Harmonic Space Research Articles

A cross-correlation analysis of CMB lensing and radio galaxy maps

Aims. The goal of this work is to clarify the origin of the seemingly anomalously large clustering signal detected at large angular separation in the wide TGSS radio survey and, in so doing, to investigate the nature and the clustering properties of the sources that populate the radio sky in the [0.15, 1.4] GHz frequency range. Methods. To achieve this goal, we cross-correlated the angular position of the radio sources in the TGSS and NVSS samples with the cosmic microwave background (CMB) lensing maps from the Planck satellite. A cross-correlation between two different tracers of the underlying mass density field has the advantage of being quite insensitive to possible systematic errors that may affect the two observables, provided that they are not correlated, which seems unlikely in our case. The cross-correlation analysis was performed in harmonic space and limited to relatively modest multipoles. These choices, together with that of binning the measured spectra, minimize the correlation among the errors in the measured spectra and allowed us to adopt the Gaussian hypothesis to perform the statistical analysis. Finally, we decided to consider the auto-angular power spectrum on top of the cross-spectrum since a joint analysis has the potential to improve the constraints on the radio source properties by lifting the degeneracy between the redshift distribution, N(z), and the bias evolution, b(z). Results. The angular cross-correlation analysis does not present the power excess at large scales for TGSS and provides a TGSS–CMB lensing cross-spectrum that is in agreement with the one measured using the NVSS catalog. This result strongly suggests that the excess found in TGSS clustering analyses can be due to uncorrected systematic effects in the data. However, we considered several cross-spectra models that rely on physically motivated combinations of N(z) and b(z) prescriptions for the radio sources and find that they all underestimate the amplitude of the measured cross-spectra on the largest angular scales considered in our analysis, ∼10°. This result is robust to the various potential sources of systematic errors, both of observational and theoretical nature, that may affect our analysis, including the uncertainties in the N(z) model. Having assessed the robustness of the results to the choice of N(z), we repeated the analysis using simpler bias models specified by a single free parameter, bg, namely, the value of the effective bias of the radio sources at redshift zero. This improves the goodness of the fit, although not even the best model, which assumes a non-evolving bias, quite matches the amplitude of the cross-spectrum at small multipoles. Moreover, the best fitting bias parameter, bg = 2.53 ± 0.11, appears to be somewhat large considering that it represents the effective bias of a sample that is locally dominated by mildly clustered star-forming galaxies and Fanaroff-Riley class I sources. Interestingly, it is the addition of the angular auto-spectrum that favors the constant bias model over the evolving one. Conclusions. The nature of the large cross-correlation signal between the radio sources and the CMB lensing maps found in our analysis at large angular scales is not clear. It probably indicates some limitation in the modeling of the radio sources, namely the relative abundance of the various populations, their clustering properties, and how these evolve with redshift. What our analysis does show is the importance of combining the auto-spectrum with the cross-spectrum, preferably obtained with unbiased tracers of the large-scale structure, such as CMB lensing, for answering these questions.

Maximal Domains of Radial Harmonic Functions

We examine the maximal domain of radial harmonic functions on harmonic spaces in the context of positive, zero, and negative curvature.

Machine learning light hypernuclei

We employ a feed-forward artificial neural network to extrapolate at large model spaces the results of ab-initio hypernuclear No-Core Shell Model calculations for the Λ separation energy BΛ of the lightest hypernuclei, Λ3H, Λ4H and Λ4He, obtained in computationally accessible harmonic oscillator basis spaces using chiral nucleon-nucleon, nucleon-nucleon-nucleon and hyperon-nucleon interactions. The overfitting problem is avoided by enlarging the size of the input dataset and by introducing a Gaussian noise during the training process of the neural network. We find that a network with a single hidden layer of eight neurons is sufficient to extrapolate correctly the value of the Λ separation energy to model spaces of size Nmax=100. The results obtained are in agreement with the experimental data in the case of Λ3H and the 0+ state of Λ4He, although they are off of the experiment by about 0.3 MeV for both the 0+ and 1+states of Λ4H and the 1+ state of Λ4He. We find that our results are in excellent agreement with those obtained using other extrapolation schemes of the No-Core Shell Model calculations, showing this that an ANN is a reliable method to extrapolate the results of hypernuclear No-Core Shell Model calculations to large model spaces.

Two theorems on the intersections of horospheres in asymptotically harmonic spaces

We use Busemann functions to construct volume preserving mappings in an asymptotically harmonic manifold. If the asymptotically harmonic manifold satisfies the visibility condition, we construct mappings which preserve distances in some directions. We also prove that some integrals on the intersection of horospheres are independent of the differences between the values of the corresponding Busemann functions and we establish an upper bound of the volume of the intersection of two horospheres which is independent of the difference between values of corresponding Busemann functions.

Maximum likelihood kinetic Sunyaev-Zel’dovich velocity reconstruction

The kinetic Sunyaev Zel'dovich (kSZ) effect, cosmic microwave background (CMB) temperature anisotropies induced by the scattering of CMB photons from free electrons, will be measured by near-term CMB experiments at high significance. By combining CMB temperature anisotropies with a tracer of structure, such as a galaxy redshift survey, previous literature introduced a number of techniques to reconstruct the radial velocity field. This reconstructed radial velocity field encapsulates the majority of the cosmological information contained in the kSZ temperature anisotropies, and can provide powerful new tests of the standard cosmological model and theories beyond it. In this paper, we introduce a new estimator for the radial velocity field based on a coarse-grained maximum likelihood fit for the kSZ component of the temperature anisotropies, given a tracer of the optical depth. We demonstrate that this maximum likelihood estimator yields a higher fidelity reconstruction than existing quadratic estimators in the low-noise and high-resolution regime targeted by upcoming CMB experiments. We describe implementations of the maximum likelihood estimator in both harmonic space and map space, using either direct measurements of the optical depth field or a galaxy survey as a tracer. We comment briefly on the impact of biases introduced by imperfect reconstruction of the optical depth field.

An HMM-Based Approach for Cross-Harmonization of Jazz Standards

This paper presents a methodology for generating cross-harmonizations of jazz standards, i.e., for harmonizing the melody of a jazz standard (Song A) with the harmonic context of another (Song B). Specifically, the melody of Song A, along with the chords that start and end its sections (chord constraints), are used as a basis for generating new harmonizations with chords and chord transitions taken from Song B. This task involves potential incompatibilities between the components drawn from the two songs that take part in the cross-harmonization. In order to tackle such incompatibilities, two methods are introduced that are integrated in the Hidden Markov Model and the Viterbi algorithm. First, a rudimentary approach to chord grouping is presented that allows interchangeable utilization of chords belonging to the same group, depending on melody compatibility. Then, a “supporting” harmonic space of chords and probabilities is employed, which is learned from the entire dataset of the available jazz standards; this space provides local solutions when there are insurmountable conflicts between the melody and constraints of Song A and the harmonic context of Song B. Statistical and expert evaluation allow an analysis of the methodology, providing valuable insight about future steps.

Pseudo-Random Signal Injection for Position Sensorless Control of Five-Phase IPMSM Based on Third Harmonic Space

Pseudo-Random Signal Injection for Position Sensorless Control of Five-Phase IPMSM Based on Third Harmonic Space

Composition operators from harmonic $ \mathcal{H}^{\infty} $ space into harmonic Zygmund space

<abstract><p>This research paper sought to characterize the boundedness and compactness of composition operators from the space $ \mathcal{H}^{\infty} $ of bounded harmonic mappings into harmonic Zygmund space $ \mathcal{Z}_H $, on the open unit disk. Furthermore, we obtain an estimate of the essential norms of such an operator. These results extends the similar results that were proven for composition operators on analytic function spaces.</p></abstract>

Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH3OH–Cu(111)

A method for computing anharmonic thermophysical properties for adsorbates on metal surfaces has been extended to include libration, or frustrated rotation. Classical phase space integration is used with Monte Carlo sampling of the configuration space to obtain the partition function of CO on Pt(111) and CH3OH on Cu(111). A minima-preserving neural network potential energy surrogate is used within the integration routines. Direct state counting using discrete variable representation is used to benchmark the results. We find that the phase space integration approach is in excellent agreement with the direct state counting results. Comparison with standard models such as the harmonic oscillator indicates that anharmonicity contributes significantly to the thermodynamic properties of CH3OH on Cu(111). We find that there is also a considerable difference between the harmonic oscillator and phase space integration for CO on Pt(111), although the discrepancy can largely be attributed to the presence of multiple binding sites within the unit cell. We demonstrate that a multisite harmonic oscillator model might be sufficient for CO–Pt(111). A more thorough description of the potential energy surface, which can be achieved with phase space integration, is necessary for weakly bound adsorbates such as CH3OH. The thermophysical properties were used to calculate free energies of adsorption on the respective metals, and subsequently the equilibrium constants and Langmuir isotherms in relevant temperature ranges. The results show that the choice of model to obtain partition functions greatly affects the resulting surface coverages in kinetic models.

Entropy, Probabilistic Harmonic Space, and the Harmony of Antonio Carlos Jobim

This paper introduces a theoretical framework derived from a deep and detailed harmonic analysis of songs composed by Antonio Carlos Jobim, focusing on two components, namely, “semantic” (related to the idea of chord type) and “syntactic” (involving binary relations between contiguous chords). The research is mainly focused on investigating the correlations between compositional style (here related to the harmonic construction) and the concepts of probability, expectance, and, especially entropy, being the latter defined as a measure of uncertainty or “surprise” of events along time. After a bibliographical review of these topics and their applications to music, a section exposes Markov Chains, a mathematical tool used to formalize the “semantic-syntactic” harmonic relations statistically inferred in the analyzed corpus of Jobim’s works. Then it follows the formalization of a probabilistic harmonic space and the concept of probabilistic index, directly associated with the entropy of the observed binary relations. This approach opens a new analytical perspective, also allowing the generalization of the presented theoretical and methodological technology for the examination of other repertoires and posterior comparison, presenting then as a new mean of investigation on the nature of style.

Extending the Design Space of Class E Mode to Design a Multi-Octave Power Amplifier

This brief presents a new extended continuum of class E (ECCE) mode for multi-octave power amplifier (PA) design. The impedance space of class E mode is expanded by considering the resistive component in the second harmonic impedance. This provides an overlap between the fundamental and second harmonic loads, which is for the first time explored for class E mode, enabling its design beyond the octave band. This mode offers a wide impedance range for the third harmonic termination, unlike a fixed point (open/short) in other extended continuous modes. This wide third harmonic design space provides high flexibility to design output matching. To verify the validity of the proposed mode, a PA has been designed using a 10W GaN HEMT CGH40010F from Wolfspeed. A design scheme is also presented to obtain the feasible matching loads at desired frequencies. The PA operates over a multi-octave band from 0.45-2.9 GHz, corresponding to the fractional bandwidth of 146.27%. This circuit provides drain efficiency of 60-72.9% and the output power between 39.6-41.7 dBm over the operating band.

Impedance modelling and stability analysis of modular multilevel converter with different types of grid‐forming control schemes

With the increasing penetration of power electronics, grid-forming modular multilevel converters (MMCs) have attracted great attention in the upcoming MMC-based high-voltage direct current transmission (HVDC) projects. Power synchronization control (PSC) and direct power control (DPC) are two typical grid-forming control schemes for MMCs. This paper sets out to investigate the impedance-based stability characteristics of PSC-MMC and DPC-MMC. Utilizing the harmonic state space (HSS), equivalent impedance models of PSC-MMC and DPC-MMC are developed with the consideration of complete controllers and MMC internal dynamic characteristics. Impedance shaping effects of the major controllers are further analyzed to identify the frequency bands where the MMCs have negative resistive impedance characteristics. Finally, potential instability phenomena of the interconnected system are shown through the case studies, and the virtual impedance method is introduced as the stabilization control scheme. The electromagnetic transient simulation results based on PSCAD/EMTDC verify the accuracy of the impedance models and the effectivity of the stabilization control scheme.

A systematic study of a droplet breakup process in decaying homogeneous isotropic turbulence using a mesoscopic simulation approach

ABSTRACT The breakup of a spherical droplet in a decaying homogeneous isotropic turbulence is studied by solving the Cahn–Hilliard–Navier–Stokes equations. This flow provides a great opportunity to study the interactions of turbulent kinetic energy and interfacial free energy and their effects on the breakup dynamics. Three distinct stages of droplet evolution, namely, the deformation stage, the breakup stage, and the restoration stage, are identified and then analysed systematically from several perspectives: a geometric perspective, a dynamic perspective, a global energetic perspective, and a multiscale energy transfer perspective. It is found that the ending time of the breakup stage can be estimated by the Hinze criterion. The kinetic energy of the two-phase flow during the breakup stage is found to have a power-law decay with an exponent , compared to for the single-phase flow, mainly due to the enhanced viscous dissipation generated by the daughter droplets. Energy spectra of the two-phase flow show power-law decay, with a slope between and , at high wave numbers, both in the Fourier spectral space and in the spherical harmonics space.

Spatial imagery in extractive capitalism: form and strength in corporate social responsibility diagrams

In the contemporary capitalism of flows, companies that strongly depend on territorial resources adopt social private policies so as to ensure the spatial insertion of their projects. In order to preserve their reputation, they also take part in a dispute for the legitimate representation of social space through the growing use of the visual instrument of diagrams. From among the corporate uses of diagrams, two types will be discussed herein. Whereas “corporate social responsibility” diagrams presuppose a harmonic space of partnership and cooperation, social risk mapping reveals the presence of dissensus and threats to the business climate. The text makes a critical reading of the business management literature and the diagrammatic material that composes it, and discusses diagrams published in the sustainability and corporate social responsibility reports of large corporations in the mineral extractive sector.

Polynomial null solutions to bosonic Laplacians, bosonic Bergman and Hardy spaces

AbstractA bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second-order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group, hence of the spin group. In this paper, we firstly introduce some properties for homogeneous polynomial null solutions to bosonic Laplacians, which give us some important results, such as an orthogonal decomposition of the space of polynomials in terms of homogeneous polynomial null solutions to bosonic Laplacians, etc. This work helps us to introduce Bergman spaces related to bosonic Laplacians, named as bosonic Bergman spaces, in higher spin spaces. Reproducing kernels for bosonic Bergman spaces in the unit ball and a description of bosonic Bergman projection are given as well. At the end, we investigate bosonic Hardy spaces, which are considered as generalizations of harmonic Hardy spaces. Analogs of some well-known results for harmonic Hardy spaces are provided here. For instance, connections to certain complex Borel measure spaces, growth estimates for functions in the bosonic Hardy spaces, etc.

The BINGO project

Context. A new and promising technique for observing the Universe and study the dark sector is the intensity mapping of the redshifted 21 cm line of neutral hydrogen (H I). The Baryon Acoustic Oscillations [BAO] from Integrated Neutral Gas Observations (BINGO) radio telescope will use the 21 cm line to map the Universe in the redshift range 0.127 ≤ z ≤ 0.449 in a tomographic approach, with the main goal of probing the BAO. Aims. This work presents the forecasts of measuring the transversal BAO signal during the BINGO phase 1 operation. Methods. We used two clustering estimators: the two-point angular correlation function (ACF) in configuration space, and the angular power spectrum (APS) in harmonic space. We also used a template-based method to model the ACF and APS estimated from simulations of the BINGO region and to extract the BAO information. The tomographic approach allows the combination of redshift bins to improve the template fitting performance. We computed the ACF and APS for each of the 30 redshift bins and measured the BAO signal in three consecutive redshift blocks (lower, intermediate, and higher) of ten channels each. Robustness tests were used to evaluate several aspects of the BAO fitting pipeline for the two clustering estimators. Results. We find that each clustering estimator shows different sensitivities to specific redshift ranges, although both of them perform better at higher redshifts. In general, the APS estimator provides slightly better estimates, with smaller uncertainties and a higher probability of detecting the BAO signal, achieving ≳90% at higher redshifts. We investigate the contribution from instrumental noise and residual foreground signals and find that the former has the greater impact. It becomes more significant with increasing redshift, in particular for the APS estimator. When noise is included in the analysis, the uncertainty increases by up to a factor of ∼2.2 at higher redshifts. Foreground residuals, in contrast, do not significantly affect our final uncertainties. Conclusions. In summary, our results show that even when semi-realistic systematic effects are included, BINGO has the potential to successfully measure the BAO scale at radio frequencies.

Equivalent Impedance Modeling and Stability Analysis of MMC-HVDC with Wind Farm

The risk of resonances may exist in the power electronic transmission systems composed of wind farm (WF) and the high-voltage direct-current system consisting of modular multilevel converter (MMC-HVDC). And the oscillation frequency will show coupling characteristics. The frequency dynamic interaction effect causes the WF interconnected with MMC-HVDC system exhibit multiple-input multiple-output (MIMO) characteristics. The stability determination of the system will become very difficult. Therefore, using frequency dynamic interaction effect as one of the constraints, this paper uses the harmonic state space (HHS) method to establish the two-dimensional impedance model of the wind farm side MMC(WFMMC) and the grid-side converter (GSC) of the wind farm, and further an accurate dimensionality reduction method is proposed. Finally, the results of the simulation system built based on MATLAB/Simulink verify the accuracy of the established impedance model and show that using the established model for stability analysis can obtain more accurate analysis results.

Cosmic shear in harmonic space from the Dark Energy Survey Year 1 Data: compatibility with configuration space results

ABSTRACT We perform a cosmic shear analysis in harmonic space using the first year of data collected by the Dark Energy Survey (DES-Y1). We measure the cosmic weak lensing shear power spectra using the metacalibration catalogue and perform a likelihood analysis within the framework of CosmoSIS. We set scale cuts based on baryonic effects contamination and model redshift and shear calibration uncertainties as well as intrinsic alignments. We adopt as fiducial covariance matrix an analytical computation accounting for the mask geometry in the Gaussian term, including non-Gaussian contributions. A suite of 1200 lognormal simulations is used to validate the harmonic space pipeline and the covariance matrix. We perform a series of stress tests to gauge the robustness of the harmonic space analysis. Finally, we use the DES-Y1 pipeline in configuration space to perform a similar likelihood analysis and compare both results, demonstrating their compatibility in estimating the cosmological parameters S8, σ8, and Ωm. We use the DES-Y1 metacalibration shape catalogue, with photometric redshifts estimates in the range of 0.2−1.3, divided in four tomographic bins finding σ8(Ωm/0.3)0.5 = 0.766 ± 0.033 at 68 per cent CL. The methods implemented and validated in this paper will allow us to perform a consistent harmonic space analysis in the upcoming DES data.

Turning the volvelle: Exploring Jack Douthett's voice leading dynamics

This paper explores Jack Douthett's model of dynamical voice leading on the level of harmonic states. It investigates global contiguous and stroboscopic dynamical systems on the entire state space and introduces a measure of effectiveness for the trajectories under consideration. Special attention is paid to the harmonic state spaces behind second-order Clough-Myerson scales, such as diatonic triads and seventh chords. Finally, a set of trajectories as a tiling of exemplifies the connection with the Spectral Conjecture.

Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation

We study the observation of a stochastic gravitational-wave background (SGWB) made by a pulsar-timing array in the spherical harmonic space of the observable. The observable is a timing residual which is the time-averaged redshift fluctuation of a pulsar over the duration of observation. Using the Sachs-Wolfe line-of-sight integral for the redshift fluctuation, we derive the power spectrum of the timing residual, from which we develop a fast algorithm to compute the overlap reduction functions for the SGWB intensity and polarization anisotropies. We find that the algorithm is less complicated and more efficient than our previous work which is based on the expansion of the polarization basis tensors in terms of spherical harmonics. Also, we use the power spectrum to construct the bipolar spherical harmonic coefficients that characterize the statistical isotropy of the SGWB. In particular, the coefficients for the linear-polarization anisotropy are worked out for the first time. Our harmonic-space method is useful for the data analysis in future pulsar-timing-array observation on a large number of pulsars as well as for the measurement of the statistical isotropy of the SGWB.