Analytic m-isometries and weighted Dirichlet-type spaces

Corresponding to any $(m-1)$-tuple of semi-spectral measures on the unit circle, a weighted Dirichlet-type space is introduced and studied. We prove that the operator of multiplication by the coordinate function on these weighted Dirichlet-type spaces acts as an analytic $m$-isometry and satisfies a certain set of operator inequalities. Moreover, it is shown that an analytic $m$-isometry which satisfies this set of operator inequalities can be represented as an operator of multiplication by the coordinate function on a weighted Dirichlet-type space induced from an $(m-1)$-tuple of semi-spectral measures on the unit circle. This extends a result of Richter as well as of Olofsson on the class of analytic $2$-isometries. We also prove that all left invertible $m$-concave operators satisfying the aforementioned operator inequalities admit a Wold-type decomposition. This result serves as a key ingredient to our model theorem and also generalizes a result of Shimorin on a class of $3$-concave operators.Comment: This is a minor revision of the previous versio

Redshifted 21-cm bispectrum II: Impact of the spin temperature fluctuations and redshift space distortions on the signal from the Cosmic Dawn

We present a study of the 21-cm signal bispectrum (which quantifies the non-Gaussianity in the signal) from the Cosmic Dawn (CD). For our analysis, we have simulated the 21-cm signal using radiative transfer code GRIZZLY, while considering two types of sources (mini-QSOs and HMXBs) for Ly$\alpha$ coupling and the X-ray heating of the IGM. Using this simulated signal, we have, for the first time, estimated the CD 21-cm bispectra for all unique $k$-triangles and for a range of $k$ modes. We observe that the redshift evolution of the bispectra magnitude and sign follow a generic trend for both source models. However, the redshifts at which the bispectra magnitude reach their maximum and minimum values and show their sign reversal depends on the source model. When the Ly$\alpha$ coupling and the X-ray heating of the IGM occur simultaneously, we observe two consecutive sign reversals in the bispectra for small $k$-triangles (irrespective of the source models). One arising at the beginning of the IGM heating and the other at the end of Ly$\alpha$ coupling saturation. This feature can be used in principle to constrain the CD history and/or to identify the specific CD scenarios. We also quantify the impact of the spin temperature ($T_{\rm S}$) fluctuations on the bispectra. We find that $T_{\rm S}$ fluctuations have maximum impact on the bispectra magnitude for small $k$-triangles and at the stage when Ly$\alpha$ coupling reaches saturation. Furthermore, we are also the first to quantify the impact of redshift space distortions (RSD), on the CD bispectra. We find that the impact of RSD on the CD 21-cm bispectra is significant ($> 20\%$) and the level depends on the stages of the CD and the $k$-triangles for which the bispectra are being estimated.Comment: 15 pages, 9 figures. Accepted for publication in the MNRAS. Replaced to match the accepted versio

Redshifted 21-cm bispectrum: Impact of the source models on the signal and IGM physics from the Cosmic Dawn

The radiations from the first luminous sources drive the fluctuations in the 21-cm signal at Cosmic Dawn (CD) via two dominant astrophysical processes i.e. the Ly$\alpha$ coupling and X-ray heating, making this signal highly non-Gaussian. The impact of these processes on the 21-cm signal and its non-Gaussianity vary depending on the properties of these first sources of light. In this work, we consider different CD scenarios by varying two major source parameters i.e. the minimum halo mass $M_{\rm h,\, min}$ and X-ray photon production efficiency $f_{\rm X}$ in a 1D radiative transfer code GRIZZLY. We study the impact of variation in these source parameters on the large scale ($k_1 = 0.16 {\, \rm Mpc}^{-1}$) 21-cm bispectrum for all possible unique triangles in the Fourier domain. Our detailed and comparative analysis of the power spectrum and bispectrum shows that the shape, sign and magnitude of the bispectrum combinedly provide the best measure of the signal fluctuations and its non-Gaussianity compared to the power spectrum. We also conclude that it is important to study the sequence of sign changes along with the variations in the shape and magnitude of the bispectrum throughout the CD history to arrive at a robust conclusion about the dominant IGM processes at different cosmic times. We further observe that among all the possible unique $k$-triangles, the large-scale non-Gaussianity in signal is best probed by the small $k$-triangles in the squeezed limit and by triangles of similar shapes. This opens up the possibility of constraining the source parameters during the CD using the 21-cm bispectrum.Comment: 29 pages, 8 figures, comments are welcom

Flow cytometry of bone marrow aspirates from neuroblastoma patients is a highly sensitive technique for quantification of low-level neuroblastoma [version 1; peer review: awaiting peer review]

Background: Bone marrow involvement is an important aspect of determining staging of disease and treatment for childhood neuroblastoma. Current standard of care relies on microscopic examination of bone marrow trephine biopsies and aspirates respectively, to define involvement. Flow cytometric analysis of disaggregated tumour cells, when using a panel of neuroblastoma specific markers, allows for potentially less subjective determination of the presence of tumour cells. / Methods: A retrospective review of sequential bone marrow trephine biopsies and aspirates, performed at Great Ormond Street Hospital, London, between the years 2015 and 2018, was performed to assess whether the addition of flow cytometric analysis to these standard of care methods provided concordant or additional information. / Results: There was good concurrence between all three methods for negative results 216/302 (72%). Positive results had a concordance of 52/86 (61%), comparing samples positive by flow cytometry and positive by either or both cytology and histology. Of the remaining samples, 20/86 (23%) were positive by either or both cytology and histology, but negative by flow cytometry. Whereas 14/86 (16%) of samples were positive only by flow cytometry. / Conclusions: Our review highlights the ongoing importance of expert cytological and histological assessment of bone marrow results. Flow cytometry is an objective, quantitative method to assess the level of bone marrow disease in aspirates. In this study, flow cytometry identified low-level residual disease that was not detected by cytology or histology. The clinical significance of this low-level disease warrants further investigation

Assessing the impact of two independent direction-dependent calibration algorithms on the LOFAR 21-cm signal power spectrum

Detecting the 21-cm signal from the Epoch of Reionisation (EoR) is challenging due to the strong astrophysical foregrounds, ionospheric effects, radio frequency interference and instrumental effects. Understanding and calibrating these effects are crucial for the detection. In this work, we introduce a newly developed direction-dependent (DD) calibration algorithm DDECAL and compare its performance with an existing algorithm, SAGECAL, in the context of the LOFAR-EoR 21-cm power spectrum experiment. In our data set, the North Celestial Pole (NCP) and its flanking fields were observed simultaneously. We analyse the NCP and one of its flanking fields. The NCP field is calibrated by the standard pipeline, using SAGECAL with an extensive sky model and 122 directions, and the flanking field is calibrated by DDECAL and SAGECAL with a simpler sky model and 22 directions. Additionally, two strategies are used for subtracting Cassiopeia A and Cygnus A. The results show that DDECAL performs better at subtracting sources in the primary beam region due to the application of a beam model, while SAGECAL performs better at subtracting Cassiopeia A and Cygnus A. This indicates that including a beam model during DD calibration significantly improves the performance. The benefit is obvious in the primary beam region. We also compare the 21-cm power spectra on two different fields. The results show that the flanking field produces better upper limits compared to the NCP in this particular observation. Despite the minor differences between DDECAL and SAGECAL due to the beam application, we find that the two algorithms yield comparable 21-cm power spectra on the LOFAR-EoR data after foreground removal. Hence, the current LOFAR-EoR 21-cm power spectrum limits are not likely to depend on the DD calibration method.Comment: 28 pages, 14 figures, accepted for publication in A&

Degree-scale galactic radio emission at 122 MHz around the North Celestial Pole with LOFAR-AARTFAAC

Large scale structure and cosmolog

Effects of the sources of reionization on 21-cm redshift-space distortions

The observed 21 cm signal from the epoch of reionization will be distorted along the line of sight by the peculiar velocities of matter particles. These redshift-space distortions will affect the contrast in the signal and will also make it anisotropic. This anisotropy contains information about the cross-correlation between the matter density field and the neutral hydrogen field, and could thus potentially be used to extract information about the sources of reionization. In this paper, we study a collection of simulated reionization scenarios assuming different models for the sources of reionization. We show that the 21 cm anisotropy is best measured by the quadrupole moment of the power spectrum. We find that, unless the properties of the reionization sources are extreme in some way, the quadrupole moment evolves very predictably as a function of global neutral fraction. This predictability implies that redshift-space distortions are not a very sensitive tool for distinguishing between reionization sources. However, the quadrupole moment can be used as a model-independent probe for constraining the reionization history. We show that such measurements can be done to some extent by first-generation instruments such as LOFAR, while the SKA should be able to measure the reionization history using the quadrupole moment of the power spectrum to great accuracy

Nature's Swiss Army Knives: Ovipositor Structure Mirrors Ecology in a Multitrophic Fig Wasp Community

Resource partitioning is facilitated by adaptations along niche dimensions that range from morphology to behaviour. The exploitation of hidden resources may require specially adapted morphological or sensory tools for resource location and utilisation. Differences in tool diversity and complexity can determine not only how many species can utilize these hidden resources but also how they do so.The sclerotisation, gross morphology and ultrastructure of the ovipositors of a seven-member community of parasitic wasps comprising of gallers and parasitoids developing within the globular syconia (closed inflorescences) of Ficus racemosa (Moraceae) was investigated. These wasps also differ in their parasitism mode (external versus internal oviposition) and their timing of oviposition into the expanding syconium during its development. The number and diversity of sensilla, as well as ovipositor teeth, increased from internally ovipositing to externally ovipositing species and from gallers to parasitoids. The extent of sclerotisation of the ovipositor tip matched the force required to penetrate the syconium at the time of oviposition of each species. The internally ovipositing pollinator had only one type of sensillum and a single notch on the ovipositor tip. Externally ovipositing species had multiple sensilla types and teeth on their ovipositors. Chemosensilla were most concentrated at ovipositor tips while mechanoreceptors were more widely distributed, facilitating the precise location of hidden hosts in these wasps which lack larval host-seeking behaviour. Ovipositor traits of one parasitoid differed from those of its syntopic galler congeners and clustered with those of parasitoids within a different wasp subfamily. Thus ovipositor tools can show lability based on adaptive necessity, and are not constrained by phylogeny.Ovipositor structure mirrored the increasingly complex trophic ecology and requirements for host accessibility in this parasite community. Ovipositor structure could be a useful surrogate for predicting the biology of parasites in other communities

Comparing foreground removal techniques for recovery of the LOFAR-EoR 21 cm power spectrum

We compare various foreground removal techniques that are being utilised to remove bright foregrounds in various experiments aiming to detect the redshifted 21cm signal of neutral hydrogen from the Epoch of Reionization. In this work, we test the performance of removal techniques (FastICA, GMCA, and GPR) on 10 nights of LOFAR data and investigate the possibility of recovering the latest upper limit on the 21cm signal. Interestingly, we find that GMCA and FastICA reproduce the most recent 2σ upper limit of Δ221< (73)2 mK2 at k=0.075 hcMpc−1, which resulted from the application of GPR. We also find that FastICA and GMCA begin to deviate from the noise-limit at \textit{;k};-scales larger than ∼0.1 hcMpc−1. We then replicate the data via simulations to see the source of FastICA and GMCA's limitations, by testing them against various instrumental effects. We find that no single instrumental effect, such as primary beam effects or mode-mixing, can explain the poorer recovery by FastICA and GMCA at larger \textit{;k};-scales. We then test scale- independence of FastICA and GMCA, and find that lower \textit{;k};-scales can be modelled by a smaller number of independent components. For larger scales (k≳0.1 hcMpc−1), more independent components are needed to fit the foregrounds. We conclude that, the current usage of GPR by the LOFAR collaboration is the appropriate removal technique. It is both robust and less prone to overfitting, with future improvements to GPR's fitting optimisation to yield deeper limits

Constraining the intergalactic medium at z ≈ 9.1 using LOFAR Epoch of Reionization observations

We derive constraints on the thermal and ionization states of the intergalactic medium (IGM) at redshift ≈ 9.1 using new upper limits on the 21-cm power spectrum measured by the LOFAR radio telescope and a prior on the ionized fraction at that redshift estimated from recent cosmic microwave background (CMB) observations. We have used results from the reionization simulation code GRIZZLY and a Bayesian inference framework to constrain the parameters which describe the physical state of the IGM. We find that, if the gas heating remains negligible, an IGM with ionized fraction 0.13 and a distribution of the ionized regions with a characteristic size 8 h−1 comoving megaparsec (Mpc) and a full width at half-maximum (FWHM) 16 h−1 Mpc is ruled out. For an IGM with a uniform spin temperature TS 3 K, no constraints on the ionized component can be computed. If the large-scale fluctuations of the signal are driven by spin temperature fluctuations, an IGM with a volume fraction 0.34 of heated regions with a temperature larger than CMB, average gas temperature 7–160 K, and a distribution of the heated regions with characteristic size 3.5–70 h−1 Mpc and FWHM of 110 h−1 Mpc is ruled out. These constraints are within the 95 per cent credible intervals. With more stringent future upper limits from LOFAR at multiple redshifts, the constraints will become tighter and will exclude an increasingly large region of the parameter space