Diagonal Terms Research Articles

Non-commutative probability insights into the double-scaling limit SYK model with constant perturbations: moments, cumulants and q-independence

Extending the results of Wu (2022 J. Phys. A 55 415207), we study the double-scaling limit Sachdev–Ye–Kitaev model with an additional diagonal matrix with a fixed number c of nonzero constant entries θ. This constant diagonal term can be rewritten in terms of Majorana fermion products. Its specific formula depends on the value of c. We find exact expressions for the moments of this model. More importantly, by proposing a moment-cumulant relation, we reinterpret the effect of introducing a constant term in the context of non-commutative probability theory. This gives rise to a q~ dependent mixture of independences within the moment formula. The parameter q~ , derived from the q-Ornstein–Uhlenbeck (q-OU) process, controls this transformation. It interpolates between classical independence ( q~=1 ) and Boolean independence ( q~=0 ). The underlying combinatorial structures of this model provide the non-commutative probability connections. Additionally, we explore the potential relation between these connections and their gravitational path integral counterparts.

Suprathermal Electron Transport in the Solar Wind: Effects of Coulomb Collisions and Whistler Turbulence

The nature and radial evolution of solar wind electrons in the suprathermal energy range are studied. A wave–particle interaction tensor and a Fokker–Planck Coulomb collision operator are introduced into the kinetic transport equation describing electron collisions and resonant interactions with whistler waves. The diffusion tensor includes diagonal and off-diagonal terms, and the Coulomb collision operator applies to arbitrary electron velocities describing collisions with both background protons and electrons. The background proton and electron densities and temperatures are based on previous turbulence models that mediate the supersonic solar wind. The electron velocity distribution functions and electron heat flux are calculated. Comparison and analysis of the numerical results with analytical solutions and observations in the near-Sun region are made. The numerical results reproduce well the creation of the sunward electron deficit observed in the near-Sun region. The deficit of the electron velocity distribution function below the core Maxwellian fit at low velocities results from Coulomb collisions, and the excess part above the core Maxwellian fit at high velocities is determined by strong wave–particle interactions.

GSSF: Generalized Structural Sparse Function for Deep Cross-Modal Metric Learning.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner.

Investigating the impact of quantum confinement on the THz behavior of Nanoscale FinFETs

The stationary and transient behavior of a 3 nm wide on-insulator type FinFET is investigated. The focus is laid on the evaluation and characterization of the effect of quantum confinement on the amplifier behavior. The high computational burden related to the time-resolved analysis of such three-dimensional simulations is dealt with by applying a mode-space approach onto a Quantum Liouville-type Equation. It is shown that the diagonal coupling terms related to the mode-space approach should be taken into consideration for the analysis of FinFETs. An increase in gain compression and higher order harmonic distortion is observed, when the fin height is decreased and, therefore, stronger quantum confinement occurs. The 1 dB compression point is shown to decrease by as much as 8 dB when reducing the fin height from 7 to 3 nm.

Kernel Block Diagonal Representation Subspace Clustering with Similarity Preservation

Subspace clustering methods based on the low-rank and sparse model are effective strategies for high-dimensional data clustering. However, most existing low-rank and sparse methods with self-expression can only deal with linear structure data effectively, but they cannot handle data with complex nonlinear structure well. Although kernel subspace clustering methods can efficiently deal with nonlinear structure data, some similarity information between samples may be lost when the original data are reconstructed in the kernel space. Moreover, these kernel subspace clustering methods may not obtain an affinity matrix with an optimal block diagonal structure. In this paper, we propose a novel subspace clustering method termed kernel block diagonal representation subspace clustering with similarity preservation (KBDSP). KBDSP contains three contributions: (1) an affinity matrix with block diagonal structure is generated by introducing a block diagonal representation term; (2) a similarity-preserving regularizer is constructed and embedded into our model by minimizing the discrepancy between inner products of original data and inner products of reconstructed data in the kernel space, which better preserve the similarity information between original data; (3) the KBDSP model is proposed by integrating the block diagonal representation term and similarity-preserving regularizer into the kernel self-expressing frame. The optimization of our proposed model is solved efficiently by utilizing the alternating direction method of multipliers (ADMM). Experimental results on nine datasets demonstrate the effectiveness of the proposed method.

Goodwillie’s cosimplicial model for the space of long knots and its applications

We work out the details of a correspondence observed by Goodwillie between cosimplicial spaces and good functors from a category of open subsets of the interval to the category of compactly generated weak Hausdorff spaces. Using this, we compute the first page of the integral Bousfield–Kan homotopy spectral sequence of the tower of fibrations, given by the Taylor tower of the embedding functor associated to the space of long knots. Based on the methods in Conant (Am J Math 130(2):341–357. https://doi.org/10.1353/ajm.2008.0020, 2008), we give a combinatorial interpretation of the differentials d^1 mapping into the diagonal terms, by introducing the notion of (i, n)-marked unitrivalent graphs.

Tunable correlation effects of magnetic impurities by cubic Rashba spin-orbit coupling

We theoretically study the influence of the $k$-cubic Rashba spin-orbit coupling (SOC) on the correlation effects of magnetic impurities by combining the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) simulations. Markedly different from the normal $k$-linear Rashba SOC, even a small cubic Rashba term can greatly alter the band structure and induce a Van Hove singularity in a wide range of energy; thus, the single impurity local moment becomes largely tunable. The cubic Rashba SOC adopted in this paper breaks the rotational symmetry, but the host material is still invariant under the operations ${\mathcal{R}}^{z}(\ensuremath{\pi}), {\mathcal{IR}}^{z}(\ensuremath{\pi}/2), {\mathcal{M}}_{xz}, {\mathcal{M}}_{yz}$, where ${\mathcal{R}}^{z}(\ensuremath{\theta})$ is the rotation of angle $\ensuremath{\theta}$ about the $z$ axis, $\mathcal{I}$ is the inversion operator, and ${\mathcal{M}}_{xz}$ (${\mathcal{M}}_{yz}$) is the mirror reflection about the $x\text{\ensuremath{-}}z$ ($y\text{\ensuremath{-}}z$) principal plane. Saliently, various components of spin-spin correlation between the single magnetic impurity and the conduction electrons show three- or sixfold rotational symmetry. This unique feature is due to the triple winding of the spins with a $2\ensuremath{\pi}$ rotation of $\mathbf{k}$, which is a hallmark of the cubic Rashba effect, and can possibly be an identifier to distinguish the cubic Rashba SOC from the normal $k$-linear Rashba term in experiments. Although the cubic Rashba term drastically alters the electronic properties of the host, we find that the spatial decay rate of the spin-spin correlation function remains essentially unchanged. Moreover, the carrier-mediated Ruderman-Kittel-Kasuya-Yosida interactions between two magnetic impurities show twisted features, the ferromagnetic diagonal terms dominate when two magnetic impurities are very close, but the off-diagonal terms become important at long distances.

The Effect of Anisotropic Gaussian Schell-Model Sources in Generalized Phase Space Stokes Parameters

Phase-space transforms describe spatial and angular information about light sources where one example is the Wigner functions in wave optics. Stokes parameters, on the other hand, supply information about the polarization of light beams. The generalized phase space Stokes parameters of 2D stochastic electromagnetic beams are already developed. In this article, the application of anisotropic light sources in generalized phase space Stokes parameters is theoretically investigated and numerically analyzed. There are several different ways of studying electromagnetic light beams depending on the spatial domain. But, most measure of the polarization of random light fields is carried out within the Stokes parameters context. In this account we study the electromagnetism, Stokes parameters, phase space, and the anisotropy properties of random light beams at once. We find here that when an anisotropy introduced in phase space then the cross terms of the Wigner matrix depart from the diagonal terms, which is not the same in configuration space. As a result, anisotropy has a different effect in Phase space, i.e. an anisotropic source introduces a phase and a variance change only in the cross terms of Wigner matrix. This is due to the use of anisotropy in the shifted kernel of Wigner transform.

Abnormal phonon angular momentum due to off-diagonal elements in the density matrix induced by a temperature gradient

Nonzero mean value of phonon angular momentum (PAM) in chiral materials can be generated when a temperature gradient is applied. We find that both diagonal and off-diagonal terms of PAM contribute to mean PAM by using the Kubo formula where both diagonal and off-diagonal elements of the heat current operator are considered. The calculation results show that the off-diagonal term is dominant when the phonon scattering is strong enough. This finding reveals that the quantum transition between different phonon modes induced by temperature gradient strongly affects the local atomic rotation. Our discovery provides an explanation of the recently observed chiral phonon activated spin Seebeck effect.

Delay-dependent stability conditions for fundamental characteristic functions

This paper is devoted to the investigation on the stability for two characteristic functions $f_1(z) = z^2+pe^{-z\tau }+q$ and $f_2(z) = z^2+pz e^{-z\tau }+q$, where $p$ and $q$ are real numbers and $\tau >0$. The obtained theorems describe the explicit stability dependence on the changing delay $\tau $. Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

RT-YOLO: A Residual Feature Fusion Triple Attention Network for Aerial Image Target Detection

In recent years, target detection of aerial images of unmanned aerial vehicle (UAV) has become one of the hottest topics. However, target detection of UAV aerial images often presents false detection and missed detection. We proposed a modified you only look once (YOLO) model to improve the problems arising in object detection in UAV aerial images: (1) A new residual structure is designed to improve the ability to extract features by enhancing the fusion of the inner features of the single layer. At the same time, triplet attention module is added to strengthen the connection between space and channel and better retain important feature information. (2) The feature information is enriched by improving the multi-scale feature pyramid structure and strengthening the feature fusion at different scales. (3) A new loss function is created and the diagonal penalty term of the anchor frame is introduced to improve the speed of training and the accuracy of reasoning. The proposed model is called residual feature fusion triple attention YOLO (RT-YOLO). Experiments showed that the mean average precision (mAP) of RT-YOLO is increased from 57.2% to 60.8% on the vehicle detection in aerial image (VEDAI) dataset, and the mAP is also increased by 1.7% on the remote sensing object detection (RSOD) dataset. The results show that the RT-YOLO outperforms other mainstream models in UAV aerial image object detection.

ПОВЫШЕНИЕ УСТОЙЧИВОСТИ ЛИНЕЙНОЙ РЕГРЕССИИ

The paper considers a method for increasing the stability of a linear regression equation, the coefficientsof which are the solution of a system of normal equations. The instability of the equation isdetermined by the presence of a linear relationship between the experimental data; the quantitativecharacteristics of the dependence are determined from the correlation matrix, which can also serve as amatrix of the system of equations. To reduce the correlation coefficients, Ridge (ridge) regression istraditionally used, which involves an increase in the diagonal members of the matrix by the same positivenumber. As a result, the matrix condition number decreases and the regression equation becomesmore stable: a small change in the input results in a small change in the solution. The number by whichthe diagonal terms of the matrix increase is called the penalty imposed in ridge regression on all regressioncoefficients. In the proposed method, penalties, and different ones, are imposed only on those coefficientsthat correspond to data with high correlation. This leads to an increase in the stability of theequation due to a decrease in the values of the coefficients corresponding to correlated data. The choiceof elements to be increased is based on the analysis of the correlation matrix of the original data set bydecomposing it into diagonal matrices using the square root method. In addition to increasing the stabilityusing the proposed method, a reduction in the dimension of the regression model can be achieved -a decrease in the number of terms of the corresponding equation, for which the LASSO and LARS algorithmsare usually used. The effectiveness of the method is tested on a known data set, and a comparisonis made not only with Ridge regression, but also with the results of known dimensionality reductionalgorithms.

Illumination guided sparse geometry optimization for target-oriented full-waveform inversion: An ocean bottom node synthetic study

For full-waveform inversion (FWI) with sparse survey layout, it is crucial to optimize the source and receiver geometry toward full-wave illumination. We propose a sparse geometry optimization method and workflow for target-oriented FWI using finite-frequency illumination analysis. The frequency-dependent impact of a source-receiver pair to the wavefield sensitivity kernel and diagonal terms of approximate Hessian matrix are derived under visco-acoustic model assumptions. Based on the reciprocity principle, we use virtual sources in target zone to efficiently calculate the Green's function and illumination from acquisition surface. Optimal locations of sparse receivers are determined by comparing band-limited illumination at reference stations and their surrounding region through an illumination attribute scan. FWI model residual errors are used to evaluate the performance of optimized geometry layout for a given target zone. The performances of different geometries are compared to determine a suitable frequency band for FWI geometry optimization. Synthetic deep water model and ocean bottom node acquisition geometry are used to verify the feasibility of the workflow. Numerical tests in target-oriented FWI show that optimized geometry with constraints of band-limited illumination below10 Hz has better performance than that above 10 Hz. An extension of our geometry optimization method to sparse source configuration is straightforward.

Binomial Edge Ideals of Weakly Closed Graphs

Abstract Closed graphs have been characterized by Herzog et al. as the graphs whose binomial edge ideals have a quadratic Gröbner basis with respect to a diagonal term order. In this paper, we focus on a generalization of closed graphs, namely weakly closed graphs (or co-comparability graphs). Building on some results about Knutson ideals of generic matrices, we characterize weakly closed graphs as the only graphs whose binomial edge ideals are Knutson ideals for a certain polynomial $f$. In doing so, we re-prove Matsuda’s theorem about the F-purity of binomial edge ideals of weakly closed graphs in positive characteristic and we extend it to generalized binomial edge ideals. Furthermore, we give a characterization of weakly closed graphs in terms of the minimal primes of their binomial edge ideals and we characterize all minimal primes of Knutson ideals for this choice of $f$.

New Method Determines Optimized Reference SDM for MIMO Testing

Abstract The paper presents a new method for vibration testing of articles such as satellites, aerospace subsystems, transportation subsystems, civil structures, or articles whose reliability in operation may be evaluated using either mechanical or acoustic vibration testing. The method can be used for direct field or reverberant acoustic test facility testing (acoustic) systems or multiple-exciter (mechanical) testing systems to perform vibration testing. The method improves the ability of Multiple-Input-Multiple-Output (MIMO) acoustic testing systems to create diffuse or other types of acoustic fields and MIMO mechanical testing systems to produce vibration responses conforming to an initial reference Spectral Density Matrix (SDM) specification in the least mean-square error (LMSE) sense. It provides an updated positive definite or semi-definite reference SDM that enables such tests to run with less error, using minimum required drive power, as a function of the initial definition of the reference SDM, by modifying its coherence and phase off-diagonal terms, to approximate initially defined off-diagonal terms in the LMSE sense, but maintaining its initially defined diagonal terms exactly, while accounting for physical limitations existing in the overall MIMO testing system.

Numerical study of viscosity and heat flux role in heavy species dynamics in Hall thruster discharge

A two- and three-dimensional velocity space axisymmetric hybrid-PIC model of Hall thruster discharge called Hybrid2D has been developed. The particle-in-cell (PIC) method was used for neutrals and ions (heavy species), and fluid dynamics on a magnetic field-aligned (MFA) mesh was used for electrons. A time-saving method for heavy species moment interpolation on a MFA mesh was developed. The method comprises using regular rectangle and irregular triangle meshes, connected to each other on a pre-processing stage. The electron fluid model takes into account neither inertia terms nor viscous terms and includes an electron temperature equation with a heat flux term. The developed model was used to calculate all heavy species moments up to the third one in a stationary case. The analysis of the viscosity and the heat flux impact on the force and energy balance has shown that for the calculated geometry of the Hall thruster, the viscosity and the heat flux terms have the same magnitude as the other terms and could not be omitted. Also, it was shown that the heat flux is not proportional to the temperature gradient and, consequently, the highest moments should be calculated to close the neutral fluid equation system. At the same time, ions can only be modeled as a cold non-viscous fluid when the sole aim of modeling is the calculation of the operating parameters or distribution of the local parameters along the centerline of the discharge channel. This is because the magnitude of the viscosity and the temperature gradient terms are negligible at the centerline. However, when a simulation’s focus is either on the radial divergence of the plume or on magnetic pole erosion, three components of the ion temperature should be taken into consideration. The non-diagonal terms of ion pressure tensor have a lower impact than the diagonal terms. According to the study, a zero heat flux condition could be used to close the ion equation system in calculated geometry.

Including connecting elements into the Lagrange multiplier state-space substructuring formulation

This paper extends the inverse substructuring (IS) approach into the state-space domain and presents a novel state-space substructuring (SSS) technique that embeds the dynamics of connecting elements (CEs) in the Lagrange Multiplier State-Space Substructuring (LM-SSS) formulation via compatibility relaxation. This coupling approach makes it possible to incorporate into LM-SSS connecting elements that are suitable for being characterized by inverse substructuring (e.g. rubber mounts) by simply using information from one of its off diagonal apparent mass terms. Therefore, the information obtained from an in-situ experimental characterization of the CEs is enough to include them into the coupling formulation. Moreover, LM-SSS with compatibility relaxation makes it possible to couple an unlimited number of components and CEs, requiring only one matrix inversion to compute the coupled state-space model (SSM). Two post-processing procedures to enable the computation of minimal-order coupled models by using this approach are also presented. Numerical and experimental substructuring applications are exploited to prove the validity of the proposed state-space realization of IS and the inclusion of CEs into the LM-SSS formulation via compatibility relaxation. It is found that the IS approach can be accurately applied on state-space models representative of components linked by CEs to identify models representative of the diagonal apparent mass terms of the CEs, provided that the CEs can be accurately characterized by the underlying assumptions of IS. In this way, state-space models representative of experimentally characterized CEs can be found without performing decoupling operations. Hence, these models are not contaminated with spurious states. Furthermore, it was found that the developed coupling approach is reliable, when the dynamics of the CEs can be accurately characterized by IS, thus making it possible to compute reliable coupled models that are not composed by spurious states.

Nonlinear chirped interferometry for frequency-shift measurement and χ(3) spectroscopy

Four-wave mixing processes are ubiquitous in ultrafast optics and the determination of the coefficients of the χ(3) tensor is thus essential. We introduce a novel time-resolved ultrafast spectroscopic method to characterize the third-order nonlinearity on the femtosecond time-scale. This approach, coined as “nonlinear chirped interferometry,” makes use of the variation of the optical group delay of a transmitted probe under the effect of an intense pump pulse in the nonlinear medium of interest. The observable is the spectral interference between the probe and a reference pulse sampled upstream and the metric is the transient swing of the probe group delay. We show that the detected signal is enhanced when the pulses are weakly chirped, and that, although interferometric, the method is intrinsically less sensitive to environmental phase fluctuations and drifts. By chirping adequately the reference pulse, the transient frequency shift of the probe pulses is also detected in the time domain and the detected nonlinear signal is enhanced. Nonlinear phase shifts as low as 10 mrad, corresponding to a frequency shift of 30 GHz, i.e., 0.01% of the carrier frequency, are detected without heterodyne detection or active phase-stabilization. The diagonal and/or non-diagonal terms of reference glasses (SiO2) and crystals (Al2O3, BaF2, CaF2) are characterized. The method is finally applied to measure the soft vibration mode of KTiOAsO4 (KTA).

Mechanical coupling effects of 2D lattices uncovered by decoupled micropolar elasticity tensor and symmetry operation

Mechanical couplings such as axial–shear and axial–bending have great potential in the design of active mechanical metamaterials with directional control of input and output loads in sensors and actuators. However, the current ad hoc design of mechanical coupling without theoretical support of elasticity cannot provide design guidelines for mechanical coupling with lattice geometries. Moreover, the correlation between mechanical coupling effects and geometric symmetry is not yet clearly understood. In this work, we systematically search for all possible mechanical couplings in 2D lattice structures by determining the non-zero diagonal terms in the decomposed micropolar elasticity tensor. We also correlate the mechanical couplings with the point-group symmetry of 2D lattices by applying the symmetry operation to the decomposed micropolar elasticity tensor. The decoupled micropolar constitutive equation uncovers eight coupling effects for 2D lattice structures. The symmetry operation of the decoupled micropolar elasticity tensor reveals the correlation of the mechanical coupling with the point groups. Our findings can strengthen the design of mechanical metamaterials with potential applications in areas including sensors, actuators, soft robots, and active metamaterials for elastic/acoustic wave guidance and thermal management.

The applicability of hydrodynamics in heavy ion collisions at sqrt{s_mathrm{NN}} = 2.4–7.7 GeV

To assess the degree of equilibration of the matter created in heavy-ion reactions at low to intermediate beam energies, a hadronic transport approach (SMASH) is employed. By using a coarse-graining method, we compute the energy momentum tensor of the system at fixed time steps and evaluate the degree of isotropy of the diagonal terms and the relative magnitude of the off-diagonal terms. This study focuses mostly on Au+Au collisions in the energy range {sqrt{s}_mathrm{NN}} = 2.4–7.7 GeV, but central collisions of lighter ions like C+C, Ar+KCl and Ag+Ag are considered as well. We find that the conditions concerning local equilibration for a hydrodynamic description are reasonably satisfied in a large portion of the system for a significant amount of time (several fm/c) when considering the average evolution of many events, yet they are rarely fulfilled on an event by event basis. This is relevant for the application of hybrid approaches at low beam energies as they are or will be reached by the HADES experiment at GSI, the future CBM experiment at FAIR as well as the beam energy scan program at RHIC.