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The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfven Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfven Mach number $M_A$. We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to Davis-Chandrasekhar-Fermi way of obtaining the magnetic field strength., Comment: 31 pages, 11 figures, submitted to ApJ

Exclusion zones in the cross-correlations between critical points (peak-void, peak-wall, filament-wall, filament-void) of the density field define quasi-standard rulers that can be used to constrain dark matter and dark energy cosmological parameters. The average size of the exclusion zone is found to scale linearly with the typical distance between extrema. The latter changes as a function of the matter content of the universe in a predictable manner, but its comoving size remains essentially constant in the linear regime of structure growth on large scales, unless the incorrect cosmology is assumed in the redshift-distance relation. This can be used to constrain the dark energy parameters when considering a survey that scans a range of redshifts. The precision of the parameter estimation is assessed using a set of cosmological simulations, and is found to be a 4$\sigma$ detection of a change in matter content of 5%, or about 3.8$\sigma$ detection of 50% shift in the dark energy parameter using a full sky survey up to redshift 0.5., Comment: 12 pages (including a 3-page appendix, 9 figures, 2 tables. Submitted to MNRAS

This monograph is the English version of the book "Quantum systems with hidden symmetry. Interbasis expansions" published in 2006 by the publishing house FIZMATLIT (Moscow) in Russian. When compiling this version of the book, typos and inaccuracies noted since the release of the Russian edition have been corrected.

We build a model to predict from first principles the properties of major mergers. We predict these from the coalescence of peaks and saddle points in the vicinity of a given larger peak, as one increases the smoothing scale in the initial linear density field as a proxy for cosmic time. To refine our results, we also ensure, using a suite of $\sim 400$ power-law Gaussian random fields smoothed at $\sim 30$ different scales, that the relevant peaks and saddles are topologically connected: they should belong to a persistent pair before coalescence. Our model allows us to (a) compute the probability distribution function of the satellite-merger separation in Lagrangian space: they peak at three times the smoothing scale; (b) predict the distribution of the number of mergers as a function of peak rarity: haloes typically undergo two major mergers ($>$1:10) per decade of mass growth; (c) recover that the typical spin brought by mergers: it is of the order of a few tens of percent., Comment: 12 pages, accepted to MNRAS; comments welcome

The alignment of striated intensity structures in thin neutral hydrogen (HI) spectroscopic channels with Galactic magnetic fields has been observed. However, the origin and nature of these striations are still debatable. Some studies suggest that the striations result solely from real cold-density filaments without considering the role of turbulent velocity fields, i.e., the velocity caustics effect in shaping the channel's intensity distribution. To determine the relative contribution of density and velocity in forming the striations in channel maps, we analyze synthetic observations of channel maps obtained with simulations that represent realistic magnetized multi-phase HI. We vary the thickness of the channel maps and apply the Velocity Decomposition Algorithm to separate the velocity and density contributions. In parallel, we analyze GALFA HI observations and compare the results. Our analysis shows that the thin channels are dominated by velocity contribution, and velocity caustics mainly generate the HI striations. We show that velocity caustics can cause a correlation between unsharp-masked HI structures and far-infrared emission. We demonstrate that the linear HI fibers revealed by the Rolling Hough Transform (RHT) in thin velocity channels originate from velocity caustics. As the thickness of channel maps increases, the relative contribution of density to fluctuations in channel maps also increases. As a result, more RHT-detected fibers tend to be perpendicular to the magnetic field. Conversely, the alignment with the magnetic field is the most prominent in thin channels. We conclude that similar to the Velocity Channel Gradients (VChGs) approach, RHT traces magnetic fields through the analysis of velocity caustics in thin channel maps., Comment: 26 pages, 18 figures, accepted for publication in MNRAS

The mean plane-of-sky magnetic field strength is traditionally obtained from the combination of polarization and spectroscopic data using the Davis-Chandrasekhar-Fermi (DCF) technique. However, we identify the major problem of the DCF to be its disregard of the anisotropic character of MHD turbulence. On the basis of the modern MHD turbulence theory we introduce a new way of obtaining magnetic field strength from observations. Unlike the DCF, the new technique uses not the dispersion of the polarization angle and line of sight velocities, but increments of these quantities given by the structure functions. To address the variety of the astrophysical conditions for which our technique can be applied, we consider the turbulence in both media with magnetic pressure larger than the gas pressure corresponding e.g. to molecular and the gas pressure larger than the magnetic pressure corresponding to the warm neutral medium. We provide general expressions for arbitrary admixture of Alfv\'en, slow and fast modes in these media and consider in detail the particular cases relevant to diffuse media and molecular clouds. We successfully test our results using synthetic observations obtained from MHD turbulence simulations. We demonstrate that our Differential Measure Approach (DMA), unlike the DCF, can be used to measure the distribution of magnetic field strengths, can provide magnetic field measurements with limited data and is much more stable in the presence of large scale variations induces of non-turbulent nature. In parallel, our study uncover the deficiencies of the earlier DCF research., Comment: 53 pages, 32 figures, Accepted by ApJ for publications. Code: https://github.com/kyuen2/MHD_Mode

The upcoming WEAVE-QSO survey will target a high density of quasars over a large area, enabling the reconstruction of the 3D density field through Lyman-$\alpha$ tomography over unprecedented volumes smoothed on intermediate scales ($\approx$ 16 Mpc/$h$). We produce mocks of the Lyman-$\alpha$ forest using LyMAS, and reconstruct the 3D density field between sightlines through Wiener filtering in a configuration compatible with the future WEAVE-QSO observations. The fidelity of the reconstruction is assessed by measuring one- and two-point statistics from the distribution of critical points in the cosmic web. In addition, initial Lagrangian statistics are predicted from first principles, and measurements of the connectivity of the cosmic web are performed. The reconstruction captures well the expected features in the auto- and cross-correlations of the critical points. This remains true after a realistic noise is added to the synthetic spectra, even though sparsity of sightlines introduces systematics, especially in the cross-correlations of points with mixed signature. Specifically, for walls and filaments, the most striking clustering features could be measured with up to 4 sigma of significance with a WEAVE-QSO-like survey. Moreover, the connectivity of each peak identified in the reconstructed field is globally consistent with its counterpart in the original field, indicating that the reconstruction preserves the geometry of the density field not only statistically, but also locally. Hence the critical points relative positions within the tomographic reconstruction could be used as standard rulers for dark energy by WEAVE-QSO and similar surveys., Comment: 26 pages, 22 figures, submitted to MNRAS

Focusing on both small separations and Baryonic Acoustic Oscillation scales, the cosmic evolution of the clustering properties of peak, void, wall, and filament-type critical points is measured using two-point correlation functions in $\Lambda$CDM dark matter simulations as a function of their relative rarity. A qualitative comparison to the corresponding theory for Gaussian Random fields allows us to understand the following observed features: i) the appearance of an exclusion zone at small separation, whose size depends both on rarity and on the signature (\ie the number of negative eigenvalues) of the critical points involved; ii) the amplification of the Baryonic Acoustic Oscillation bump with rarity and its reversal for cross-correlations involving negatively biased critical points; iii) the orientation-dependent small-separation divergence of the cross-correlations of peaks and filaments (voids and walls) which reflects the relative loci of such points in the filament's (wall's) eigenframe. The most significant features of the correlations are tabulated. The (cross-) correlations involving the most non-linear critical points (peaks, voids) display significant variation with redshift, while those involving less non-linear critical points seem mostly insensitive to redshift evolution, which should prove advantageous to model. The relative distances to the maxima of the peak-to-wall and peak-to-void over that of the peak-to-filament cross-correlation are in ratios of $\sim\sqrt{2}$ and $\sim\sqrt{3}$, respectively which could be interpreted as an indication of the cosmic crystal being on average close to a cubic lattice. The insensitivity to redshift evolution suggests that the absolute and relative clustering of critical points could become a topologically robust alternative to standard clustering techniques when analyzing upcoming large scale surveys such as Euclid or LSST., Comment: 19 pages, 11 figures, 6 tables, submitted to MNRAS

Magnetic turbulence is anisotropic as the directions of motion are constrained by the magnetic field. Such anisotropy can be observed in velocity centroids obtained from spectroscopic observations. We use magnetohydrodynamics (MHD) simulations to produce synthetic spectroscopic observations (position-position-velocity data) and study the anisotropy in the structure function of velocity centroid maps. We decomposed the velocity in the simulations into Alfv\'en, slow and fast-modes and studied how each of them contribute to the observed anisotropy. We found that when the angle between the line of sight and the mean magnetic field is large the Alfv\'en-mode dominates the observed anisotropy, while for smaller angles the anisotropy is not large enough to be used to probe the magnetization of the media, and it is dominated by the slow-mode. Our results are in fair agreement with the theoretical predictions in Kandel et al.(2016,2017)., Comment: 17 pages, 7 figures, accepted for publication in The Astrophysical Journal

The merging rate of cosmic structures is computed, relying on the Ansatz that they can be predicted in the initial linear density field from the coalescence of critical points with increasing smoothing scale, used here as a proxy for cosmic time. Beyond the mergers of peaks with saddle points (a proxy for halo mergers), we consider the coalescence and nucleation of all sets of critical points, including wall-saddle to filament-saddle and wall-saddle to minima (a proxy for filament and void mergers respectively), as they impact the geometry of galactic infall, and in particular filament disconnection. Analytical predictions of the one-point statistics are validated against multiscale measurements in 2D and 3D realisations of Gaussian random fields (the corresponding code being available upon request) and compared qualitatively to cosmological $N$-body simulations at early times ($z\geq 10$) and large scales ($\geq 5\, \mathrm{Mpc}/h$). The rate of filament coalescence is compared to the merger rate of haloes and the two-point clustering of these events is computed, along with their cross-correlations with critical points. These correlations are qualitatively consistent with the preservation of the connectivity of dark matter haloes, and the impact of the large scale structures on assembly bias. The destruction rate of haloes and voids as a function of mass and redshift is quantified down to $z=0$ for a $\Lambda$CDM cosmology. The one-point statistics in higher dimensions are also presented, together with consistency relations between critical point and critical event counts., Comment: 22 pages, 19 figures. Accepted for publication in MNRAS

We introduce two new ways of obtaining the strength of plane-of-sky (POS) magnetic field by simultaneous use of spectroscopic Doppler-shifted lines and the information on magnetic field direction. The latter can be obtained either through polarization measurements or using the velocity gradient technique. We show the advantages that our techniques have compared to the traditional Davis-Chandrasekhar-Fermi (DCF) technique of estimating magnetic field strength from observations. The first technique that we describe in detail employs structure functions of velocity centroids and structure functions of Stokes parameters. We provide analytical expressions for obtaining magnetic field strength from observational data. We successfully test our results using synthetic observations obtained with results of MHD turbulence simulations. We measure velocity and magnetic field fluctuations at small scales using two, three and four point structure functions and compare the performance of these tools. We show that, unlike the DCF, our technique is capable of providing the detailed distribution of POS magnetic field and it can measure magnetic field strength in the presence of both velocity and magnetic field distortions arising from external shear and self-gravity. The second technique applies the velocity gradient technique to velocity channel maps in order to obtain the Alfven Mach number and uses the amplitudes of the gradients to obtain the sonic Mach number. The ratio of these two Mach numbers provides the intensity of magnetic field in the region contributing to the emission in the channel map. We test the technique and discuss obtaining the 3D distribution of POS galactic Magnetic field with it. We discuss the application of the second technique to synchrotron data., Comment: 30 pages, 10 figures, submitted to ApJ

We investigate the impact of the number of filaments connected to the nodes of the cosmic web on the physical properties of their galaxies using the Sloan Digital Sky Survey. We compare these measurements to the cosmological hydrodynamical simulations Horizon-(no)AGN and Simba. We find that more massive galaxies are more connected, in qualitative agreement with theoretical predictions and measurements in dark matter only simulation. The star formation activity and morphology of observed galaxies both display some dependence on the connectivity of the cosmic web at fixed stellar mass: less star forming and less rotation supported galaxies also tend to have higher connectivity. These results qualitatively hold both for observed and virtual galaxies, and can be understood given that the cosmic web is the main source of fuel for galaxy growth. The simulations show the same trends at fixed halo mass, suggesting that the geometry of filamentary infall impacts galaxy properties beyond the depth of the local potential well. Based on simulations, it is also found that AGN feedback is key in reversing the relationship between stellar mass and connectivity at fixed halo mass. Technically, connectivity is a practical observational proxy for past and present accretion (minor mergers or diffuse infall)., Comment: 16 pages, 15 figures, submitted to MNRAS

In modern cosmology, many efforts have been put to detect primordial B-mode of cosmic microwave background (CMB) polarization from the gravitational waves generated during inflation. Considering the foreground dust contamination of microwave polarization maps, it is essential to obtain a precise prediction for polarization in dust emission. In this work, we show a new method to produce synthetic maps of dust polarization in magnetized turbulent ISM from more abundant high-resolution HI data. By using Velocity Channel Gradient (VChG) technique, we are able to predict both direction and degree of dust polarization by investigating spectroscopic HI information in position-position-velocity (PPV) space. We applied our approach to The Galactic Arecibo L-band feed Array HI (GALFA-HI) data, and find a good correspondence between synthesized maps and PLANCK's polarization measurements at 353 GHz., Comment: 15 pages, 8 figures, submitted to MNRAS

The aim of this work was to find a minimal set of structurally stable pentapeptides, which allows forming a polypeptide chain of a required 3D structure. To search for factors that ensure structural stability of the pentapeptide, we generated peptide sequences with no more than three functional groups, based on the alanine pentapeptide AAAAA. We analyzed 44,860 structures of peptides by the molecular dynamics method and found that 1,225 pentapeptides over 80% of the simulation time were in a stable conformation. Clustering of these conformations revealed 54 topological types of conformationally stable pentapeptides. These conformations relate to different combined elements of the protein secondary structure. So, we obtained a minimal set of amino acid structures of conformationally stable pentapeptides, creating a complete set of different topologies that ensure the formation of pre-folded conformation of protein structures.

A recent publication by Clark et.al (2019, CX19) uses both GALFA-HI observational data and numerical simulations to address the nature of intensity fluctuations in Position-Position-Velocity (PPV) space. The study questions the validity and applicability of the statistical theory of PPV space fluctuations formulated in Lazarian & Pogosyan (2000, LP00) to HI gas and concludes that $"${\it a significant reassessment of many observational and theoretical studies of turbulence in HI}$"$. This implies that dozens of papers that used LP00 theory to explore interstellar turbulence as well as the ongoing research based on LP00 theory are in error. This situation motivates the urgency of our public response. In our Comment we explain why we believe the criticism in CX19 is based on the incorrect understanding of the LP00 theory. In particular, we illustrate that the correlation between PPV slices and dust emissions in CX19 does not properly reveal the relative importance of velocity and density fluctuations in velocity channel maps. While CX19 provides an explanation of the change of the spectral index with respect to the thickness of PPV slice based on the two-phase nature of H1 gas, we failed to see any observational support for this idea. On the contrary, we show that the observations both in two-phase HI and one phase CO show similar results. Moreover, the observed change is in good agreement with LP00 predictions and spectral indexes of velocity and density spectra that are obtained following LP00 procedures are in good agreement with the numerically confirmed expectations of compressible MHD turbulence theory. In short, we could not find any justification of the criticism of LP00 theory that is provided in CX19. On the contrary, our analysis testifies that both available observational and numerical data agree well with the predictions of LP00 theory., Comment: 10 pages, 4 figures

In this work we effectively calculated the two-dimensional Minkowski functionals for cosmic microwave background (CMB) temperature maps generated by single field models of inflation with a standard kinetic term. We started with calculation of the bispectrum of initial perturbations and then calculated the two-dimensional configuration space cubic moments for temperature fluctuations. These cubic moments give rise to first order non-Gaussian correction terms to the Minkowski functionals. Thus, we developed a robust mechanism to predict the amount of non-Gaussianity generated by inflation in the CMB temperature maps using Minkowski functionals., Comment: arXiv admin note: substantial text overlap with arXiv:1506.01212

Cosmic connectivity and multiplicity, i.e. the number of filaments globally or locally connected to a given cluster is a natural probe of the growth of structure and in particular of the nature of dark energy. It is also a critical ingredient driving the assembly history of galaxies as it controls mass and angular momentum accretion. The connectivity of the cosmic web is investigated here via the persistent skeleton. This tool identifies topologically the set of ridges of the cosmic landscape which allows us to investigate in details how the nodes of the cosmic web are connected together. When applied to Gaussian random fields, it is found that on average the nodes are connected to exactly $\kappa=4$ neighbours in two dimensions and ~6.1 in three dimensions. Investigating spatial dimensions up to d=11, typical departures from a cubic lattice $\kappa=2d$ are shown to scale like the power 7/4 of the dimension. These numbers strongly depend on the height of the peaks: the higher the peak the larger the connectivity. Locally, the number of filaments sticking out from a node is not equal to its number of connections. At small distance, the peak has an ellipsoidal shape so that only two filaments emerge. Further away, filaments are subdivided at bifurcation points. At the resolution of the maps, the local number of filaments is 3 on average in 2D and 4 in 3D, depending on the height of the peak. Predictions from first principles based on peak theory are shown to reproduce well the connectivity and multiplicity of Gaussian random fields and cosmological simulations. As an illustration, this connectivity is quantified in galaxy lensing convergence maps and large dark haloes catalogues. As a function of redshift and scale the mean connectivity decreases in a cosmology dependent way. As a function of halo mass it scales like 10/3 times the log of the mass., Comment: 23 pages, matches version published in MNRAS