Covariant Approach Research Articles

Demands and scaffolds for explaining the connection of multiple representations: Revisiting the bottle-filling task

Explaining the connections of multiple representations can enhance students’ conceptual understanding (e.g., in the bottle-filling task for functional graphs). But it poses high discursive demands that need to be further unpacked. The design research study qualitatively investigates the potentials and demands that fourteen second-language learners face when explaining the connection between functional graphs and filling glasses. The qualitative analysis of students’ pathways towards good explanations identifies (a) demands to construct a mental contextual representation of the filling process, (b) demands to unpack the holistic perspective into more refined concept elements of covariation and correspondence approaches, (c) highly intertwined demands to identify the relevant variables in view. For each of these underlying demands, we identify scaffolds to enable students – even recent second-language learners – to engage in mathematically and discursively demanding practices and to enable teachers to support them.

Nuclear clustering over the nuclear chart from a covariant EDF approach

Nuclear clustering has been studied with covariant Energy Density Functional approaches for more than a decade. It recently allowed to bridge microscopically the description of cluster states in light nuclei with the one of cluster and alpha decays in heavy ones. The proper use of theoretical tools, such as the density and the nucleonic localization function, allows to shed light on the mechanisms of formation and identification of clusters in nuclei. Finally, a global analysis of nuclear clustering is discussed, in order to identify control parameters for a nuclear cluster phase.

Covariant canonical formulations of classical field theories

We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

Statistical field theory of mechanical stresses in Coulomb fluids: general covariant approach vs Noether’s theorem

In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether’s first theorem for the case of a fluctuating order parameter to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and fluctuation corrections derived through the one-loop approximation. The correction for fluctuations includes a term that accounts for the thermal fluctuations of the local electrostatic potential and field in the vicinity of the mean-field configuration. This correlation stress tensor determines how electrostatic correlation affects local stresses in a nonuniform Coulomb fluid. We also use a previously formulated general covariant methodology (Brandyshev and Budkov 2023 J. Chem. Phys. 158 174114) in conjunction with a functional Legendre transformation method and derive within it the same total stress tensor. We would like to emphasize that our general approaches are applicable not only to Coulomb fluids but also to nonionic simple or complex fluids, for which the field-theoretic Hamiltonian is known as a function of the relevant scalar order parameters.

Application of diffusional kurtosis imaging for insights into structurally aberrant topology in Parkinson's disease.

Parkinson's disease (PD) has been regarded as a disconnection syndrome with functional and structural disturbances. However, as the anatomic determinants, the structural disconnections in PD have yet to be fully elucidated. To non-invasively construct structural networks based on microstructural complexity and to further investigate their potential topological abnormalities in PD given the technical superiority of diffusion kurtosis imaging (DKI) to the quantification of microstructure. The microstructural data of gray matter in both the PD group and the healthy control (HC) group were acquired using DKI. The structural networks were constructed at the group level by a covariation approach, followed by the calculation of topological properties based on graph theory and statistical comparisons between groups. A total of 51 patients with PD and 50 HCs were enrolled. Individuals were matched between groups with respect to demographic characteristics (P >0.05). The constructed structural networks in both the PD and HC groups featured small-world properties. In comparison with the HC group, the PD group exhibited significantly altered global properties, with higher normalized characteristic path lengths, clustering coefficients, local efficiency values, and characteristic path lengths and lower global efficiency values (P <0.05). In terms of nodal centralities, extensive nodal disruptions were observed in patients with PD (P <0.05); these disruptions were mainly distributed in the sensorimotor network, default mode network, frontal-parietal network, visual network, and subcortical network. These findings contribute to the technical application of DKI and the elucidation of disconnection syndrome in PD.

Variational field theory of macroscopic forces in coulomb fluids.

Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of the local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory.

Semileptonic decays B_{c} meson to S-wave charmonia and X(3872) within the covariant light-front approach

In this work, we investigate the semileptonic decays of B_{c} meson to eta _{c}(1S,2S,3S), psi (1S,2S,3S) and X(3872) within the framework of covariant light-front quark model (CLFQM). We combine the helicity amplitudes via the corresponding form factors to obtain the branching ratios of the semileptonic decays B_{c}rightarrow eta _{c}(1S, 2S, 3S)ell nu _{ell }, B_{c}rightarrow psi (1S, 2S, 3S))ell nu _{ell } and B_{c}rightarrow X(3872)ell nu _{ell }, with ell =e,mu ,tau . In view of the R_{J/Psi } anomaly released by the LHCb collaboration, it is necessary to systematically calculate the ratios R_X with X=psi (1S,2S,3S),eta _c(1S,2S,3S),X(3872), which are helpful for checking the lepton flavor universality (LFU). We also take into account another two physical observables, the longitudinal polarization fraction f_{L} and the forward–backward asymmetry A_{FB}, which can provide new clues for understanding the R_{J /Psi } anomaly. Such theoretical predictions are necessary and interesting, and can be tested in future LHCb experiments.

The covariant approach to static spacetimes in Einstein and extended gravity theories

We present a covariant study of static space-times, as such and as solutions of gravity theories. By expressing the relevant tensors through the velocity and the acceleration vectors that characterise static space-times, the field equations provide a natural non-redundant set of scalar equations. The same vectors suggest the form of a Faraday tensor, that is studied in itself and in (non)-linear electrodynamics. In spherical symmetry, we evaluate the explicit expressions of the Ricci, the Weyl, the Cotton and the Bach tensors. Simple restrictions on the coefficients yield well known and new solutions in Einstein, f(R), Cotton and Conformal gravity, with or without charges, in vacuo or with fluid source.

On Chaplygin models in f(G) gravity

This work treats cosmological perturbation in a mixture of standard matter, Chaplygin gas as well as Gauss–Bonnet fluids using a 1+3 covariant approach in the context of modified [Formula: see text] gravity. We define the gradient variables to obtain linear perturbation equations. After scalar and redshift transformations, we consider both an original Chaplygin and generalized Chaplygin gas models under Gauss–Bonnet gravity. For pedagogical purposes, the consideration of polynomial [Formula: see text] gravity model was used to solve the perturbation equations for short- and long-wavelength modes and investigate the late-time evolution. The numerical solutions were obtained. The results show that the energy overdensity perturbations decay with an increase in redshift. The treatment recovers GR results under limiting cases.

The unpolarized TMD valence quark distributions of light mesons in the statistical covariant parton model approach

We investigate the unpolarized transverse momentum dependent (TMD) structure of light mesons at low Q^2 scales in nonperturbative region of quantum chromodynamics (QCD). To this end, we calculate the unpolarized TMD valence quark distribution functions of pion and kaon based on the covariant parton model in which the flavour dependent covariant momentum distribution of quarks is needed. We apply the statistical model for this momentum distribution, for the first time, and also consider the quarks to be massive. The results of TMD valence distributions of light mesons show convenient general properties. We also obtain the integrated valence quark distributions of pion and kaon and compare our results with those of other models.

Leptonic Decay Widths for the Composite System of Two Relativistic Fermions

The new relativistic semiclassical leptonic decay widths of vector mesons as the relativistic systems of two quarks with arbitrary masses interacting by means of the funnel-type potentials with Coulomb interaction are obtained. The behavior of the relativistic leptonic decay widths of vector mesons is investigated. Comparison of the behavior for new expression with its relativistic spinless analog is given. Consideration is conducted within the framework of completely covariant quasipotential approach in the Hamiltonian formulation of quantum field theory via a transition to the relativistic configurational representation in the case of two relativistic spin particles of arbitrary masses.

On 1 + 3 covariant perturbations of the quasi-Newtonian spacetime in modified Gauss–Bonnet gravity

The consideration of a [Formula: see text] covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of [Formula: see text] gravity theory in this study. This approach reveals the existence of integrability conditions which do not appear in noncovariant treatments. We constructed the integrability conditions in modified Gauss–Bonnet [Formula: see text] gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in [Formula: see text] gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian spacetime were constructed in the context of modified [Formula: see text] gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behavior of the overdensity and velocity perturbations using [Formula: see text] model was made. On the other hand, we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short- and long-wavelength modes in a dust-Gauss–Bonnet fluids was done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to [Formula: see text]CDM, it means [Formula: see text] the considered [Formula: see text] model results coincide with [Formula: see text]CDM.

Targeted visual cortex stimulation (TVCS): a novel neuro-navigated repetitive transcranial magnetic stimulation mode for improving cognitive function in bipolar disorder

A more effective and better-tolerated site for repetitive transcranial magnetic stimulation (rTMS) for treating cognitive dysfunction in patients with bipolar disorder (BD) is needed. The primary visual cortex (V1) may represent a suitable site. To investigate the use of the V1, which is functionally linked to the dorsolateral prefrontal cortex (DLPFC) and anterior cingulate cortex (ACC), as a potential site for improving cognitive function in BD. Seed-based functional connectivity (FC) analysis was used to locate targets in the V1 that had significant FC with the DLPFC and ACC. Subjects were randomly assigned to 4 groups, namely, the DLPFC active-sham rTMS (A1), DLPFC sham-active rTMS (A2), ACC active-sham rTMS (B1), and ACC sham-active rTMS groups (B2). The intervention included the rTMS treatment once daily, with five treatments a week for four weeks. The A1 and B1 groups received 10 days of active rTMS treatment followed by 10 days of sham rTMS treatment. The A2 and B2 groups received the opposite. The primary outcomes were changes in the scores of five tests in the THINC-integrated tool (THINC-it) at week 2 (W2) and week 4 (W4). The secondary outcomes were changes in the FC between the DLPFC/ACC and the whole brain at W2 and W4. Of the original 93 patients with BD recruited, 86 were finally included, and 73 finished the trial. Significant interactions between time and intervention type (Active/Sham) were observed in the scores of the accuracy of the Symbol Check in the THINC-it tests at baseline (W0) and W2 in groups B1 and B2 (F = 4.736, p = 0.037) using a repeated-measures analysis of covariance approach. Group B1 scored higher in the accuracy of Symbol Check at W2 compared with W0 (p < 0.001), while the scores of group B2 did not differ significantly between W0 and W2. No significant interactions between time and intervention mode were seen between groups A1 and A2, nor was any within-group significance of FC between DLPFC/ACC and the whole brain observed between baseline (W0) and W2/W4 in any group. One participant in group B1 experienced disease progression after 10 active and 2 sham rTMS sessions. The present study demonstrated that V1, functionally correlated with ACC, is a potentially effective rTMS stimulation target for improving neurocognitive function in BD patients. Further investigation using larger samples is required to confirm the clinical efficacy of TVCS.

On the Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

The theoretical prediction of the stochastic property of the quantum cosmological constant and the quantum stochastic nature of event horizons has crucial implications on the physics of space-time and black holes in particular. One of these consequences concerns a new mechanism, which is investigated here, for the stochastic regularization of singular black-hole solutions of classical general relativity. The problem is posed in the context of the theory of covariant quantum gravity (CQG-theory), namely the manifestly covariant, constraint-free and finite graviton-mass quantum Hamiltonian approach developed by Cremaschini and Tessarotto (2015–2022), which permits to cast the theory in a frame-independent setting. It is precisely the trajectory-dependence feature of the theory and the intrinsic stochastic property of quantum gravity which turn out to be crucial properties for reaching quantum regularization of classical singular solutions.

Covariant light-front approach for B_c decays into charmonium: implications on form factors and branching ratios

In this work, we investigate the form factors of B_c decays into J/Psi , psi (2S,3S),eta _c, eta _c(2,S,3,S), chi _{c0}, chi _{c1}, h_c, and X(3872) mesons in the covariant light-front quark model (CLFQM). For the purpose of the branching ratio calculation, the form factors of B_crightarrow D^{(*)}, D^{(*)}_s transitions are also included. In order to obtain the form factors for the physical transition processes, we need to extend these form factors from the space-like region to the time-like region. The q^2 dependence for each transition form factor is also plotted. Then, using the factorization method, we calculate the branching ratios of 80 B_c decay channels with a charmonium involved in each mode. Most of our predictions are comparable to the results given by other approaches. As to the decays with the radially excited-state S-wave charmonia involved, such as psi (2S,3S) and eta _c(2S,3S), two sets of parameters for their light-front wave functions, corresponding to scenario I (SI) and scenario II (SII), are adopted to calculate the branching ratios. By comparing with the future experimental data, one can discriminate which parameters are more favored.

Polytropic representation of non-isotropic kinetic pressure tensor for non-ideal plasma fluids in relativistic jets

Non-ideal fluids are likely to be affected by the occurrence of pressure anisotropy effects, whose understanding for relativistic systems requires knowledge of the energy–momentum tensor. In this paper, the case of magnetized jet plasmas at equilibrium is considered, in which both microscopic velocities of constituent particles and the continuum fluid flow are treated as relativistic ones. A theoretical framework based on covariant statistical kinetic approach is implemented, which permits the proper treatment of single-particle and phase-space kinetic constraints and, ultimately, the calculation of the system continuum fluid fields associated with physical observables. A Gaussian-like solution for the kinetic distribution function (KDF) is constructed, in which the physical mechanism responsible for the generation of temperature anisotropy is identified with magnetic moment conservation. A Chapman–Enskog representation of the same KDF is then obtained in terms of expansion around an equilibrium isotropic Juttner distribution. This permits the analytical calculation of the fluid 4-flow and stress–energy tensor and the consequent proof that the corresponding kinetic pressure tensor is non-isotropic. As a notable result, the validity of a polytropic representation for the perturbative non-isotropic pressure contributions is established, whereby directional pressures exhibit specific power-law functional dependences on fluid density.

Subcortical structural covariance predicts symptoms in children with different subtypes of ADHD.

Attention-deficit/hyperactivity disorder has increasingly been conceptualized as a disorder of abnormal brain connectivity. However, far less is known about the structural covariance in different subtypes of this disorder and how those differences may contribute to the symptomology of these subtypes. In this study, we used a combined volumetric-based methodology and structural covariance approach to investigate structural covariance of subcortical brain volume in attention-deficit/hyperactivity disorder-combined and attention-deficit/hyperactivity disorder-inattentive patients. In addition, a linear support vector machine was used to predict patient's attention-deficit/hyperactivity disorder symptoms. Results showed that compared with TD children, those with attention-deficit/hyperactivity disorder-combined exhibited decreased volume of both the left and right pallidum. Moreover, we found increased right hippocampal volume in attention-deficit/hyperactivity disorder-inattentive children. Furthermore and when compared with the TD group, both attention-deficit/hyperactivity disorder-combined and attention-deficit/hyperactivity disorder-inattentive groups showed greater nonhomologous inter-regional correlations. The abnormal structural covariance network in the attention-deficit/hyperactivity disorder-combined group was located in the left amygdala-left putamen/left pallidum/right pallidum and right pallidum-left pallidum; in the attention-deficit/hyperactivity disorder-inattentive group, this difference was noted in the left hippocampus-left amygdala/left putamen/right putamen and right hippocampus-left amygdala. Additionally, different combinations of abnormalities in subcortical structural covariance were predictive of symptom severity in different attention-deficit/hyperactivity disorder subtypes. Collectively, our findings demonstrated that structural covariance provided valuable diagnostic markers for attention-deficit/hyperactivity disorder subtypes.

Clustering of Health Behaviors in Canadians: A Multiple Behavior Analysis of Data from the Canadian Longitudinal Study on Aging.

Health behaviors such as physical inactivity, unhealthy eating, smoking tobacco, and alcohol use are each leading risk factors for non-communicable chronic disease. Better understanding which behaviors tend to co-occur (i.e., cluster together) and co-vary (i.e., are correlated) may provide novel opportunities to develop more comprehensive interventions to promote multiple health behavior change. However, whether co-occurrence or co-variation-based approaches are better suited for this task remains relatively unknown. To compare the utility of co-occurrence vs. co-variation-based approaches for understanding the interconnectedness between multiple health-impacting behaviors. Using baseline and follow-up data (N = 40,268) from the Canadian Longitudinal Study of Aging, we examined the co-occurrence and co-variation of health behaviors. We used cluster analysis to group individuals based on their behavioral tendencies across multiple behaviors and to examine how these clusters are associated with demographic characteristics and health indicators. We compared outputs from cluster analysis to behavioral correlations and compared regression analyses of clusters and individual behaviors predicting future health outcomes. Seven clusters were identified, with clusters differentiated by six of the seven health behaviors included in the analysis. Sociodemographic characteristics varied across several clusters. Correlations between behaviors were generally small. In regression analyses individual behaviors accounted for more variance in health outcomes than clusters. Co-occurrence-based approaches may be more suitable for identifying sub-groups for intervention targeting while co-variation approaches are more suitable for building an understanding of the relationships between health behaviors.

Noether's second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids.

In this paper, we present a covariant approach that utilizes Noether's second theorem to derive a symmetric stress tensor from the grand thermodynamic potential functional. We focus on the practical case where the density of the grand thermodynamic potential is dependent on the first and second coordinate derivatives of the scalar order parameters. Our approach is applied to several models of inhomogeneous ionic liquids that consider electrostatic correlations of ions or short-range correlations related to packing effects. Specifically, we derive analytical expressions for the symmetric stress tensors of the Cahn-Hilliard-like model, Bazant-Storey-Kornyshev model, and Maggs-Podgornik-Blossey model. All of these expressions are found to be consistent with respective self-consistent field equations.

Heterogeneous Transformer: A Scale Adaptable Neural Network Architecture for Device Activity Detection

To support modern machine-type communications, a crucial task during the random access phase is device activity detection, which is to identify the active devices from a large number of potential devices based on the received signal at the access point. By utilizing the statistical properties of the channel, state-of-the-art covariance based methods have been demonstrated to achieve better activity detection performance than compressed sensing based methods. However, covariance based methods require to solve a high dimensional nonconvex optimization problem by updating the estimate of the activity status of each device sequentially. Since the number of updates is proportional to the device number, the computational complexity and delay make the iterative updates difficult for real-time implementation especially when the device number scales up. Inspired by the success of deep learning for real-time inference, this paper proposes a learning based method with a customized heterogeneous transformer architecture for device activity detection. By adopting an attention mechanism in the architecture design, the proposed method is able to extract features reflecting relevance among device pilots and received signal, permutation equivariant with respect to devices, and its training parameter number is independent of the device number. Simulation results demonstrate that the proposed method achieves better activity detection performance with much shorter computation time than state-of-the-art covariance approach, and generalizes well to different numbers of devices and BS-antennas, different pilot lengths, transmit powers, and cell radii.