numerical Simulation of Hydrogen Diffusion in Cement Sheath of Wells Used for Underground Hydrogen Storage

The negative environmental impact of carbon emissions from fossil fuels has promoted hydrogen utilization and storage in underground structures. Hydrogen leakage from storage structures through wells is a major concern due to the small hydrogen molecules that diffuse fast in the porous well cement sheath. The second-order parabolic partial differential equation describing the hydrogen diffusion in well cement was solved numerically using the finite difference method (FDM). The numerical model was verified with an analytical solution for an ideal case where the matrix and fluid have invariant properties. Sensitivity analyses with the model revealed several possibilities. Based on simulation studies and underlying assumptions such as non-dissolvable hydrogen gas in water present in the cement pore spaces, constant hydrogen diffusion coefficient, cement properties such as porosity and saturation, etc., hydrogen should take about 7.5 days to fully penetrate a 35 cm cement sheath under expected well conditions. The relatively short duration for hydrogen breakthrough in the cement sheath is mainly due to the small molecule size and high hydrogen diffusivity. If the hydrogen reaches a vertical channel behind the casing, a hydrogen leak from the well is soon expected. Also, the simulation result reveals that hydrogen migration along the axial direction of the cement column from a storage reservoir to the top of a 50 m caprock is likely to occur in 500 years. Hydrogen diffusion into cement sheaths increases with increased cement porosity and diffusion coefficient and decreases with water saturation (and increases with hydrogen saturation). Hence, cement with a low water-to-cement ratio to reduce water content and low cement porosity is desirable for completing hydrogen storage wells.

Income distribution in Thailand is scale-invariant.

This study examines whether income distribution in Thailand has a property of scale invariance or self-similarity across years. By using the data on income shares by quintile and by decile of Thailand from 1988 to 2021, the results from 306-pairwise Kolmogorov-Smirnov tests indicate that income distribution in Thailand is statistically scale-invariant or self-similar across years with p-values ranging between 0.988 and 1.000. Based on these empirical findings, this study would like to propose that, in order to change income distribution in Thailand whose pattern had been persisted for over three decades, the change itself cannot be gradual but has to be like a phase transition of substance in physics.

An effective digital image watermarking scheme incorporating DCT, DFT and SVD transformations.

Image watermarking prevents copyright infringements by attaching visible/invisible watermark images as authentication identities in the owner's documents. The article made analysis on the advantages of different transformations for choosing better combinations to make the watermark embedding process and observed that watermarking techniques incorporating discrete cosine transform (DCT) provide better resistance towards JPEG based potential attacks, discrete Fourier transform (DFT) has strong energy compaction with geometrical invariance properties to resist geometric attacks while singular value decomposition (SVD) provides stability, proportion invariance and rotation invariance properties and it provides strong resistance against noise based attacks. Considering these advantages of different transformations, the article presents a new non-blind watermarking algorithm by utilizing advantages of DFT, DCT and SVD transforms while attaching secret contents in cover images. The algorithm starts by applying DFT followed by onion peel decomposition (OPD) for decomposing Fourier domain carrier image to four frequency sub images. The scheme then applies DCT on the frequency bands and orders them in zigzag fashion to form four individual frequency arrays. In the final step of embedding process, it embeds four copies of watermark singular value contents in DFT domain with the carrier image singular value contents to produce the watermarked image. The experimental results based on subjective and objective metrics on various test images from standard image databases with different test conditions demarcate the stability of new algorithm in producing high quality watermarked images with fewer distortions even when the watermarked images are extremely distorted by potential attacks.

Uniqueness in phaseless inverse electromagnetic scattering problem with known superposition of incident electric dipoles

In this paper, we consider the uniqueness of the phaseless inverse electromagnetic scattering problems. The phaseless data are the modulus of the tangential component of the far‐field pattern measured on the unit sphere and generated by the scatterer as well as the electric dipoles. Based on the superpositions of two electric dipoles with different positions and polarization vectors as the incident fields, the translation invariance property of the phaseless far‐field pattern corresponding to a single incident wave can be broken. A rigorous argument is given to illustrate that the location, shape, and boundary conditions of the obstacle or the refractive index of the medium can be uniquely determined by the phaseless far‐field data. Different from the existing method, we do not need to introduce an additional reference sphere. Thus our method makes the argument of uniqueness much simpler and clearer.

A General Tensor Prediction Framework Based on Graph Neural Networks.

Graph neural networks (GNNs) have been shown to be extremely flexible and accurate in predicting the physical properties of molecules and crystals. However, traditional invariant GNNs are not compatible with directional properties, which currently limits their usage to the prediction of only invariant scalar properties. To address this issue, here we propose a general framework, i.e., an edge-based tensor prediction graph neural network, in which a tensor is expressed as the linear combination of the local spatial components projected on the edge directions of clusters with varying sizes. This tensor decomposition is rotationally equivariant and exactly satisfies the symmetry of the local structures. The accuracy and universality of our new framework are demonstrated by the successful prediction of various tensor properties from first to third order. The framework proposed in this work will enable GNNs to step into the broad field of prediction of directional properties.

Statistical solutions and Liouville theorem for the second order lattice systems with varying coefficients

In this article, we first verify the global well-posedness of the second order lattice systems with varying coefficients. Then we prove that the solution mappings form a continuous process on the time-dependent phase spaces and the process has a time-dependent pullback attractor. Afterwards, we establish that there exists a family of Borel probability measures carried by the time-dependent pullback attractor which possesses invariant property under the action of the process. Further, we formulate the definition of statistical solution for the addressed evolution equations on time-dependent phase spaces and prove its existence. Our results reveal that the statistical solution of the second order lattice systems with varying coefficients satisfies the Liouville theorem in Statistical Mechanics. Finally, we propose some interesting issues concerning the singular limiting behavior as the varying coefficients tend to zero.

Inference on extended-spectrum beta-lactamase Escherichia coli and Klebsiella pneumoniae data through SMC2

Abstract We propose a novel stochastic model for the spread of antimicrobial-resistant bacteria in a population, together with an efficient algorithm for fitting such a model to sample data. We introduce an individual-based model for the epidemic, with the state of the model determining which individuals are colonised by the bacteria. The transmission rate of the epidemic takes into account both individuals’ locations, individuals’ covariates, seasonality, and environmental effects. The state of our model is only partially observed, with data consisting of test results from individuals from a sample of households. Fitting our model to data is challenging due to the large state space of our model. We develop an efficient SMC2 algorithm to estimate parameters and compare models for the transmission rate. We implement this algorithm in a computationally efficient manner by using the scale invariance properties of the underlying epidemic model. Our motivating application focuses on the dynamics of community-acquired extended-spectrum beta-lactamase-producing Escherichia coli and Klebsiella pneumoniae, using data collected as part of the Drivers of Resistance in Uganda and Malawi project. We infer the parameters of the model and learn key epidemic quantities such as the effective reproduction number, spatial distribution of prevalence, household cluster dynamics, and seasonality.

Measurement invariance and psychometric properties of a German-language Conformity to Masculine Norms Inventory among cisgender sexual minority and heterosexually identified women and men.

Measurement invariance and psychometric properties of a German-language Conformity to Masculine Norms Inventory among cisgender sexual minority and heterosexually identified women and men.

Measuring college belongingness: Structure and measurement of the Sense of Social Fit Scale.

Sense of belonging is theorized to be a fundamental human need and has been shown to have important implications in many domains of life, including academic achievement. The Sense of Social Fit scale (SSF; Walton & Cohen, 2007) is widely used to assess college belongingness, particularly to study differences in academic experiences along lines of gender and race. Despite its wide use, the instrument's latent factor structure and measurement invariance properties have not been reported in the published literature to date. Consequently, researchers regularly use subsets of the SSF's items without psychometric justification. Here, we explore and validate the SSF's factor structure and other psychometric properties, and we provide recommendations about how to score the measure. A one-factor model in Study 1 showed poor fit, and exploratory factor analyses extracted a four-factor solution. Study 2's confirmatory factor analyses demonstrated superior fit of a bifactor model with four specific factors (from Study 1) and one general factor. Ancillary analyses supported a total scale scoring method for the SSF and did not support computing raw subscale scores. We also tested the bifactor model's measurement invariance across gender and race, compared latent mean scores between groups, and established the model's criterion and concurrent validity. We discuss implications and suggestions for future research. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

The geometrical and Möbius-invariant properties of parabolic cycles

Abstract We have studied parabolic cycles and given their equivalent matrix representations. Invariant properties of matrices under similarity have contributed to the Möbius-invariant properties in cycles. We have further discussed the inner product in the cycle space. Also, the geometrical properties of orthogonality and reflection have been studied to obtain the irregular points in the cycle space.

Dead-Beat Terminal Sliding Mode Control With Application to DC–DC Buck Converters

In this paper, a novel definition describing a switching steady-state motion, such that the tracking error always remains within a steady-state error domain, is introduced. Both the dead-beat reaching law and discrete terminal sliding mode function are proposed and applied to the design of the dead-beat terminal sliding mode controller which drives the tracking error to a steady-state error domain. In order to characterize the attractiveness and invariance properties of the controlled system, the upper/lower bounds of the steady-state error domain and the bound on absolute attractive layer of the tracking error are systematically derived. Finally, both numerical simulation and experimental results on the dc-dc buck converters in three different cases, i.e., the load resistance variation, the input voltage variation, and the desired output voltage variation, confirm the usefulness of the proposed method.

Strengthening transferability of adversarial examples by adaptive inertia and amplitude spectrum dropout

Deep neural networks are sensitive to adversarial examples and would produce wrong results with high confidence. However, most existing attack methods exhibit weak transferability, especially for adversarially trained models and defense models. In this paper, two methods are proposed to generate highly transferable adversarial examples, namely Adaptive Inertia Iterative Fast Gradient Sign Method (AdaI2-FGSM) and Amplitude Spectrum Dropout Method (ASDM). Specifically, AdaI2-FGSM aims to integrate adaptive inertia into the gradient-based attack, and leverage the looking ahead property to search for a flatter maximum, which is essential to strengthen the transferability of adversarial examples. By introducing a loss-preserving transformation in the frequency domain, the proposed ASDM with the dropout invariance property can craft the copies of input images to overcome the poor generalization on the surrogate models. Furthermore, AdaI2-FGSM and ASDM can be naturally integrated as an efficient gradient-based attack method to yield more transferable adversarial examples. Extensive experimental results on the ImageNet-compatible dataset demonstrate that higher transferability is achieved by our method than some advanced gradient-based attacks.

Forgery Detection by Weighted Complementarity between Significant Invariance and Detail Enhancement

Generative adversarial networks have shown impressive results in the modeling of movies and games, but what if such powerful image generation capability is used to harm the Multimedia? The face replacement methods represented by Deepfakes are becoming a threat to everyone, so the development of image authenticity detection methods has become a top priority. For achieving accurate detection resistant to compression effects, we propose a weighted complementary dual-stream detection method. Firstly, to alleviate the influence of image compression on manipulation detection, we propose the concept of pixel-wise saliency invariance. We map fake images onto saliency maps via Quaternary Fourier Transform, which discovers the invariant properties of image phase spectra on different compressions. Meanwhile, to capture boundary traces more easily, we propose the concept of pixel-wise detail enhancement. We apply Bilateral Filtering to preserve the texture edges of fake images and amplify the fake boundaries. Finally, to take full advantage of the two proposed concepts, a weighted complementary dual-stream network (WCD Network) is designed as a classifier to fuse features and identify real and fake. On different benchmarks like FaceForensics++(FF++), Celeb-DF and DFDC, the experimental results show that the proposed method has the average best detection accuracy compared to existing methods.

A stochastic model for evaluating the peaks of commodities' returns

AbstractThis paper proposes a probabilistic model for the evaluation of the peak components of the return of a commodity. The ground of the study lies in the evidence that the spikes in the returns are due to the shocks occurring in the external environment. We follow an approach based on a particular class of point processes—the Spatial Mixed Poisson Processes—by exploiting an invariance property for such a class. The theoretical framework is used for presenting an estimation the procedure of the returns based on the available information. An empirical instance based on different commodities' returns and the abnormal returns of the volatility index as external shocks are presented to motivate our theoretical approach.

A New Perspective on Predicting Roughness of Discontinuity from Fractal Dimension D of Outcrops

In tunnel construction, predicting the roughness of discontinuity is significant for preventing the collapse of the excavation face. However, currently, we are unable to use a parameter with invariant properties to quantify and predict the roughness of discontinuity. Fractal dimension D is one such parameter that be used to characterize the roughness of discontinuity. The study proposes a new method to predict the roughness of discontinuity from the fractal dimension D of outcrops. The measurement method of the coordinates of outcrops is firstly summarized, and the most suitable method of calculating fractal dimension D is then provided. For characterizing the spatial variability of fractal dimension D, the random field of fractal dimension D is discretized, and the prediction model is then established based on Bayesian theory. The proposed method is applied to one tunnel for predicting the roughness of discontinuity, and the results indicate that the relative errors of prediction are less than 1.5%. The sensitivities of correlation function and discontinuity size are analyzed. It is found that the different correlation functions have no obvious effect on the prediction results, and the proposed method is well applied to relatively large sizes of discontinuity.

Mathematical and chemical properties of geometry-based invariants and its applications

Recently, based on elementary geometry, Gutman proposed several geometry-based invariants (i.e., SO, SO1, SO2, SO3, SO4, SO5, SO6). The Sombor index was defined as SO(G)=∑uv∈E(G)du2+dv2, the first Sombor index was defined as SO1(G)=12∑uv∈E(G)|du2−dv2|, where du denotes the degree of vertex u.In this paper, we consider the mathematical properties of these geometry-based invariants. We determine the maximum trees (resp. unicyclic graphs) with given diameter, the maximum trees with given matching number, the maximum trees with given pendent vertices, the maximum trees (resp. minimum trees) with given branching number, the minimum trees with given maximum degree and second maximum degree, the minimum unicyclic graphs with given maximum degree and girth, the minimum connected graphs with given maximum degree and pendent vertices, and some properties of maximum connected graphs with given pendent vertices with respect to the first Sombor index SO1. As an application, we inaugurate these geometry-based invariants and verify their chemical applicability.

RamanNet: a generalized neural network architecture for Raman spectrum analysis

Raman spectroscopy provides a vibrational profile of the molecules and thus can be used to uniquely identify different kinds of materials. This sort of molecule fingerprinting has thus led to the widespread application of Raman spectrum in various fields like medical diagnosis, forensics, mineralogy, bacteriology, virology, etc. Despite the recent rise in Raman spectra data volume, there has not been any significant effort in developing generalized machine learning methods targeted toward Raman spectra analysis. We examine, experiment, and evaluate existing methods and conjecture that neither current sequential models nor traditional machine learning models are satisfactorily sufficient to analyze Raman spectra. Both have their perks and pitfalls; therefore, we attempt to mix the best of both worlds and propose a novel network architecture RamanNet. RamanNet is immune to the invariance property in convolutional neural networks (CNNs) and at the same time better than traditional machine learning models for the inclusion of sparse connectivity. This has been achieved by incorporating shifted multi-layer perceptrons (MLP) at the earlier levels of the network to extract significant features across the entire spectrum, which are further refined by the inclusion of triplet loss in the hidden layers. Our experiments on 4 public datasets demonstrate superior performance over the much more complex state-of-the-art methods, and thus, RamanNet has the potential to become the de facto standard in Raman spectra data analysis.

Comparing FRET Pairs that Report on Intersubunit Rotation in Bacterial Ribosomes

Mediated by elongation factor G (EF-G), ribosome translocation along mRNA is accompanied by rotational movement between ribosomal subunits. Here, we reassess whether the intersubunit rotation requires GTP hydrolysis by EF-G or can occur spontaneously. To that end, we employ two independent FRET assays, which are based on labeling either ribosomal proteins (bS6 and bL9) or rRNAs (h44 of 16S and H101 of 23S rRNA). Both FRET pairs reveal three FRET states, corresponding to the non-rotated, rotated and semi-rotated conformations of the ribosome. Both FRET assays show that in the absence of EF-G, pre-translocation ribosomes containing deacylated P-site tRNA undergo spontaneous intersubunit rotations between non-rotated and rotated conformations. While the two FRET pairs exhibit largely similar behavior, they substantially differ in the fraction of ribosomes showing spontaneous fluctuations. Nevertheless, instead of being an invariable intrinsic property of each FRET pair, the fraction of spontaneously fluctuating molecules changes in both FRET assays depending on experimental conditions. Our results underscore importance of using multiple FRET pairs in studies of ribosome dynamics and highlight the role of thermally-driven large-scale ribosome rearrangements in translation.