Search

We perform the first broadband study of Mrk421 from radio to TeV gamma rays with simultaneous measurements of the X-ray polarization from IXPE. The data were collected within an extensive multiwavelength campaign organized between May and June 2022 using MAGIC, Fermi-LAT, NuSTAR, XMM-Newton, Swift, and several optical and radio telescopes to complement IXPE. During the IXPE exposures, the measured 0.2-1 TeV flux is close to the quiescent state and ranges from 25% to 50% of the Crab Nebula without intra-night variability. Throughout the campaign, the VHE and X-ray emission are positively correlated at a $4\sigma$ significance level. The IXPE measurements unveil a X-ray polarization degree that is a factor of 2-5 higher than in the optical/radio bands; that implies an energy-stratified jet in which the VHE photons are emitted co-spatially with the X-rays, in the vicinity of a shock front. The June 2022 observations exhibit a rotation of the X-ray polarization angle. Despite no simultaneous VHE coverage being available during a large fraction of the swing, the Swift-XRT monitoring unveils an X-ray flux increase with a clear spectral hardening. It suggests that flares in high synchrotron peaked blazars can be accompanied by a polarization angle rotation, as observed in some flat spectrum radio quasars. Finally, during the polarization angle rotation, NuSTAR data reveal two contiguous spectral hysteresis loops in opposite directions (clockwise and counter-clockwise), implying important changes in the particle acceleration efficiency on $\sim$hour timescales., Comment: Accepted for publication in Astronomy & Astrophysics. 29 pages, 22 figures. Corresponding authors: Axel Arbet Engels, Felix Schmuckermaier, David Paneque

The variations in Ly$\alpha$ forest opacity observed at $z>5.3$ between lines of sight to different background quasars are too strong to be caused by fluctuations in the density field alone. The leading hypothesis for the cause of this excess variance is a late, ongoing reionization process at redshifts below six. Another model proposes strong ionizing background fluctuations coupled to a short, spatially varying mean free path of ionizing photons, without explicitly invoking incomplete reionization. With recent observations suggesting a short mean free path at $z\sim6$, and a dramatic improvement in $z>5$ Ly$\alpha$ forest data quality, we revisit this latter possibility. Here we apply the likelihood-free inference technique of approximate Bayesian computation to jointly constrain the hydrogen photoionization rate $\Gamma_{\rm HI}$ and the mean free path of ionizing photons $\lambda_{\rm mfp}$ from the effective optical depth distributions at $z=5.0$-$6.1$ from XQR-30. We find that the observations are well-described by fluctuating mean free path models with average mean free paths that are consistent with the steep trend implied by independent measurements at $z\sim5$-$6$, with a concomitant rapid evolution of the photoionization rate., Comment: 23 pages, 13 figures, resubmitted to ApJ after referee's comments

The Event Horizon Telescope (EHT) observations carried out in 2018 April at 1.3 mm wavelengths included 9 stations in the array, comprising 7 single-dish telescopes and 2 phased arrays. The metadata package for the 2018 EHT observing campaign contains calibration tables required for the a-priori amplitude calibration of the 2018 April visibility data. This memo is the official documentation accompanying the release of the 2018 EHT metadata package, providing an overview of the contents of the package. We describe how telescope sensitivities, gain curves and other relevant parameters for each station in the EHT array were collected, processed, and validated to produce the calibration tables., Comment: 26 pages, 7 figures, EHT Memo Series 2023-L1-01

We establish, for every family of orthogonal polynomials in the $q$-Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths on the lecture hall graph. This generalizes the previous results of Corteel and Kim for the little $q$-Jacobi polynomials. We build these combinatorial models by bootstrapping, beginning with polynomials at the bottom and working towards Askey-Wilson polynomials which sit at the top of the $q$-Askey scheme. As an application of the theory, we provide the first combinatorial proof of the symmetries in the parameters of the Askey-Wilson polynomials., Comment: 43 pages, 23 figures

Measurements of the mean free path of Lyman-continuum photons in the intergalactic medium during the epoch of reionization can help constrain the nature of the sources as well as sinks of hydrogen-ionizing radiation. A recent approach to this measurement has been to utilize composite spectra of multiple quasars at $z\sim 6$, and infer the mean free path after correcting the spectra for the presence of quasar proximity zones. This has revealed not only a steep drop in the mean free path from $z=5$ to $z=6$, but also potentially a mild tension with reionization simulations. We critically examine such direct measurements of the mean free path for biases due to quasar environment, incomplete reionization, and quasar proximity zones. Using cosmological radiative transfer simulations of reionization combined with one-dimensional radiative transfer calculations of quasar proximity zones, we find that the bias in the mean free path due to overdensities around quasars is minimal at $z\sim 6$. Patchiness of reionization at this redshift also does not affect the measurements significantly. Fitting our model to the data results in a mean free path of $\lambda_{\mathrm{mfp}}=1.49^{+0.47}_{-0.52}$~pMpc at $z=6$, which is consistent with the recent measurements in the literature, indicating robustness with respect to the modelling of quasar proximity zones. We also compare various ways in which the mean free path has been defined in simulations before the end of reionization. Overall, our finding is that recent measurements of the mean free path appear to be robust relative to several sources of potential bias., Comment: Accepted in MNRAS. Mean free path measurement revised to a higher value with narrower uncertainty using full data covariance

We present an analysis of the ultraviolet (UV) continuum slopes ($\beta$) for a sample of $172$ galaxy candidates at $8 < z_{\mathrm{phot}} < 16$ selected from a combination of JWST NIRCam imaging and COSMOS/UltraVISTA ground-based near-infrared imaging. Focusing primarily on a new sample of $121$ galaxies at $\langle z \rangle \simeq 11$ selected from $\simeq 320$ arcmin$^2$ of public JWST imaging data across $15$ independent data sets, we investigate the evolution of $\beta$ in the galaxy population at $z \geq 9$. We find a significant trend between $\beta$ and redshift, with the inverse-variance weighted mean UV slope evolving from $\langle \beta \rangle = -2.17 \pm 0.06$ at $z = 9.5$ to $\langle \beta \rangle = -2.59 \pm 0.06$ at $z = 11.5$. Based on a comparison with stellar population models including nebular continuum emission, we find that at $z>10.5$ the average UV continuum slope is consistent with the intrinsic blue limit of dust-free stellar populations $(\beta_{\mathrm{int}} \simeq -2.6)$. These results suggest that the moderately dust-reddened galaxy population at $z < 10$ was essentially unattenuated at $z \simeq 11$. The extremely blue galaxies being uncovered at $z>10$ place important constraints on dust attenuation in galaxies in the early Universe, and imply that the already observed galaxy population is likely supplying an ionising photon budget capable of maintaining ionised IGM fractions of $\gtrsim 5$ per cent at $z\simeq11$., Comment: 18 pages, 12 figures, MNRAS accepted

We conducted a polarimetry campaign from radio to X-ray wavelengths of the high-synchrotron-peak (HSP) blazar Mrk 421, including Imaging X-ray Polarimetry Explorer (IXPE) measurements on 2022 December 6-8. We detected X-ray polarization of Mrk 421 with a degree of $\Pi_{\rm X}$=14$\pm$1$\%$ and an electric-vector position angle $\psi_{\rm X}$=107$\pm$3$^{\circ}$ in the 2-8 keV band. From the time variability analysis, we find a significant episodic variation in $\psi_{\rm X}$. During 7 months from the first IXPE pointing of Mrk 421 in 2022 May, $\psi_{\rm X}$ varied across the range of 0$^{\circ}$ to 180$^{\circ}$, while $\Pi_{\rm X}$ maintained similar values within $\sim$10-15$\%$. Furthermore, a swing in $\psi_{\rm X}$ in 2022 June was accompanied by simultaneous spectral variations. The results of the multiwavelength polarimetry show that the X-ray polarization degree was generally $\sim$2-3 times greater than that at longer wavelengths, while the polarization angle fluctuated. Additionally, based on radio, infrared, and optical polarimetry, we find that rotation of $\psi$ occurred in the opposite direction with respect to the rotation of $\psi_{\rm X}$ over longer timescales at similar epochs. The polarization behavior observed across multiple wavelengths is consistent with previous IXPE findings for HSP blazars. This result favors the energy-stratified shock model developed to explain variable emission in relativistic jets. The accompanying spectral variation during the $\psi_{\rm X}$ rotation can be explained by a fluctuation in the physical conditions, e.g., in the energy distribution of relativistic electrons. The opposite rotation direction of $\psi$ between the X-ray and longer-wavelength polarization accentuates the conclusion that the X-ray emitting region is spatially separated from that at longer wavelengths., Comment: 17 pages, 13 figures, 4 tables; Accepted for publication in A&A

We report the first statistical analyses of [CII] and dust continuum observations in six strong OI absorber fields at the end of the reionization epoch obtained by the Atacama Large Millimeter/Submillimeter Array (ALMA). Combined with one [CII] emitter reported in Wu et al. (2021), we detect one OI-associated [CII] emitter in six fields. At redshifts of OI-absorbers in non-detection fields, no emitters are brighter than our detection limit within impact parameters of 50 kpc and velocity offsets between $\pm200\ {\rm km\ s^{-1}}$. The averaged [CII]-detection upper limit is $< 0.06$ Jy ${\rm km\ s^{-1}}$ (3$\sigma$), corresponding to the [CII] luminosity of $L_{\rm [CII]} <5.8\times 10^7\ L_{\odot}$ and the [CII]-based star formation rate of ${\rm SFR_{\rm [CII]}} < 5.5$ $M_\odot$ yr$^{-1}$. Cosmological simulations suggest that only $\sim10^{-2.5}$ [CII] emitters around [OI] absorbers have comparable SFR to our detection limit. Although the detection in one out of six fields is reported, an order of magnitude number excess of emitters obtained from our ALMA observations supports that the contribution of massive galaxies that caused the metal enrichment cannot be ignored. Further, we also found 14 tentative galaxy candidates with S/N of $\approx4.3$ at large impact parameters ($>50$ kpc) and having larger outflow velocities within $\pm 600$ km s$^{-1}$. If these detections are confirmed in the future, then the mechanism of pushing metals at larger distances with higher velocities needs to be further explored from the theoretical side., Comment: Accepted for publication in ApJ. Main text 10 pages, 5 figures

We present polarization measurements in the $2-8 \thinspace \mathrm{keV}$ band from blazar 1ES 0229+200, the first extreme high synchrotron peaked source to be observed by the Imaging X-ray Polarimetry Explorer (IXPE). Combining two exposures separated by about two weeks, we find the degree of polarization to be $\Pi_{X} = 17.9 \pm 2.8 \%$ at an electric-vector position angle $\psi_X = 25.0 \pm 4.6^{\circ}$ using a spectropolarimetric fit from joint IXPE and XMM-Newton observations. There is no evidence for the polarization degree or angle varying significantly with energy or time on both short time scales (hours) or longer time scales (days). The contemporaneous polarization degree at optical wavelengths was $>$7$\times$ lower, making 1ES 0229+200 the most strongly chromatic blazar yet observed. This high X-ray polarization compared to the optical provides further support that X-ray emission in high-peaked blazars originates in shock-accelerated, energy-stratified electron populations, but is in tension with many recent modeling efforts attempting to reproduce the spectral energy distribution of 1ES 0229+200 which attribute the extremely high energy synchrotron and Compton peaks to Fermi acceleration in the vicinity of strongly turbulent magnetic fields., Comment: 17 Pages, 6 Figures, Resubmitted to ApJ after addressing referee comments

We study the asymptotics of bounded lecture hall tableaux. Limit shapes form when the bounds of the lecture hall tableaux go to infinity linearly in the lengths of the partitions describing the large-scale shapes of these tableaux. We prove Conjecture 6.1 in \cite{SKN21}, stating that the slopes of the rescaled height functions in the scaling limit satisfy a complex Burgers equation. We also show that the fluctuations of the unrescaled height functions converge to the Gaussian free field. The proof is based on new construction and analysis of Schur generating functions for the lecture hall tableaux, whose corresponding particle configurations do not form a Gelfand-Tsetlin scheme; and the corresponding dimer models are not doubly periodic.

This study introduces novel constraints on the free-streaming of thermal relic warm dark matter (WDM) from Lyman-$\alpha$ forest flux power spectra. Our analysis utilises a high-resolution, high-redshift sample of quasar spectra observed using the HIRES and UVES spectrographs ($z=4.2-5.0$). We employ a Bayesian inference framework and a simulation-based likelihood that encompasses various parameters including the free-streaming of dark matter, cosmological parameters, the thermal history of the intergalactic medium, and inhomogeneous reionization, to establish lower limits on the mass of a thermal relic WDM particle of $5.7\;\mathrm{keV}$ (at 95\% C.L.). This result surpasses previous limits from the Lyman-$\alpha$ forest through reduction of the measured uncertainties due to a larger statistical sample and by measuring clustering to smaller scales ($k_{\rm max}=0.2\;\mathrm{km^{-1}\,s}$). The approximately two-fold improvement due to the expanded statistical sample suggests that the effectiveness of Lyman-$\alpha$ forest constraints on WDM models at high redshifts are limited by the availability of high-quality quasar spectra. Restricting the analysis to comparable scales and thermal history priors as in prior studies ($k_{\rm max}<0.1\;\mathrm{km^{-1}\,s}$) lowers the bound on the WDM mass to $4.1\;\mathrm{keV}$. As the precision of the measurements increases, it becomes crucial to examine the instrumental and modelling systematics. On the modelling front, we argue that the impact of the thermal history uncertainty on the WDM particle mass constraint has diminished due to improved independent observations. At the smallest scales, the primary source of modeling systematic arises from the structure in the peculiar velocity of the intergalactic medium and inhomogeneous reionization., Comment: 22 pages, 14 figures, 2 tables; published in PRD on Feb 8 2024

Recently, the Lyman-$\alpha$ (Ly$\alpha$) forest flux auto-correlation function has been shown to be sensitive to the mean free path of hydrogen-ionizing photons, $\lambda_{\text{mfp}}$, for simulations at $z \geq 5.4$. Measuring $\lambda_{\text{mfp}}$ at these redshifts will give vital information on the ending of reionization. Here we present the first observational measurements of the Ly$\alpha$ forest flux auto-correlation functions in ten redshift bins from $5.1 \leq z \leq 6.0$. We use a sample of 35 quasar sightlines at $z > 5.7$ from the extended XQR-30 data set, this data has signal-to-noise ratios of $> 20$ per spectral pixel. We carefully account for systematic errors in continuum reconstruction, instrumentation, and contamination by damped Ly$\alpha$ systems. With these measurements, we introduce software tools to generate auto-correlation function measurements from any simulation. For an initial comparison, we show our auto-correlation measurements with simulation models for recently measured $\lambda_{\text{mfp}}$ values and find good agreements. Further work in modeling and understanding the covariance matrices of the data is necessary to get robust measurements of $\lambda_{\text{mfp}}$ from this data., Comment: 17 pages, 13 figures, submitted to MNRAS

For cosmic microwave background (CMB) polarization observations, calibration of detector polarization angles is essential. We have developed a fully remote controlled calibration system with a sparse wire grid that reflects linearly polarized light along the wire direction. The new feature is a remote-controlled system for regular calibration, which has not been possible in sparse wire grid calibrators in past experiments. The remote control can be achieved by two electric linear actuators that load or unload the sparse wire grid into a position centered on the optical axis of a telescope between the calibration time and CMB observation. Furthermore, the sparse wire grid can be rotated by a motor. A rotary encoder and a gravity sensor are installed on the sparse wire grid to monitor the wire direction. They allow us to achieve detector angle calibration with expected systematic error of $0.08^{\circ}$. The calibration system will be installed in small-aperture telescopes at Simons Observatory.

The Event Horizon Telescope (EHT) observed in 2017 the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), at a frequency of 228.1 GHz ($\lambda$=1.3 mm). The fundamental physics tests that even a single pulsar orbiting Sgr A* would enable motivate searching for pulsars in EHT datasets. The high observing frequency means that pulsars - which typically exhibit steep emission spectra - are expected to be very faint. However, it also negates pulse scattering, an effect that could hinder pulsar detections in the Galactic Center. Additionally, magnetars or a secondary inverse Compton emission could be stronger at millimeter wavelengths than at lower frequencies. We present a search for pulsars close to Sgr A* using the data from the three most-sensitive stations in the EHT 2017 campaign: the Atacama Large Millimeter/submillimeter Array, the Large Millimeter Telescope and the IRAM 30 m Telescope. We apply three detection methods based on Fourier-domain analysis, the Fast-Folding-Algorithm and single pulse search targeting both pulsars and burst-like transient emission; using the simultaneity of the observations to confirm potential candidates. No new pulsars or significant bursts were found. Being the first pulsar search ever carried out at such high radio frequencies, we detail our analysis methods and give a detailed estimation of the sensitivity of the search. We conclude that the EHT 2017 observations are only sensitive to a small fraction ($\lesssim$2.2%) of the pulsars that may exist close to Sgr A*, motivating further searches for fainter pulsars in the region., Comment: 33 pages, 7 figures, 6 Tables. Accepted for publication in ApJ

Ly$\alpha$ damping wings in the spectra of bright objects at high redshift are a useful probe of the ionization state of the intergalactic medium during the reionization epoch. It has recently been noted that, despite the inhomogeneous nature of reionization, these damping wings have a characteristic shape which is a strong function of the volume-weighted average neutral hydrogen fraction of the intergalactic medium. We present here a closer examination of this finding using a simulation of patchy reionization from the Sherwood-Relics simulation suite. We show that the characteristic shape and scatter of the damping wings are determined by the average neutral hydrogen density along the line of sight, weighted by its contribution to the optical depth producing the damping wing. We find that there is a redshift dependence in the characteristic shape due to the expansion of the Universe. Finally, we show that it is possible to differentiate between the shapes of damping wings in galaxies and young (or faint) quasars at different points in the reionization history at large velocity offsets from the point where the transmission first reaches zero., Comment: 5 pages, 4 figures. Submitted to MNRAS Letters

Spatial variations in the Lyman-$\alpha$ forest opacity at $z<6$ seem to require a late end to cosmic reionization. In this picture, the universe contains neutral hydrogen 'islands' of up to 100 cMpc$/h$ in extent down to redshifts as low as $z\sim 5.3$. This delayed end to reionization also seems to be corroborated by various other observables. An implication of this scenario is that the power spectrum of the cosmological 21-cm signal at $z<6$ is enhanced relative to conventional reionization models by orders of magnitude. However, these neutral hydrogen islands are also predicted to be at the locations of the deepest voids in the cosmological large-scale structure. As a result, the distribution of the 21-cm signal from them is highly non-Gaussian. We derive the 21-cm bispectrum signal from these regions using high-dynamic-range radiative transfer simulations of reionization. We find that relative to conventional models in which reionization is complete at $z>6$, our model has a significantly larger value of the 21-cm bispectrum. The neutral islands also imprint a feature in the isosceles bispectrum at a characteristic scale of $\sim 1$ cMpc$^{-1}$. We also study the 21-cm bispectrum for general triangle configuration by defining a triangle index. It should be possible to detect the 21-cm bispectrum signal at $\nu\gtrsim 200$ MHz using SKA1-LOW for 1080 hours of observation, assuming optimistic foreground removal., Comment: 12 pages, 12 figures

Spectra of the highest redshift galaxies taken with JWST are now allowing us to see into the heart of the reionization epoch. Many of these observed galaxies exhibit strong damping wing absorption redward of their Lyman-$\alpha$ emission. These observations have been used to measure the redshift evolution of the neutral fraction of the intergalactic medium and sizes of ionized bubbles. However, these estimates have been made using a simple analytic model for the intergalactic damping wing. We explore the recent observations with models of inhomogeneous reionization from the Sherwood-Relics simulation suite. We carry out a comparison between the damping wings calculated from the simulations and from the analytic model. We find that although the agreement is good on the red side of the Lyman-$\alpha$ emission, there is a discrepancy on the blue side due to residual neutral hydrogen present in the simulations, which saturates the intergalactic absorption. For this reason, we find that it is difficult to reproduce the claimed observations of large bubble sizes at z ~ 7, which are driven by a detection of transmitted flux blueward of the Lyman-$\alpha$ emission. We suggest instead that the observations can be explained by a model with smaller ionized bubbles and larger intrinsic Lyman-$\alpha$ emission from the host galaxy., Comment: 13 pages, 7 figures. Submitted to MNRAS

The mean free path of ionizing photons, $\lambda_{\rm mfp}$, is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements of $\lambda_{\rm mfp}$ from QSO spectra over the redshift range $5

Let $K$ be a local field of characteristic $p>0$ with perfect residue field and let $G$ be a finite $p$-group. In this paper we use Saltman's construction of a generic $G$-extension of rings of characteristic $p$ to construct totally ramified $G$-extensions $L/K$ that have Galois scaffolds. We specialize this construction to produce $G$-extensions $L/K$ such that the ring of integers $O_L$ is free of rank 1 over its associated order $A_0$, and extensions such that $A_0$ is a Hopf order in the group ring $K[G]$., Comment: 23 pages

The lower energy peak of the spectral energy distribution of blazars has commonly been ascribed to synchrotron radiation from relativistic particles in the jets. Despite the consensus regarding jet emission processes, the particle acceleration mechanism is still debated. Here, we present the first X-ray polarization observations of PG 1553+113, a high-synchrotron-peak blazar observed by the Imaging X-ray Polarimetry Explorer (IXPE). We detect an X-ray polarization degree of $(10\pm2)\%$ along an electric-vector position angle of $\psi_X=86^{\circ}\pm8^{\circ}$. At the same time, the radio and optical polarization degrees are lower by a factor of $\sim$3. During our IXPE pointing, we observed the first orphan optical polarization swing of the IXPE era, as the optical angle of PG 1553+113 underwent a smooth monotonic rotation by about 125$^\circ$, with a rate of $\sim$17 degrees per day. We do not find evidence of a similar rotation in either radio or X-rays, which suggests that the X-ray and optically emitting regions are separate or, at most, partially co-spatial. Our spectro-polarimetric results provide further evidence that the steady-state X-ray emission in blazars originates in a shock-accelerated and energy-stratified electron population., Comment: Accepted for pubblication in The Astrophysical Journal Letters. 3 Figures, 13 pages

Early prediction of Alzheimer's disease (AD) is crucial for timely intervention and treatment. This study aims to use machine learning approaches to analyze longitudinal electronic health records (EHRs) of patients with AD and identify signs and symptoms that can predict AD onset earlier. We used a case-control design with longitudinal EHRs from the U.S. Department of Veterans Affairs Veterans Health Administration (VHA) from 2004 to 2021. Cases were VHA patients with AD diagnosed after 1/1/2016 based on ICD-10-CM codes, matched 1:9 with controls by age, sex and clinical utilization with replacement. We used a panel of AD-related keywords and their occurrences over time in a patient's longitudinal EHRs as predictors for AD prediction with four machine learning models. We performed subgroup analyses by age, sex, and race/ethnicity, and validated the model in a hold-out and "unseen" VHA stations group. Model discrimination, calibration, and other relevant metrics were reported for predictions up to ten years before ICD-based diagnosis. The study population included 16,701 cases and 39,097 matched controls. The average number of AD-related keywords (e.g., "concentration", "speaking") per year increased rapidly for cases as diagnosis approached, from around 10 to over 40, while remaining flat at 10 for controls. The best model achieved high discriminative accuracy (ROCAUC 0.997) for predictions using data from at least ten years before ICD-based diagnoses. The model was well-calibrated (Hosmer-Lemeshow goodness-of-fit p-value = 0.99) and consistent across subgroups of age, sex and race/ethnicity, except for patients younger than 65 (ROCAUC 0.746). Machine learning models using AD-related keywords identified from EHR notes can predict future AD diagnoses, suggesting its potential use for identifying AD risk using EHR notes, offering an affordable way for early screening on large population., Comment: 24 pages

In a companion paper \cite{jon-fei}, we established asymptotic formulae for the joint moments of derivatives of the characteristic polynomials of CUE random matrices. The leading order coefficients of these asymptotic formulae are expressed as partition sums of derivatives of determinants of Hankel matrices involving I-Bessel functions, with column indices shifted by Young diagrams. In this paper, we continue the study of these joint moments and establish more properties for their leading order coefficients, including structure theorems and recursive relations. We also build a connection to a solution of the $\sigma$-Painlev\'{e} III$'$ equation. In the process, we give recursive formulae for the Taylor coefficients of the Hankel determinants formed from I-Bessel functions that appear and find differential equations that these determinants satisfy. The approach we establish is applicable to determinants of general Hankel matrices whose columns are shifted by Young diagrams., Comment: 49 pages. Some typos are modified

We derive explicit asymptotic formulae for the joint moments of the $n_1$-th and $n_2$-th derivatives of the characteristic polynomials of CUE random matrices for any non-negative integers $n_1, n_2$. These formulae are expressed in terms of determinants whose entries involve modified Bessel functions of the first kind. We also express them in terms of two types of combinatorial sums. Similar results are obtained for the analogue of Hardy's $Z$-function. We use these formulae to formulate general conjectures for the joint moments of the $n_1$-th and $n_2$-th derivatives of the Riemann zeta-function and of Hardy's $Z$-function. Our conjectures are supported by comparison with results obtained previously in the number theory literature., Comment: 29 pages. We modified some typos and added some references

We present 1.3 mm (230 GHz) observations of the recent and nearby Type II supernova, SN2023ixf, obtained with the Submillimeter Array (SMA) at 2.6-18.6 days after explosion. The observations were obtained as part the SMA Large Program POETS (Pursuit of Extragalactic Transients with the SMA). We do not detect any emission at the location of SN2023ixf, with the deepest limits of $L_\nu(230\,{\rm GHz})\lesssim 8.6\times 10^{25}$ erg s$^{-1}$ Hz$^{-1}$ at 2.7 and 7.7 days, and $L_\nu(230\,{\rm GHz})\lesssim 3.4\times 10^{25}$ erg s$^{-1}$ Hz$^{-1}$ at 18.6 days. These limits are about a factor of 2 times dimmer than the mm emission from SN2011dh (IIb), about an order of magnitude dimmer compared to SN1993J (IIb) and SN2018ivc (IIL), and about 30 times dimmer than the most luminous non-relativistic SNe in the mm-band (Type IIb/Ib/Ic). Using these limits in the context of analytical models that include synchrotron self-absorption and free-free absorption we place constraints on the proximate circumstellar medium around the progenitor star, to a scale of $\sim 2\times 10^{15}$ cm, excluding the range $\dot{M}\sim {\rm few}\times 10^{-6}-10^{-2}$ M$_\odot$ yr$^{-1}$ (for a wind velocity, $v_w=115$ km s$^{-1}$, and ejecta velocity, $v_{\rm eje}\sim (1-2)\times 10^4$ km s$^{-1}$). These results are consistent with an inference of the mass loss rate based on optical spectroscopy ($\sim 2\times 10^{-2}$ M$_\odot$ yr$^{-1}$ for $v_w=115$ km s$^{-1}$), but are in tension with the inference from hard X-rays ($\sim 7\times 10^{-4}$ M$_\odot$ yr$^{-1}$ for $v_w=115$ km s$^{-1}$). This tension may be alleviated by a non-homogeneous and confined CSM, consistent with results from high-resolution optical spectroscopy., Comment: Submitted