Second-order Description Research Articles

Closed-Form Capacity Reliability Analysis of Multiuser MIMO System in the Presence of Generalized Multipath Fading.

This research studies the problem of a joint capacity/capacity reliability analysis of the multiuser multi-input multioutput (MIMO) system functioning in the presence of generalized multipath fading. The study presents the derived results of the closed-form analytical statistical description of the ergodic sum-rate capacity, the capacity reliability and the capacity's higher-order statistics in the case of complex Nakagami-m distributed channel transmission coefficients. A numerical verification of the derived expressions was performed, and it demonstrated excellent correspondence with the simulation. The system performance was evaluated with the help of a numerical analysis of the joint first- and second-order statistics description, depending on the channel and system parameters. The results demonstrated several peculiarities, e.g., the existence of a specific extremum of the capacity reliability for small-sized MIMO systems, its opposite behavior (in terms of the varying number of antenna elements) for heavy and light fading, and the existing asymptotic regions of the system and the channel parameters.

An EEG-Based Brain-Computer Interface Using Spectral Correlation Function

Brain-Computer Interface (BCI) is a promising technique because of its wide variety of applications, from treating cognition in humans to person authentication. Brain signals can be transmitted straight to a prosthetic device from the BCI system, without the need for nerve or muscle activity. For accurately identifying the transmitted signals at the prosthetic device, considering the nature of the Electroencephalography (EEG) signal, and extracting the most informative features are effective keys. In this paper, we studied the cyclostationarity of the Slow Cortical Potential (SCP) EEG signals for BCI applications, following our previous studies. Cyclostationary analysis reveals the hidden periodicity in the signal and provides a second-order statistical description in the frequency domain. We used the FFT Accumulation Method (FAM), an effective computational algorithm, to extract the features of the Spectral Correlation Function (SCF). The features are classified using SVM RBF, SVM polynomial, and K-Nearest Neighbor classifiers, and they are considered with different pre-processing. Our research indicates that the SCP EEG signal has cyclostationary properties and this idea is applied to the BCIs as well. The classification accuracy on the BCI Competition 2003 dataset Ia’s increased considerably, by spotting the intrinsic correlation between just two EEG signals.

A Multiorder Attentional Spatial Interactive Convolutional Neural Network (MoAS-CNN) for Low-Resolution Haptic Recognition

In haptic recognition, pressure information is usually represented as an image, and then used for feature extraction and classification. Deep learning that processes haptic information in end-to-end manner has attracted attention. This study proposes a multiorder attentional spatial interactive convolutional neural network (MoAS-CNN) for haptic recognition. The asymmetric dual-stream all convolutional neural network with integrated channel attention module is applied for automatic first-order feature extraction. Later on, the spatial interactive features based on the overall feature map are computed to improve the second-order description capability. Finally, the multiorder features are summed to improve the feature utilization efficiency. To validate the MoAS-CNN, we construct a haptic acquisition platform based on three-scale pressure arrays and collect haptic letter-shape (A–Z) datasets with complex contours. The recognition accuracies are 95.73% for 16 × 16, 98.37% for 20 × 20 and 98.65% for 32 × 32, which significantly exceeds the traditional first- and second-order CNNs and local SIFT feature.

Order-theoretic Trees: Monadic Second-order Descriptions and Regularity

An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch (a maximal linearly ordered subset) can be any countable linear order. Such generalized infinite trees yield convenient definitions of the rank-width and the modular decomposition of countable graphs. We define an algebra based on only four operations that generate up to isomorphism and via infinite terms these order-theoretic trees and forests.We prove that the associated regular objects, i.e., those defined by regular terms, are exactly the ones that are the unique models of monadic second-order sentences. We adapt some tools that we have used in a previous article for proving a similar result for join-trees, i.e., for order-theoretic trees such that any two nodes have a least upper-bound.

Quantum thermal transport beyond second order with the reaction coordinate mapping.

Standard quantum master equation techniques, such as the Redfield or Lindblad equations, are perturbative to second order in the microscopic system-reservoir coupling parameter λ. As a result, the characteristics of dissipative systems, which are beyond second order in λ, are not captured by such tools. Moreover, if the leading order in the studied effect is higher-than-quadratic in λ, a second-order description fundamentally fails even at weak coupling. Here, using the reaction coordinate (RC) quantum master equation framework, we are able to investigate and classify higher-than-second-order transport mechanisms. This technique, which relies on the redefinition of the system-environment boundary, allows for the effects of system-bath coupling to be included to high orders. We study steady-state heat current beyond second-order in two models: The generalized spin-boson model with non-commuting system-bath operators and a three-level ladder system. In the latter model, heat enters in one transition and is extracted from a different one. Crucially, we identify two transport pathways: (i) System's current, where heat conduction is mediated by transitions in the system, with the heat current scaling as jq ∝ λ2 to the lowest order in λ. (ii) Inter-bath current, with the thermal baths directly exchanging energy between them, facilitated by the bridging quantum system. To the lowest order in λ, this current scales as jq ∝ λ4. These mechanisms are uncovered and examined using numerical and analytical tools. We contend that the RC mapping brings, already at the level of the mapped Hamiltonian, much insight into transport characteristics.

Dynamic economic dispatch of wind-storage combined system based on conditional value-at-risk

Wind power's uncertainty is from the intermittency and fluctuation of wind speed, which brings a great challenge to solving the power system's dynamic economic dispatch problem. With the wind-storage combined system, this paper proposes a dynamic economic dispatch model considering AC optimal power flow based on Conditional Value-at-Risk (CVaR). Since the proposed model is hard to solve, we use the big-M method and second-order cone description technique to transform it into a trackable mixed-integer second-order conic programming (MISOCP) model. By comparing the dispatching cost of the IEEE 30-bus system and the IEEE 118-bus system at different confidence levels, it is indicated that CVaR method can adequately estimate dispatching risk and assist decision-makers in making reasonable dispatching schedules according to their risk tolerance. Meanwhile, the optimal operational energy storage capacity and initial/final energy storage state can be determined by analyzing the dispatching cost risk under different storage capacities and initial/final states.

The {mathcal {S}}-cone and a primal-dual view on second-order representability

The {mathcal {S}}-cone provides a common framework for cones of polynomials or exponential sums which establish non-negativity upon the arithmetic-geometric inequality, in particular for sums of non-negative circuit polynomials (SONC) or sums of arithmetic-geometric exponentials (SAGE). In this paper, we study the {mathcal {S}}-cone and its dual from the viewpoint of second-order representability. Extending results of Averkov and of Wang and Magron on the primal SONC cone, we provide explicit generalized second-order descriptions for rational {mathcal {S}}-cones and their duals.

Identification of physically realistic state-space models for accurate component synthesis

For components that are difficult to model with conventional analytical or numerical tools, experimentally derived state-space models can instead be used in system synthesis. For successful state-space synthesis, a physically realistic model must be identified. For this purpose, a hybrid first- and second-order system description is used here as the basis for identification. In the identification procedure, a physically motivated rigid body rank constraint is imposed together with a reciprocity constraint. The two constraints are enforced during a re-estimation phase of the state-space matrices following after a traditional state-space subspace identification phase. In this paper, two complex and modally dense industrial components are combined into a dynamical system. An experimental model of a car body-in-white structure is identified. The identified subsystem model is coupled with a finite element model of a rear subframe in a system synthesis. The two subsystems are attached through four rubber bushings modelled by finite element procedures. It is shown that the experimental-analytical assembly successfully predicts the reference measured system, with higher accuracy than what could be achieved with a model based solely on finite elements. It is also shown that synthesis with individually calibrated rear subframe models can capture the variability in the coupled system.

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and the arbitrarily large deviations from thermal equilibrium that are present in the plasma periphery of tokamak devices. The formulation of the gyrokinetic model is based on a second-order accurate description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behaviour of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function. The collisional effects are included by a nonlinear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a Hermite–Laguerre velocity-space polynomial basis. Then, the gyrokinetic equation is projected onto the same basis yielding the spatial and temporal evolution of the Hermite–Laguerre expansion coefficients. A closed set of fluid equations for the lowest-order coefficients is presented. The Hermite–Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell equations derived from a variational principle where the velocity integrals are explicitly evaluated.

Space–Time Channel Model for Rain-Affected Communication Networks

This paper presents a new comprehensive space–time model of rainfall rate and its associated rainfield synthesizer called Grid Rain Attenuation Model (GRAM). A great deal of care is placed on explicitly including the rain/no rain condition so that the planning and simulation of high-frequency radio wave communication systems can be achieved with full consideration of rain intermittency effects. We also look in some details at the modification of the first- and second-order statistical descriptions of the rain precipitation rate upon the application of space and time integration to point rainfall rate.

Sub-wavelength sensing of bi-periodic materials using topological sensitivity of second-order homogenized model

We aim to detect defects or perturbations of periodic media, e.g. due to a defective manufacturing process. To this end, we consider scalar waves in such media through the lens of a second-order macroscopic description, and we compute the sensitivities of the germane effective parameters due to topological perturbations of a microscopic unit cell. Specifically, our analysis focuses on the tensorial coefficients in the governing mean-field equation – including both the leading order (i.e. quasi-static) terms, and their second-order companions bearing the effects of incipient wave dispersion. Then, we present a method that permits sub-wavelength sensing of periodic media, given the (anisotropic) phase velocity of plane waves illuminating the considered medium for several angles and wavenumbers.

Harmonics generation and the mechanics of saturation in flow over an open cavity: a second-order self-consistent description

The flow over an open cavity is an example of supercritical Hopf bifurcation leading to periodic limit-cycle oscillations. One of its distinctive features is the existence of strong higher harmonics, which results in the time-averaged mean flow being strongly linearly unstable. For this class of flows, a simplified formalism capable of unravelling how exactly the instability grows and saturates is lacking. This study builds on previous work by Mantič-Lugo et al. (Phys. Rev. Lett., vol. 113, 2014, 084501) to fill in the gap using a parametrized approximation of an instantaneous, phase-averaged mean flow, coupled in a quasi-static manner to multiple linear harmonic disturbances interacting nonlinearly with one another and feeding back on the mean flow via their Reynolds stresses. This provides a self-consistent modelling of the mean flow–fluctuation interaction, in the sense that all perturbation structures are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations. The first harmonic is sought as the superposition of two components, a linear component generated by the instability and aligned along the leading eigenmode of the mean flow, and a nonlinear orthogonal component generated by the higher harmonics, which progressively distorts the linear growth rate and eigenfrequency of the eigenmode. Saturation occurs when the growth rate of the first harmonic is zero, at which point the stabilizing effect of the second harmonic balances exactly the linear instability of the eigenmode. The model does not require any input from numerical or experimental data, and accurately predicts the transient development and the saturation of the instability, as established from comparison to time and phase averages of direct numerical simulation data.

Stylistic iconicity and Love's two orders of language

My aim here is to put integrationism's anti-systematicity into close conjunction with stylistics' craving for linguistic explanation of literary effects, to see whether any kind of rapprochement, even of conceptual inclusion of the latter within the former, is remotely possible—or whether such an effort only highlights the mutual incompatibility of the two mind-sets. Love's idea of two orders of language activity helps to focus the difficulties. Applying these to the practice and principles of stylistics, they prompt several basic questions: Is stylistics doomed to the adoption of one ‘second order’ descriptive machine after another, in a futile effort to capture the essence, the life, of the literary texts it analyses? Are readers' actual engagements with poems, their ‘first order’ experiencing of poems, never to be satisfactorily or usefully explained by these abstracting, unit-manipulating, second-order systems? In moving towards answers to these questions I will suggest that stylisticians are not unaware of their difficulties (sometimes more aware than other linguistic analysts of texts), and that one concept that some have adopted as part of an effort to forge a strong connection from the second-order description back to the first-order experience, is that of iconicity. I discuss whether ‘iconicity’ is stylistics' attempt to bridge the second-order/first-order gulf.

Cyclic spectral analysis of electrocardiogram signals based on GARCH model

Abstract In this paper, the capability of Cyclic Spectral Density (CSD) is evaluated for ECG signal analyzing and a new feature generation method for them is presented. Although, the CSD presents a second-order statistical description in the frequency domain and reveals the hidden periodicity in EEG signals, it needs an efficient algorithm for calculating and also a suitable model for describing. By employing an efficient computational algorithm which is called the FFT accumulation method (FAM), the CSD of ECG signals can be computed. In this study, In order to choose an efficient statistical model for the Cyclic Spectral Analysis (CSA) coefficients of ECG signals, their statistical features are investigated at various regions of bi-frequency plane. It is revealed that the CSA coefficients are heteroscedastic and the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) is a suitable model for them. Hence, The GARCH parameters of CSA sub-bands are calculated and are employed to classify the ECG using a support vector machine (SVM) classifier. Evidently, the results reveal that the performance of the new method in ECG classification outperforms the former studies.

Impact of the spatial structure of the hydraulic conductivity field on vorticity in three-dimensional flows.

A material fluid element within a porous medium experiences deformations due to the disordered spatial distribution of the Darcy scale velocity field, caused by the heterogeneity of hydraulic conductivity. A physical consequence of this heterogeneity is the presence of localized kinematical features such as straining, shearing and vorticity in the fluid element. These kinematical features will influence the shape of solute clouds and their fate. Studies on the deformation of material surfaces highlighted the importance of stretching and shearing, whereas vorticity received so far less attention, though it determines folding, a deformation associated with the local rotation of the velocity field. We study vorticity in a three-dimensional porous formation exploring how its fluctuations are influenced by the spatial structure of the porous media, obtained by immersing spheroidal inclusions into a matrix of constant hydraulic conductivity. By comparing porous formations with the same spatial statistics, we analyse how vorticity is affected by the different shape and arrangement of inclusions, defined as the medium 'microstructure'. We conclude that, as microstructure has a significant impact on vorticity fluctuations, the usual second-order statistical description of the conductivity field is unable to capture local deformations of the plume.

Hydrodynamics, resurgence, and transasymptotics

The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with initial conditions.

MRI Texture Analysis Reveals Bulbar Abnormalities in Friedreich Ataxia.

Texture analysis is an image processing technique that can be used to extract parameters able to describe meaningful features of an image or ROI. Texture analysis based on the gray level co-occurrence matrix gives a second-order statistical description of the image or ROI. In this work, the co-occurrence matrix texture approach was used to extract information from brain MR images of patients with Friedreich ataxia and a control group, to see whether texture parameters were different between these groups. A longitudinal analysis was also performed. Twenty patients and 21 healthy controls participated in the study. Both groups had 2 sets of T1-weighted MR images obtained 1 year apart for every subject. ROIs chosen for analysis were the medulla oblongata and pons. Texture parameters were obtained for these ROIs for every subject, for the 2 sets of images. These parameters were compared longitudinally within groups and transversally between groups. The comparison between patients and the control group showed a significant differences for the medulla oblongata (t test, P < .05, Bonferroni-corrected) but did not show a statistically significant difference for the pons. Longitudinal comparison of images obtained 1 year apart did not show differences for either patients or for controls, in any of the analyzed structures. Gray level co-occurrence matrix-based texture analysis showed statistically significant differences for the medulla oblongata of patients with Friedreich ataxia compared with controls. These results highlight the medulla as an important site of damage in Friedreich ataxia.

Second-order Lagrangian description of tri-dimensional gravity wave interactions

We revisit and supplement the description of gravity waves based on perturbation expansions in Lagrangian coordinates. A general analytical framework is developed to derive a second-order Lagrangian solution to the motion of arbitrary surface gravity wave fields in a compact and vectorial form. The result is shown to be consistent with the classical second-order Eulerian expansion by Longuet-Higgins (J. Fluid Mech., vol. 17, 1963, pp. 459–480) and is used to improve the original derivation by Pierson (1961 Models of random seas based on the Lagrangian equations of motion. Tech. Rep. New York University) for long-crested waves. As demonstrated, the Lagrangian perturbation expansion captures nonlinearities to a higher degree than does the corresponding Eulerian expansion of the same order. At the second order, it can account for complex nonlinear phenomena such as wave-front deformation that we can relate to the initial stage of horseshoe-pattern formation and the Benjamin–Feir modulational instability to shed new light on the origins of these mechanisms.

Proper-time hypersurface of nonrelativistic matter flows: Galaxy bias in general relativity

We compute the second-order density fluctuation in the proper-time hypersurface of nonrelativistic matter flows and relate it to galaxy number density fluctuation, providing physical grounds for galaxy bias in the context of general relativity. At the linear order, the density fluctuation in the proper-time hypersurface is equivalent to the density fluctuation in the comoving synchronous gauge, in which two separate gauge conditions coincide. However, at the second order, the density fluctuations in these gauge conditions differ, while both gauge conditions represent the same proper-time hypersurface. Compared to the density fluctuation in the temporal comoving and spatial $C$-gauge conditions, the density fluctuation in the commonly used gauge condition ($N=1$ and ${N}^{\ensuremath{\alpha}}=0$) violates the mass conservation at the second order. We provide their physical interpretations in each gauge condition by solving the geodesic equation and the nonlinear evolution equations of nonrelativistic matter. We apply this finding to the second-order galaxy biasing in general relativity, which complements the second-order relativistic description of galaxy clustering in Yoo and Zaldarriaga [Phys. Rev. D 90, 023513, (2014)].

Towards a Mathematical Description of Biodiversity Evolution

We outline in this work a mathematical description of biodiversity evolution based on a second-order differential equation (also known as the “inertial/Galilean view”). After discussing the motivations and explicit forms of the simplest “forces”, we are lead to an equation analogue to a harmonic oscillator. The known solutions for the homogeneous problem are then tentatively related to the biodiversity curves of Sepkoski and Alroy et al., suggesting mostly an inertial behavior of the time evolution of the number of genera and a quadratic behavior in some long-term evolution after extinction events. We present the Green function for the dynamical system and apply it to the description of the recovery curve after the Permo-Triassic extinction, as recently analyzed by Burgess, Bowring and Shen. Even though the agreement is not satisfactory, we point out direct connections between observed drop times after massive extinctions and mathematical constants and discuss why the failure ensues, suggesting a more complex form of the second-order mathematical description.