Multiple Invariance Research Articles

A generalized energy and QUadratic Invariant Preserving (GEQUIP) method for Hamiltonian systems with multiple invariants

It is well-known that the symplecticity and energy-conservation are the most characteristic properties of a Hamiltonian system. Meanwhile, many Hamiltonian problems allow the presence of multiple physical invariants, besides energy. This paper deals with a generalization of the EQUIP methods defined in Brugnano et al. [1], aimed at introducing additional parameters to attain further multiple invariants conservation properties, together with the symplecticity of the map. The solvability of the nonlinear system arising from the conservation requirements on multiple invariants is proved and the order of convergence on the method is discussed. Some numerical tests are reported in order to confirm the efficiency of the methods, which shows the good multiple invariants preserving property of the proposed method compared to Gauss collocation methods and EQUIP methods.

Analysis of Hanoi graph by using topological indices

One of the main challenges in molecular science is to model a chemical complex and predict its thermochemical properties. Various researchers have developed a number of hypothetical techniques in this regard, and one of them is focused on the topological indices. A topological index is a number associated with a molecule’s structural graph that is considered to be capable of predicting certain chemical and physical properties of molecules. Degree-based topological indices are one of the groups of topological indices that are crucial in chemical graph theory. Shannon’s entropy is a fundamental factor of a subclass of topological indices that measures the structural information of the graphs. In this study, we examine the entropy based on topological indices such as the first and second Zagreb indices, the general Randić index, the harmonic and sum-connectivity index of Hanoi graph. Moreover, we determine a number of multiplicative invariants, and different polynomials for Hanoi graphs with graphical illustrations.

High-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations

A novel class of high-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations is proposed and analyzed. With the aid of the quadratic auxiliary variable, an equivalent system is obtained from the original problem. The Fourier pseudo-spectral method is employed in spatial discretization and the symplectic Runge–Kutta method is utilized for the resulting semi-discrete system to arrive at a high-order fully discrete scheme. Simultaneously, the conservation of the original multiple invariants for the schemes are rigorously proven. Numerical experiments are performed to verify the theoretical analysis.

On invariant combinations of [formula omitted] coefficients and a novel invariant [formula omitted

Invariants of the plane-stress elasticity stiffness matrix [Q] play a key role in composite design, as they simplify design processes. Multiple invariants have been proposed independently in the past, such as the ‘trace’ Tr=trace([Q]) by Tsai and Melo or the invariants U1, U4 and U5, which are often used in context of lamination parameters.The present paper presents a parametric description of rotation-independent (invariant) linear combinations of the coefficients Qij of [Q]. It is shown that the aforementioned invariants are special cases of the developed parametric description, in which a novel invariant IQ=Q11+Q22+Q12+Q66 plays a key-role.

Structural Study of Boron Nanotubes by Shigehalli, Kanabur, and Sanskruti Indices Along with their Multiplicative Invariants

Nanotechnology revolutionized the 21st century because of its applications in many important fields like defense and security, electronics, optical engineering, nano devices, nano fabrics, computer, medicine drugs, cosmetics, and nano biotechnology. Boron nanoclusters, boron nanowires, and boron nanotubes have all been developed in the previous 20 years. Keeping in view the sensitivity of boron nanostructures, we have calculated the Shigehalli, Kanabur invariants and their multiplicative versions MSK, MSK_1 and MSK_2 indices of boron tri-hexagonal, boron tri-angular, and boron alpha nanotubes (BANT) are useful in estimating these nanostructures' chemical properties.

AdS3 gravity and RCFT ensembles with multiple invariants

We use the Poincaré series method to compute gravity partition functions associated to SU(N)1 WZW models with arbitrarily large numbers of modular invariants. The result is an average over these invariants, with the weights being given by inverting a matrix whose size is of order the number of invariants. For the chosen models, this matrix takes a special form that allows us to invert it for arbitrary size and thereby explicitly calculate the weights of this average. For the identity seed we find that the weights are positive for all N, consistent with each model being dual to an ensemble average over CFT’s.

Visualizing the evolution of income inequality

The reporting of only relative inequalities is decreasing and other inequality invariance criteria are often being considered simultaneously. Having multiple measures with potentially different conclusions on whether inequality has increased or decreased complicates communicating what these results imply about the evolution of income inequality.
 
 To facilitate understanding this evolution, we highlight the advantage of visualizing in a single graph the relationship between changes in mean income and the development of inequality according to multiple inequality invariance criteria. Not presenting how these entities relate may mislead policy makers about the evolution of income inequality and its potential causes.

Geometric invariance of determining and resonating centers: Odd- and any-number limitations of Pyragas control.

In the spirit of the well-known odd-number limitation, we study the failure of Pyragas control of periodic orbits and equilibria. Addressing the periodic orbits first, we derive a fundamental observation on the invariance of the geometric multiplicity of the trivial Floquet multiplier. This observation leads to a clear and unifying understanding of the odd-number limitation, both in the autonomous and the non-autonomous setting. Since the presence of the trivial Floquet multiplier governs the possibility of successful stabilization, we refer to this multiplier as the determining center. The geometric invariance of the determining center also leads to a necessary condition on the gain matrix for the control to be successful. In particular, we exclude scalar gains. The application of Pyragas control on equilibria does not only imply a geometric invariance of the determining center but surprisingly also on centers that resonate with the time delay. Consequently, we formulate odd- and any-number limitations both for real eigenvalues together with an arbitrary time delay as well as for complex conjugated eigenvalue pairs together with a resonating time delay. The very general nature of our results allows for various applications.

Scalable ESPRIT Processor for Direction-of-Arrival Estimation of Frequency Modulated Continuous Wave Radar

The estimation of signal parameters via rotational invariance techniques (ESPRIT) is an algorithm that uses the shift-invariant properties of the array antenna to estimate the direction-of-arrival (DOA) of signals received in the array antenna. Since the ESPRIT algorithm requires high-complexity operations such as covariance matrix and eigenvalue decomposition, a hardware processor must be implemented such that the DOA is estimated in real time. Additionally, the ESPRIT processor should support a scalable number of antenna configuration for DOA estimation in various applications because the performance of ESPRIT depends on the number of antennas. Therefore, we propose an ESPRIT processor that supports two to eight scalable antenna configuration. In addition, since the proposed ESPRIT processor is based on multiple invariances (MI) algorithm, it can achieve a much better performance than the existing ESPRIT processor. The execution time is reduced by simplifying the Jacobi method, which has the most significant computational complexity for calculating eigenvalue decomposition (EVD) in ESPRIT. Moreover, the ESPRIT processor was designed using hardware description language (HDL), and an FPGA-based verification was performed. The proposed ESPRIT processor was implemented with 10,088 slice registers, 18,207 LUTs, and 80 DSPs, and the slice register, LUT, and DSP were reduced by up to 71.45%, 54.5%, and 68.38%, respectively, compared to the existing structure.

Topics in soft collinear effective theory for gravity: The diffeomorphism invariant Wilson lines and reparametrization invariance

Two topics in soft collinear effective theory (SCET) for gravitational interactions are explored. First, the collinear Wilson lines---necessary building blocks for maintaining multiple copies of diffeomorphism invariance in gravity SCET---are extended to all orders in the SCET expansion parameter $\ensuremath{\lambda}$, where it has only been known to $O(\ensuremath{\lambda})$ in the literature. Second, implications of reparametrization invariance (RPI) for the structure of gravity SCET Lagrangians are studied. The utility of RPI is illustrated by an explicit example in which $O({\ensuremath{\lambda}}^{2})$ hard interactions of a collinear graviton are completely predicted by RPI from its $O(\ensuremath{\lambda})$ hard interactions. It is also pointed out that the multiple diffeomorphism invariances and RPI together require certain relations among $O(\ensuremath{\lambda})$ terms, thereby reducing the number of $O(\ensuremath{\lambda})$ terms that need to be fixed by matching onto the full theory in the first place.

Equivariant factorization homology of global quotient orbifolds

We introduce equivariant factorization homology, extending the axiomatic framework of Ayala-Francis to encompass multiplicative invariants of manifolds equipped with finite group actions. Examples of such equivariant factorization homology theories include Bredon equivariant homology and (twisted versions of) Hochschild homology. Our main result is that equivariant factorization homology satisfies an equivariant version of ⊗-excision, and is uniquely characterised by this property. We also discuss applications to representation theory, such as constructions of categorical braid group actions.

CoMID: Context-Based Multiinvariant Detection for Monitoring Cyber-Physical Software

Cyber-physical software continually interacts with its physical environment for adaptation in order to deliver smart services. However, the interactions can be subject to various errors when the software's assumption on its environment no longer holds, thus leading to unexpected misbehavior or even failure. To address this problem, one promising way is to conduct runtime monitoring of invariants, so as to prevent cyber-physical software from entering such errors (a.k.a. abnormal states). To effectively detect abnormal states, we in this article present an approach, named Context-based Multi-Invariant Detection (CoMID), which consists of two techniques: context-based trace grouping and multi-invariant detection. The former infers contexts to distinguish different effective scopes for CoMID's derived invariants, and the latter conducts ensemble evaluation of multiple invariants to detect abnormal states. We experimentally evaluate CoMID on real-world cyber-physical software. The results show that CoMID achieves a 5.7-28.2% higher true-positive rate and a 6.8-37.6% lower false-positive rate in detecting abnormal states, as compared with state-of-the-art approaches (i.e., Daikon and ZoomIn). When deployed in field tests, CoMID's runtime monitoring improves the success rate of cyber-physical software in its task executions by 15.3-31.7%.

Modified averaged vector field methods preserving multiple invariants for conservative stochastic differential equations

A novel class of conservative numerical methods for general conservative Stratonovich stochastic differential equations with multiple invariants is proposed and analyzed. These methods, which are called modified averaged vector field methods, are constructed by modifying the averaged vector field methods to preserve multiple invariants simultaneously. Based on the prior estimate for high order moments of the modification coefficient, the mean square convergence order $1$ of proposed methods is proved in the case of commutative noises. In addition, the effect of quadrature formula on the mean square convergence order and the preservation of invariants for the modified averaged vector field methods is considered. Numerical experiments are performed to verify the theoretical analyses and to show the superiority of the proposed methods in long time simulation.

Visual Loop Closure Detection Based on Stacked Convolutional and Autoencoder Neural Networks

Simultaneous localization and mapping is the basis for solving the problem of robotic autonomous movement. Loop closure detection is vital for visual simultaneous localization and mapping. Correct detection of closed loops can effectively reduce the accumulation error of the robot poses, which plays an important role in building a globally consistent environment map. Traditional loop closure detection adopts the method of extracting handcrafted image features, which are sensitive to dynamic environments and are poor in robustness. In this paper, a method called stacked convolutional and autoencoder neural networks is proposed to automatically extract image features and perform dimensionality reduction processing. These features have multiple invariances in image transformation. Therefore, this method is robust to environmental changes. Experiments on public datasets show that the proposed method is superior to traditional methods in terms of accuracy, recall, and average accuracy, thereby validating the effectiveness of the proposed method.

Multiple Group IRT Measurement Invariance Analysis of the Forms of Self-Criticising/Attacking and Self-Reassuring Scale in Thirteen International Samples

The purpose of this study was to examine the measurement invariance of the Forms of Self-Criticising/Attacking & Self-Reassuring Scale (FSCRS) in terms of Item Response Theory differential test functioning in thirteen distinct samples (N = 7714) from twelve different countries. We assessed differential test functioning for the three FSCRS subscales, Inadequate-Self, Hated-Self and Reassured-Self separately. 32 of the 78 pairwise comparisons between samples for Inadequate-Self, 42 of the 78 pairwise comparisons for Reassured-Self and 54 of the 78 pairwise comparisons for Hated-Self demonstrated no differential test functioning, i.e. measurement invariance. Hated-Self was the most invariant of the three subscales, suggesting that self-hatred is similarly perceived across different cultures. Nonetheless, all three subscales of FSCRS are sensitive to cross-cultural differences. Considering the possible cultural and linguistic differences in the expression of self-criticism and self-reassurance, future analyses of the meanings and connotations of these constructs across the world are necessary in order to develop or tailor a scale which allows cross-cultural comparisons of various treatment outcomes related to self-criticism.

Closed-Form Multiple Invariance ESPRIT for UCA Based on STFT

Closed-Form Multiple Invariance ESPRIT for UCA Based on STFT

Sponsorship and advertising in sport: a study of consumers’ attitude

ABSTRACTResearch question: Advertising has been considered a less efficient vehicle of marketing communication. One recent study refuted that consumers’ attitude towards advertising was rather favourable in sport. This study compared consumers’ attitudes between advertising and sponsorship in sport and examined the antecedents (beliefs) and consequence (purchase intentions) of attitude in advertising and sponsorship.Research methods: Data were collected from 324 consumers. For testing of psychometric properties of the measures, a confirmatory factor analysis and a multiple invariance test were employed. A paired t-test, structural equation modelling, and invariance tests were conducted to test the research hypotheses.Results and Findings: There was no significant difference in consumers’ attitudes between advertising and sponsorship which were both deemed favourable. The path analyses revealed two positive beliefs (product information and hedonism/pleasure) and one negative belief (falsity/no sense) as significant predictors of attitude in both models. Good for the economy was an additional significant predictor of attitude in advertising but it was not so in sponsorship. The strengths of the three path coefficients were statistically identical across the two models. Attitude was a significant indicator of purchase intentions in both models; however, the invariance test revealed that the path in adverting was statistically stronger than that in sponsorship.Implications: This study provides important knowledge about consumers’ cognitive structures that could explain their decision making processes. Sport marketers could develop their promotion strategies more successfully, conveying their intent in a manner consistent with positive beliefs and avoiding negative beliefs.

DOA Estimation for Coprime Linear Array Based on MI-ESPRIT and Lookup Table.

In order to improve the angle measurement performance of a coprime linear array, this paper proposes a novel direction-of-arrival (DOA) estimation algorithm for a coprime linear array based on the multiple invariance estimation of signal parameters via rotational invariance techniques (MI-ESPRIT) and a lookup table method. The proposed algorithm does not require a spatial spectrum search and uses a lookup table to solve ambiguity, which reduces the computational complexity. To fully use the subarray elements, the DOA estimation precision is higher compared with existing algorithms. Moreover, the algorithm avoids the matching error when multiple signals exist by using the relationship between the signal subspace of two subarrays. Simulation results verify the effectiveness of the proposed algorithm.

Multiplicity and degree as bi-Lipschitz invariants for complex sets

We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz homeomorphims at infinity in the second case). We prove that invariance of multiplicity in the local case is equivalent to invariance of degree in the global case. We prove invariance for curves and surfaces. In the way we prove invariance of the tangent cone and relative multiplicities at infinity under outer bi-Lipschitz homeomorphims at infinity, and that the abstract topology of a homogeneous surface germ determines its multiplicity.

RAM-based angle estimation with linear spatially separated polarisation sensitive array

ABSTRACTTwo-dimensional direction of arrival (2D-DOA) and polarisation estimation of multiple incident signals for linear spatially separated polarisation sensitive array (SS-PSA) is investigated with reweighted atomic norm minimisation (RAM) algorithm. Single vector sensor in this paper is composed of spatially separated three dipoles and three loops. Firstly, the received data of the proposed array with single snapshot is converted into the new received data with six virtual snapshots. Each virtual snapshot data is the data sensing by dipoles or loops located in the same direction. Secondly, based on each virtual snapshot data, the complex amplitudes and frequencies of the virtual signals are restored using RAM algorithm. Lastly, 2D-DOA and polarisation angles are derived according to the restored complex amplitudes and frequencies. Simulation results demonstrate that the RAM algorithm used in 2D-DOA and polarisation estimation with SS-PSA exhibits superior performance, which is better compared with polarisation multiple signal classification (PMUSIC) algorithm and rotational invariance techniques (ESPRIT) algorithm.