Canonical Space Research Articles

Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems.

The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.

Thiemann complexifier in classical and quantum FLRW cosmology

In the context of Loop Quantum Gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic FRW cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra. In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su(1,1) Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the su(1,1) Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale $\lambda$ and regularizes the gravitational Hamiltonian in terms of SU(2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero's canonical transformation which reduces to the classical one when $\lambda \rightarrow 0$. This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1,1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale $\lambda$, it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale

Heart rate from face videos under realistic conditions for advanced driver monitoring

Abstract The role of physiological signals has a large impact on driver monitoring systems, since it tells something about the human state. This work addresses the recursive probabilistic inference problem in time-varying linear dynamic systems to incorporate invariance into the task of heart rate estimation from face videos under realistic conditions. The invariance encapsulates motion as well as varying illumination conditions in order to accurately estimate vitality parameters from human faces using conventional camera technology. The solution is based on the canonical state space representation of an Itô process and a Wiener velocity model. Empirical results yield to excellent real-time and estimation performance of heart rates in presence of disturbing factors, like rigid head motion, talking, facial expressions and natural illumination conditions making the process of human state estimation from face videos applicable in a much broader sense, pushing the technology towards advanced driver monitoring systems.

Abstract relative Gabor transforms over canonical homogeneous spaces of semidirect product groups with Abelian normal factor

This paper introduces a unified approach to the abstract notion of relative Gabor transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let [Formula: see text] be a locally compact group, [Formula: see text] be a locally compact Abelian (LCA) group, and [Formula: see text] be a continuous homomorphism. Let [Formula: see text] be the semi-direct product of [Formula: see text] and [Formula: see text] with respect to [Formula: see text], [Formula: see text] be the canonical homogeneous space of [Formula: see text], and [Formula: see text] be the canonical relatively invariant measure on [Formula: see text]. Then we present a unified harmonic analysis approach to the theoretical aspects of the notion of relative Gabor transform over the Hilbert function space [Formula: see text].

A complementary approach for fault diagnosis of rolling bearing using canonical variate analysis based short-time energy feature

Signal decomposition is a meaningful and effective methodology which is widely used for fault diagnosis. Mode/feature selection is an inevitable topic for fault diagnosis of rolling bearing due to over-decomposition. In practical application, the selection of sensitive modes is a challenging task, so many valuable works have been performed to cope with it. However, the published works lack an effective approach to acquire few meaningful modes by avoiding the complicated mode selection procedures, prior to feature extraction. Moreover, selection of the modes of interest fails to take the residual part into account, which makes the diagnosis result sensitive to the number of modes/features retained. This paper proposes a complementary approach to extract fault features and avoid the selection of single mode of interest, which employs canonical variate analysis to convert the original variable into two complementary spaces; canonical variate space; and residual space. Then the complementary statistical indicators Hotelling T2 statistic and Q statistic are used to provide important information about the conditions of the rolling bearing. Subsequently, a new feature index, complementary short-time energy extracted from the two statistics are used as fault features which are given as an input to a classifier such as a support vector machine. Two data sets collected from different test rigs are used for demonstration of the proposed work. The experimental result shows that the troublesome feature/mode selection issue is avoided, and the diagnosis result is not sensitive to the number of canonical variate retained. Besides, the proposed approach can identify various working conditions of rolling bearing accurately, which is simple and effective for fault diagnosis of rolling bearing, compared with the existing methods.

Homomorphisms with small bound between Fourier algebras

Inspired by Kalton and Wood's work on group algebras, we describe almost completely contractive algebra homomorphisms from Fourier algebras into Fourier-Stieltjes algebras (endowed with their canonical operator space structure). We also prove that two locally compact groups are isomorphic if and only if there exists an algebra isomorphism $T$ between the associated Fourier algebras (resp. Fourier-Stieltjes algebras) with completely bounded norm $\| T \|_{cb} < \sqrt {3/2}$ (resp. $ \| T \|_{cb} < \sqrt {5}/2$). We show similar results involving the norm distortion $\| T \| \| T ^{-1} \|$ with universal but non-explicit bound. Our results subsume Walter's well-known structural theorems and also Lau's theorem on second conjugate of Fourier algebras.

Combined state and parameter estimation for Hammerstein systems with time delay using the Kalman filtering

SummaryThis paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time delay. Both the process and the measurement noises are considered in the system. On the basis of the observable canonical state space form and the key term separation, a pseudolinear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman filter–based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms, which are missed for the time delay, the Kalman filter–based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time delay, parameters, and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms.

Mapping the Fourfold Gospel: Textual Geography in the Eusebian Apparatus

Eusebius of Caesarea (ca. 260-339 c.e.) invented a paratextual apparatus for reading Matthew, Mark, Luke, and John as a fourfold unity. Yet despite Eusebius's creativity and the long afterlife of his invention, the apparatus remains underappreciated and widely misunderstood. This article argues that Michel de Certeau's distinction between itineraries and maps illuminates the innovative function of the Eusebian apparatus, which contrasts with earlier attempts at gospel harmony and synopsis. Instead of disrupting the narrative integrity of the four canonical gospels, Eusebius's map creates a canonical space that preserves gospel narrative and facilitates exegetical and liturgical appropriation.

Vibration of axially moving beam supported by viscoelastic foundation

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton’s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

The particle-hole map: Formal derivation and numerical implementation.

The particle-hole map (PHM) is a tool to visualize electronic excitations, based on representations in a canonical orbital transition space. Introduced as an alternative to the transition density matrix, the PHM has a simple probabilistic interpretation, indicating the origins and destinations of electrons and holes and, hence, the roles of different functional units of molecules during an excitation. We present a formal derivation of the PHM, starting from the particle-hole transition density matrix and projecting onto a set of single-particle orbitals. We implement the PHM using atom-centered localized basis sets and discuss the example of the molecular charge-transfer complex C2H4-C2F4.

Filtering based parameter estimation for observer canonical state space systems with colored noise

This paper surveys the identification of observer canonical state space systems affected by colored noise. By means of the filtering technique, a filtering based recursive generalized extended least squares algorithm is proposed for enhancing the parameter identification accuracy. To ease the computational burden, the filtered regressive model is separated into two fictitious sub-models, and then a filtering based two-stage recursive generalized extended least squares algorithm is developed on the basis of the hierarchical identification. The stochastic martingale theory is applied to analyze the convergence of the proposed algorithms. An experimental example is provided to validate the proposed algorithms.

A Note on Functional Observability

In this note, we propose an alternative to characterize the functional observability for linear systems. The main feature is that we obtain a necessary and sufficient condition for the existence of a stable multi-functional observer of a time-invariant linear system. The proof of this condition is constructive and it leads to design a stable observer via a new procedure, neither based on the solution of a Sylvester equation nor on the use of canonical state space forms.

Iterative Channel Estimation for MIMO-OFDM System in Fast Time-Varying Channels

A practical iterative channel estimation technique is proposed for the multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system in the high-speed mobile environment, such as high speed railway scenario. In the iterative algorithm, the Kalman filter and data detection are jointed to estimate the time-varying channel, where the detection error is considered as part of the noise in the Kalman recursion in each iteration to reduce the effect of the detection error propagation. Moreover, the employed Kalman filter is from the canonical state space model, which does not include the parameters of the autoregressive (AR) model, so the proposed method does not need to estimate the parameters of AR model, whose accuracy affects the convergence speed. Simulation results show that the proposed method is robust to the fast time-varying channel, and it can obtain more gains compared with the available methods.

Use of canonical discriminant analysis to study signatures of selection in cattle.

BackgroundCattle include a large number of breeds that are characterized by marked phenotypic differences and thus constitute a valuable model to study genome evolution in response to processes such as selection and domestication. Detection of “signatures of selection” is a useful approach to study the evolutionary pressures experienced throughout history. In the present study, signatures of selection were investigated in five cattle breeds farmed in Italy using a multivariate approach.MethodsA total of 4094 bulls from five breeds with different production aptitudes (two dairy breeds: Italian Holstein and Italian Brown Swiss; two beef breeds: Piemontese and Marchigiana; and one dual purpose breed: Italian Simmental) were genotyped using the Illumina BovineSNP50 v.1 beadchip. Canonical discriminant analysis was carried out on the matrix of single nucleotide polymorphisms (SNP) genotyping data, separately for each chromosome. Scores for each canonical variable were calculated and then plotted in the canonical space to quantify the distance between breeds. SNPs for which the correlation with the canonical variable was in the 99th percentile for a specific chromosome were considered to be significantly associated with that variable. Results were compared with those obtained using an FST-based approach.ResultsBased on the results of the canonical discriminant analysis, a large number of signatures of selection were detected, among which several had strong signals in genomic regions that harbour genes known to have an impact on production and morphological bovine traits, including MSTN, LCT, GHR, SCD, NCAPG, KIT, and ASIP. Moreover, new putative candidate genes were identified, such as GCK, B3GALNT1, MGAT1, GALNTL1, PRNP, and PRND. Similar results were obtained with the FST-based approach.ConclusionsThe use of canonical discriminant analysis on 50 K SNP genotypes allowed the extraction of new variables that maximize the separation between breeds. This approach is quite straightforward, it can compare more than two groups simultaneously, and relative distances between breeds can be visualized. The genes that were highlighted in the canonical discriminant analysis were in concordance with those obtained using the FST index.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-016-0236-7) contains supplementary material, which is available to authorized users.

Vibration of an Axially Moving String Supported by a Viscoelastic Foundation

The transverse vibration of an axially moving string supported by a viscoelastic foundation is analysed using the complex modal method. The equation of motion is developed using the generalized Hamilton principle. The exact closed-form solution of eigenvalues and eigenfunctions are obtained. The governing equation is represented in a canonical state space form defined by two matrix differential operators, and the eigenfunctions and adjoint eigenfunctions are proved to be orthogonal with respect to each operator. This orthogonality is applied so that the response to arbitrary external excitations and initial conditions can be expressed in modal expansion. Numerical examples are presented to validate the proposed approach.

On the relationship between modifications to the Raychaudhuri equation and the canonical Hamiltonian structures

The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space.

Interdependent preference models as a theory of intentions

We provide a preference framework for situations in which “intentions matter.” A behavioral type describes the individual's observable characteristics and the individual's personality. We define a canonical behavioral type space and provide a condition that identifies collections of behavioral types that are equivalent to components of the canonical type space. We also develop a reciprocity model within our framework and show how it enables us to distinguish between strategic (or instrumental) generosity and true generosity.

A direct design procedure for linear state functional observers

We propose a constructive procedure to design a Luenberger observer to estimate a linear multiple linear state functional for a linear time-invariant system. Among other features the proposed design algorithm is not based on the solution of a Sylvester equation nor on the use of canonical state space forms. The design is based on the solution set of a linear equation and a realization method. The consistency of this equation and the stability of the observer can be used as a functional observability test.

A game for crowdsourcing the segmentation of BigBrain data

The BigBrain, a high-resolution 3-D model of a human brain at nearly cellular resolution, is the best brain imaging data set in the world to establish a canonical space at both microscopic and macroscopic resolutions. However, for the cell-stained microstructural data to be truly useful, it needs to be segmented into cytoarchitectonic regions, a challenge no single lab could undertake. The principal aim of this proposal is to crowdsource the segmentation of cytoarchitectonic regions by means of a computer game, to transform an arduous, isolated task performed by experts into an engaging, collective activity of non-experts.

Null distance on a spacetime

Given a time function τ on a spacetime M, we define a null distance function, , built from and closely related to the causal structure of M. In basic models with timelike , we show that (1) is a definite distance function, which induces the manifold topology, (2) the causal structure of M is completely encoded in and τ. In general, is a conformally invariant pseudometric, which may be indefinite. We give an ‘anti-Lipschitz’ condition on τ, which ensures that is definite, and show this condition to be satisfied whenever τ has gradient vectors almost everywhere, with locally ‘bounded away from the light cones’. As a consequence, we show that the cosmological time function of Andersson et al (1998 Class. Quantum Grav. 15 309–22) is anti-Lipschitz when ‘regular’, and hence induces a definite null distance function. This provides what may be interpreted as a canonical metric space structure on spacetimes which emanate from a common initial singularity, e.g. a ‘big bang’.