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George Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function $d_2(n)$. This congruence family appears difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of $\mathbb{Z}[X]$., Comment: 31 pages, 2 figures, 3 tables. References a Mathematica supplement which can be found online at

Very little work has been done searching for astrophysical transient optical emission in the millisecond to nanosecond regime with significant sensitivity. We call this regime "Ultra-Fast Astronomy", or UFA. To investigate transients on as short time scales as possible, we developed our own customized readout system for a silicon photomultiplier (SiPM)-based UFA camera, intended for use on conventional astronomical telescopes. SiPMs, available in array packages for imaging a field, are capable of time-tagged single-photon detection in the visible wavelength range. Our readout system consists of 16 channels of 14-bit data logging. Each channel includes a 50-dB gain pre-amplifier, signal shaping circuits, an analogue front end, an analogue to digital converter, and a Xilinx UltraScale+ Field Programable Gate Array Multipurpose System on Chip (FPGA-MPSoC)board for data-logging. We show that our system successfully read out the data from SiPM at 16 ns intervals with a maximum power consumption of 300 mW per channel and capability to perform concurrent 16 channels readout., Comment: 7 pages, 7 figures

Improved measurement of the Cosmic Microwave Background polarization from Planck allows a detailed study of reionization beyond the average optical depth. The lower value of the optical depth disfavours an early onset and an early completion of reionization in favour of a redsfhit range where different astrophysical probes provide sensible information on the sources of reionization and the status of the intergalactic medium. In this work we extend our previous study in which we constrained reionization by combining three different probes - CMB, UV luminosity density and neutral hydrogen fraction data - in both treatment and data: we first allow variation in the UV source term varying the product of the efficiency of conversion of UV luminosity into ionizing photons and the escape fraction together with the reionization and cosmological parameters, and then we investigate the impact of a less conservative cut for the UV luminosity function. We find that the estimate for the efficiency is consistent within 95% C.L. with the fixed value we considered in our previous results and is mostly constrained by the QHII data. We find that allowing the efficiency to vary does not affect significantly our results for the average optical depth for monotonic reionization histories, recovering $\tau=0.0519_{-0.0008}^{+0.0010}$ at 68% CL , consistent with our previous studies. Using a less conservative cut for the UV luminosity function, we find $\tau=0.0541_{-0.0016}^{+0.0013}$ at 68% CL, due to the faint end of the luminosity function in the data we use, that also prefers a larger contribution from higher redshifts., Comment: 18 pages, 20 figures, updated version to match the published one

We present constraints on inflationary dynamics and features in the primordial power spectrum of scalar perturbations using the Cosmic Microwave Background temperature, polarization data from Planck 2018 data release and updated likelihoods. We constrain the slow-roll dynamics using Hilltop Quartic Potential and Starobinsky $R+R^2$ model in the Einstein frame using the Planck 2018 binned Plik likelihood. Using the Hilltop as base potential we construct Whipped Inflation potential to introduce suppression in the scalar power spectrum at large angular scales. We notice marginal (68% C.L.) preference of suppression from the large scale temperature angular power spectrum. However, large-scale E-mode likelihood, based on high frequency instrument cross spectrum, does not support this suppression and in the combined data the preference towards the suppression becomes negligible. Based on the Hilltop and Starobinsky model we construct the Wiggly Whipped Inflation potentials to introduce oscillatory features along with the suppression. We use unbinned data from the recently released CamSpec v12.5 likelihood which updates Planck 2018 results. We compare the Bayesian evidences of the feature models with their baseline slow-roll potentials. We find that the complete slow-roll baseline potential is moderately preferred against potentials which generate features. Compared to Planck 2015 PlikHM bin1 likelihood, we find that the significance of sharp features has decreased owing to the updates in the data analysis pipeline. We also compute the bispectra for the best fit candidates obtained from our analysis., Comment: v1: 43 pages, 18 figures and 8 tables; v2: minor changes, matches the version published in JCAP

Recently, the LIGO-Virgo Collaboration (LVC) concluded that there is no evidence for lensed gravitational waves (GW) in the first half of the O3 run, claiming "We find the observation of lensed events to be unlikely, with the fractional rate at $\mu>2$ being $3.3\times 10^{-4}$". While we agree that the chance of an individual GW event being lensed at $\mu>2$ is smaller than $10^{-3}$, the number of observed events depends on the product of this small probability times the rate of mergers at high redshift. Observational constraints from the stochastic GW background indicate that the rate of conventional mass BBH mergers (8 < M (M$_{\odot}$) < 15) in the redshift range 1

The expected event rate of lensed gravitational wave sources scales with the merger rate at redshift $z\geq 1$, where the optical depth for lensing is high. It is commonly assumed that the merger rate of the astrophysical compact objects is closely connected with the star formation rate, which peaks around redshift $z\sim 2$. However, a major source of uncertainty is the delay time between the formation and merger of compact objects. We explore the impact of delay time on the lensing event rate. We show that as the delay time increases, the peak of the merger rate of gravitational wave sources gets deferred to a lower redshift. This leads to a reduction in the event rate of the lensed events which are detectable by the gravitational wave detectors. We show that for a delay time of around $10$ Gyr or larger, the lensed event rate can be less than one per year for the design sensitivity of LIGO/Virgo. We also estimate the merger rate for lensed sub-threshold for different delay time scenarios, finding that for larger delay times the number of lensed sub-threshold events is reduced, whereas for small-delay time models they are significantly more frequent. This analysis shows for the first time that lensing is a complementary probe to explore different formation channels of binary systems by exploiting the lensing event rate from the well-detected events and sub-threshold events which are measurable using the network of gravitational wave detectors., Comment: 10 pages, 6 figures. Accepted for publication in MNRAS

We characterized the S14160-3050HS Multi-Pixel Photon Counter (MPPC), a high efficiency, single channel silicon photomultiplier manufactured by Hamamatsu Photonics K.K. All measurements were performed at a room temperature of (23.0 $\pm$ 0.3) $^{\circ}$C. We obtained an I-V curve and used relative derivatives to find a breakdown voltage of 38.88 V. At a 3 V over voltage, we find a dark count rate of 1.08 MHz, crosstalk probability of 21 $\%$, photon detection efficiency of 55 $\%$ at 450 nm, and saturation at 1.0x10$^{11}$ photons per second. The S14160-3050HS MPPC is a candidate detector for the Ultra-Fast Astronomy (UFA) telescope which will characterize the optical (320 nm - 650 nm) sky in the millisecond to sub-microsecond timescales using two photon counting arrays operated in coincidence on the 0.7 meter Nazarbayev University Transient Telescope at the Assy-Turgen Astrophysical Observatory (NUTTelA-TAO) located near Almaty, Kazakhstan. We discuss advantages and disadvantages of using the S14160-3050HS MPPC for the UFA telescope and future ground-based telescopes in sub-second time domain astrophysics., Comment: 7 pages, 6 figures, 1 table, submitted to SPIE Astronomical Telescopes + Instrumentation 2020 conference proceedings

The presence of large dark matter cores in dwarf galaxies has long been puzzling and many are now known to be surrounded by an extensive halo of stars. Distinctive core-halo structure is characteristic of dark matter as a Bose Einstein condensate, $\psi$DM, with a dense, soliton core predicted in every galaxy, representing the ground state, surrounded by a large, tenuous halo of excited density waves. A marked density transition is predicted between the core and the halo set by the de Broglie wavelength, as the soliton core is a prominent standing wave that is denser by over an order of magnitude than the surrounding halo. Here we identify this predicted behavior in the stellar profiles of the well known "isolated" dwarfs that lie outside the Milky Way, each with a clear density transition at $\simeq 1.0~{\rm kpc}$, implying a very light boson, $m_{\psi} \simeq 10^{-22}$eV. The classical dwarf galaxies orbiting within the Milky Way also show this predicted core-halo structure but with larger density transitions of over two orders of magnitude, that we show implies tidal stripping of dwarf galaxies by the Milky way, as the tenuous halo is more easily stripped than the stable soliton core. We conclude that dark matter as a light boson explains the observed family of classical dwarf profiles with tidal stripping included, in contrast to the standard heavy particle interpretation where low mass galaxies should be concentrated and core-less, quite unlike the core-halo structure observed., Comment: 16 pages, 10 figures, Revised with dynamics included

One of the most well-established applications of machine learning is in deciding what content to show website visitors. When observation data comes from high-velocity, user-generated data streams, machine learning methods perform a balancing act between model complexity, training time, and computational costs. Furthermore, when model freshness is critical, the training of models becomes time-constrained. Parallelized batch offline training, although horizontally scalable, is often not time-considerate or cost-effective. In this paper, we propose Lambda Learner, a new framework for training models by incremental updates in response to mini-batches from data streams. We show that the resulting model of our framework closely estimates a periodically updated model trained on offline data and outperforms it when model updates are time-sensitive. We provide theoretical proof that the incremental learning updates improve the loss-function over a stale batch model. We present a large-scale deployment on the sponsored content platform for a large social network, serving hundreds of millions of users across different channels (e.g., desktop, mobile). We address challenges and complexities from both algorithms and infrastructure perspectives, and illustrate the system details for computation, storage, and streaming production of training data.

Gravitational lensing allows the detection of binary black holes (BBH) at cosmological distances with chirp masses that appear to be enhanced by $1+z$ in the range $195\%$), from which we infer a factor $\simeq 5$ higher intrinsic rate of NSBH events than BBH events, reflecting a higher proportion of neutron stars formed by early star formation. We predict a distinctive locus for lensed NSBH events in the observed binary mass plane, spanning $1

Context. The increased detection rate of Fast Radio Bursts (FRBs) makes it likely to get samples of sizes $\mathcal{O}(10^2)$ to $\mathcal{O}(10^3)$ in the near future. Because of their extragalactic origin can help us in understanding the epoch of helium reionization. Aims. We try to identify the epoch of Helium II (HeII) reionization, via the observations of early FRBs in range of $z=3$ to $4$. Methods. We build a model of FRB Dispersion Measure following the HeII reionization model, density fluctuation in large scale structure, host galaxy interstellar medium and local environment of FRB contribution. The model is fit to the ideal intergalactic medium (IGM) dispersion measure model to check the goodness of constraining the HeII reionization via FRB measurement statistics. Conclusion. We report our findings under two categories, accuracy in detection of HeII reionization via FRBs assuming no uncertainty in the redshift measurement and alternatively assuming a varied level of uncertainty in redshift measurement of the FRBs. We show that under the first case, a detection of $N\sim\mathcal{O} (10^2)$ FRBs give an uncertainty of $\sigma (z_{r, fit})\sim0.5$ from the fit model, and a detection of $N\sim\mathcal{O} (10^3)$ gives an uncertainty of $\sigma (z_{r, fit})\sim0.1$. While assuming a redshift uncertainty of level $5-20\%$, changes the $\sigma (z_{r, fit})\sim0.5$ to $0.6$ for $N\sim 100$ and $\sigma (z_{r, fit})\sim0.1$ to $0.15$ for $N \sim 1000$ case., Comment: 9 pages, 8 figures

Strong lensing of gravitational waves is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Observatory (LIGO)-Virgo and in the future from the LIGO-Virgo design sensitivity stringent bounds on the lensing event rate can be imposed using the SGWB signal. Combining measurements of loud gravitational wave events with an unresolved stochastic background detection will improve estimates of the numbers of lensed events at high redshift. The proposed method is going to play a crucial in understanding the population of lensed and unlensed systems from gravitational wave observations., Comment: 18 pages, 16 figures. Matches the version accepted for publication in MNRAS

We provide an update on the constraints on extended reionization histories with the Planck 2018 cosmic microwave background anisotropy data. The Planck 2018 data on large angular scales improve the measurement of the $E$-mode polarization reionization bump at low multipoles providing the possibility to improve our previous results. Using a minor modification to the original Poly-reion model for the reionization history, we find that the Planck 2018 data significantly improve all our previous results: we find as optical depth of $\tau=0.0572_{-0.0075}^{+0.0064}$ at 68% CL, that early onsets of reionization are strongly disfavoured, i.e. redshift when the reionization begins, $z_{xe=0}=18.18_{-10.89}^{+1.61}$ at 68% CL,and that reionization duration (defined between 10% and 99% reionization) is significantly reduced, i.e. $\Delta_z^{Reion}=4.59_{-2.45}^{+1.67}$ at 68% CL. We explore possible correlations between reionization histories and cosmological parameters, including important extensions beyond $\Lambda$CDM. We find that the degeneracy between reionization and scalar spectral index,neutrino mass sum, spatial curvature, dark matter annihilation and other non-standard models are significantly reduced.The reduction of the error bars and the degeneracies, together with the shift towards lower values of the optical depth that we observe in the Poly-reion model are mainly driven by the new low-$\ell$ polarization likelihood of Planck 2018 baseline based on the HFI data. This is confirmed also by the results derived without this likelihood and the ones with different alternatives to the baseline that are presented for a subset of models., Comment: 19 pages, 16 figures

We use the celebrated circle method of Hardy and Ramanujan to develop convergent formulae for counting a restricted class of partitions that arise from the G\"ollnitz--Gordon identities.

Primordial black holes (PBHs) generated by gravitational collapse of large primordial overdensities can be a fraction of the observed dark matter. In this paper, we introduce a mechanism to produce a large peak in the primordial power spectrum (PPS) in two-field inflationary models characterized by two stages of inflation based on a large non-canonical kinetic coupling. This mechanism is generic to several two-field inflationary models, due to a temporary tachyonic instability of the isocurvature perturbations at the transition between the two stages of inflation. We numerically compute the primordial perturbations from largest scales to the small scales corresponding to that of PBHs using an extension of BINGO (BI-spectra and Non-Gaussianity Operator). Moreover we numerically compute the stochastic background of gravitational waves (SBGW) produced by second order scalar perturbations within frequencies ranging from nano-Hz to KHz that covers the observational scales corresponding to Pulsar Timing Arrays, Square Kilometer Array to that of Einstein telescope. We discuss the prospect of its detection by these proposed and upcoming gravitational waves experiments., Comment: 20 pages, 7 figures; v2 matches the version published on JCAP

In 2015 Cristian-Silviu Radu designed an algorithm to detect identities of a class studied by Ramanujan and Kolberg. This class includes the famous identities by Ramanujan which provide a witness to the divisibility properties of $p(5n+4),$ $p(7n+5)$. We give an implementation of this algorithm using Mathematica. The basic theory is first described, and an outline of the algorithm is briefly given, in order to describe the functionality and utility of our package. We thereafter give multiple examples of applications to recent work in partition theory. In many cases we have used our package to derive alternate proofs of various identities or congruences; in other cases we have improved previously established identities, and in at least one case we have confirmed a standing conjecture., Comment: To appear in the Journal of Symbolic Computation

In 2018 Liuquan Wang and Yifan Yang proved the existence of an infinite family of congruences for the smallest parts function corresponding to the third order mock theta function $\omega(q)$. Their proof took the form of an induction requiring 20 initial relations, and utilized a space of modular functions isomorphic to a free rank 2 $\mathbb{Z}[X]$-module. This proof strategy was originally developed by Paule and Radu to study families of congruences associated with modular curves of genus 1. We show that Wang and Yang's family of congruences, which is associated with a genus 0 modular curve, can be proved using a single-variable approach, via a ring of modular functions isomorphic to a localization of $\mathbb{Z}[X]$. To our knowledge, this is the first time that such an algebraic structure has been applied to the theory of partition congruences. Our induction is more complicated, and relies on sequences of functions which exhibit a somewhat irregular 5-adic growth. However, the proof ultimately rests upon the direct verification of only 10 initial relations, and is similar to the classical methods of Ramanujan and Watson.

Conjectures involving infinite families of restricted partition congruences can be difficult to verify for a number of individual cases, even with a computer. We demonstrate how the machinery of Radu's algorithm may be modified and employed to efficiently check a very large number of cases of such conjectures. This allows substantial evidence to be collected for a given conjecture, before a complete proof is attempted., Comment: To appear in the Journal of Symbolic Computation

In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, $A_1(m)$, which counted subpartitions with a structure related to the Rogers--Ramanujan identities. They conjectured the existence of an infinite class of congruences for $A_1(m)$, modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5.

Dark matter as a Bose-Einstein condensate, such as the axionic scalar field particles of String Theory, can explain the coldness of dark matter on large scales. Pioneering simulations in this context predict a rich wave-like structure, with a ground state soliton core in every galaxy surrounded by a halo of excited states that interfere on the de Broglie scale. This de Broglie scale is largest for low mass galaxies as momentum is lower, providing a simple explanation for the wide cores of dwarf spheroidal galaxies. Here we extend these "wave dark matter" ($\psi$DM) predictions to the newly discovered class of "Ultra Diffuse Galaxies" (UDG) that resemble dwarf spheroidal galaxies but with more extended stellar profiles. Currently the best studied example, DF44, has a uniform velocity dispersion of $\simeq 33$km/s, extending to at least 3 kpc, that we show is reproduced by our $\psi$DM simulations with a soliton radius of $\simeq 0.5$ kpc. In the $\psi$DM context, we show the relatively flat dispersion profile of DF44 lies between massive galaxies with compact dense solitons, as may be present in the Milky Way on a scale of 100pc and lower mass galaxies where the velocity dispersion declines centrally within a wide, low density soliton, like Antlia II, of radius 3 kpc., Comment: 10 pages, 7 figures

With Planck cosmic microwave background observations, we established the spectral amplitude and tilt of the primordial power spectrum. Evidence of a red spectral tilt ($n_\mathrm{s}=0.96$) at $8\sigma$ provides strong support for the inflationary mechanism, especially the slow-roll of the effective scalar field in its nearly flat potential as the generator of scalar primordial perturbations. With the next generation of large-scale structure surveys, we expect to probe primordial physics beyond the overall shape and amplitude of the main, smooth and slowly-changing part of the inflaton potential. Using the specifications for the upcoming Euclid survey, we investigate to what extent we can constrain the inflation potential beyond its established slow-roll behaviour. We provide robust forecasts with Euclid and Planck mock data from nine fiducial power spectra that contain suppression and wiggles at different cosmological scales, using the Wiggly Whipped Inflation (WWI) framework to generate these features in the primordial spectrum. We include both Euclid cosmic shear and galaxy clustering, with a conservative cut-off for non-linear scales. Using Markov chain Monte Carlo simulations, we obtain an improvement in constraints in the WWI potential, as well an improvement for the background cosmology parameters. We find that apart from improving the constraints on the overall scale of the inflationary potential by 40-50 per cent, we can also identify oscillations in the primordial spectrum that are present within intermediate to small scales ($k\sim0.01-0.2\,\mathrm{Mpc^{-1}}$)., Comment: 22 pages. Published in Monthly Notices of the Royal Astronomical Society, 496, 3448-3468 (2020)

The primary and secondary masses of the binary black holes (BBH) reported by LIGO/Virgo are correlated with a narrow dispersion that appears to increase in proportion to mass. The mean binary mass ratio $1.45\pm0.07$ we show is consistent with pairs drawn randomly from the mass distribution of black holes in our Galaxy. However, BBH masses are concentrated around $\simeq 30M_\odot$, whereas black holes in our Galaxy peak at $\simeq 10M_\odot$. This mass difference can be reconciled by gravitational lensing magnification which allows distant events to be detected with typically $z\simeq 2$, so the waveform is reduced in frequency by $1+z$, and hence the measured chirp masses appear 3 times larger than their intrinsic values. This redshift enhancement also accounts for the dispersion of primary and secondary masses, both of which should increase as $1+z$, thereby appearing to scale with mass, in agreement with the data. Thus the BBH component masses provide independent support for lensing, implying most high chirp mass events have intrinsic masses like the stellar mass black holes in our Galaxy, coalescing at $z>1$, with only two low mass BBH detections, of $\simeq 10M_\odot$ as expected for unlensed events in the local Universe, $z\simeq 0.1$. This lensing solution requires a rapidly declining BBH event rate below $z<1$, which together with the observed absence of BBH spin suggests most events originate within young globular clusters at $z>1$, via efficient binary capture of stellar mass black holes with randomly oriented spins., Comment: 2 figures

In our Ultra-Fast Astronomy (UFA) program, we aim to improve measurements of variability of astronomical targets on millisecond and shorter time scales. In this work, we present initial on-sky measurements of the performance of silicon photomultiplier detectors (SiPMs) for UFA. We mounted two different SiPMs at the focal plane of the 0.7-meter aperture Nazarbayev University Transient Telescope at the Assy-Turgen Astrophysical Observatory (NUTTelA-TAO), with no filter in front of the detector. The $3mm\times3mm$ SiPM single-channel detectors have a field of view of $2.2716'\times2.2716'$. During the nights of 2019 October 28-29, we measured sky background, bright stars, and an artificial source with a 100Hz flashing frequency. We compared detected SiPM counts with Gaia satellite G-band flux values to show that our SiPMs have a linear response. With our two SiPMs (models S14520-3050VS and S14160-3050HS), we measured a dark current of $\sim$130 and $\sim$85 kilo counts per second (kcps), and a sky background of $\sim$201 and $\sim$203 kcps, respectively. We measured an intrinsic crosstalk of 10.34$\%$ and 10.52$\%$ and derived a 5$\sigma$ sensitivity of 13.9 and 14.0 Gaia G-band magnitude for 200ms exposures, for the two detectors respectively. For a 10 $\mu$s window, and allowing a false alarm rate of once per 100 nights, we derived a sensitivity of 22 detected photons, or 6 Gaia G-band magnitudes. For nanosecond timescales, our detection is limited by crosstalk to 12 detected photons, which corresponds to a fluence of $\sim$155 photons per square meter.

A hundred years ago, two British expeditions measured the deflection of starlight by the sun's gravitational field, confirming the prediction made by Einstein's General theory of Relativity. One hundred years later many physicists around the world are involved in studying the consequences and use as a research tool, of the deflection of light by gravitational fields, a discipline that today receives the generic name of Gravitational Lensing. The present review aims to commemorate the centenary of Einstein's Eclipse expeditions by presenting a historical perspective of the development and milestones on gravitational light bending, covering from early XIX century speculations, to its current use as an important research tool in astronomy and cosmology., Comment: 45 pages, 26 figures, Feature Papers 2019 - Gravitational Physics

There is no consensus on the emission mechanism of $\gamma$-ray bursts (GRBs). A synchrotron model can produce $\gamma$-ray spectra with the empirical Band function form, from a piece-wise two-power-law electron energy distribution (2EPLS). This model predicts that for the same $\gamma$-ray spectrum, optical emission can be very different in $f_{\nu}$ log slope, and in flux relative to $\gamma$-rays,depending on model parameter values. The model only allows a small set of $f_{\nu}$ log slopes in the optical -thereby allowing a clear path to verification or falsification. Measurements of prompt GRB emission in the optical thus far give no useful information about the spectral shape within the band, and therefore cannot be used to evaluate such predictions. We describe an experiment that responds to GRB alerts with a fast-slewing telescope, with 3+ simultaneous, high-time resolution cameras. Three channels measure two slopes in order to evaluate the model. We propose cross-correlation of $\gamma$ and OIR light curves to verify that GRB are single-component dominated, or to quantify additional contributions. Previous CCD measurements have limited-time resolution due to read noise. Electron-multiplied CCDS (EMCCDs) can be used to greatly reduce read noise allowing exposure times of a few hundred ms. Our Nazarbayev University Transient Telescope at Assy-Turgen Astrophysical Observatory (NUTTelA-TAO) utilizes a 70 cm telescope that can point in $\le$ 8 s, with 3 optical channels. The NUTTelA-TAO is expected to measure 3-8 GRB/yr, and verify/refute the 2EPLS model with just a few bright GRBs. A space-based experiment with an IR channel would make improved measurements of the self-absorption frequency and physical conditions within the GRB jet. Additional science includes detection of dust evaporation due to GRBs, a tool to study progenitor environment dust., Comment: 19 pages, 4 figures, abstract truncated for arxiv format

We characterized the S13360-3050CS Multi-Pixel Photon Counter (MPPC), a silicon photomultiplier (SiPM) manufactured by Hamamatsu Photonics K.K.. Measurements were obtained inside a light tight dark box using 365 nm, 400 nm, 525 nm, 660 nm, 720 nm, 810 nm, and 900 nm light-emitting diodes (LED) and the Citiroc 1A front-end evaluation system manufactured by Weeroc. At a 2.95V over voltage, we measured a dark count rate of 5.07x$10^{5}$ counts per second at 26$^{\circ}$C, crosstalk probability of 8.7$\%$, photon detection efficiency of 36$\%$ at 400 nm, linear range of 1.8x$10^{7}$ photons per second, and saturation at 5x$10^8$ photons per second. The S13360-3050CS MPPC is a candidate detector for the Ultra-Fast Astronomy (UFA) telescope which will characterize the optical sky in the millisecond to nanosecond timescales using two SiPM arrays operated in coincidence mounted on the 0.7 meter Nazarbayev University Transient Telescope at the Assy-Turgen Astrophysical Observatory (NUTTelA-TAO) located near Almaty, Kazakhstan. One objective of the UFA telescope will be to search for optical counterparts to fast radio bursts (FRB) that can be used to identify the origins of FRB and probe the epoch of reionization and baryonic matter in the interstellar and intergalactic mediums., Comment: 9 pages, 9 figures, 1 table, submitted to SPIE Optics + Photonics 2019 conference proceedings

We present program objectives and specifications for the first generation Ultra-Fast Astronomy (UFA) observatory which will explore a new astrophysical phase space by characterizing the variability of the optical (320 nm - 650 nm) sky in the millisecond to nanosecond timescales. One of the first objectives of the UFA observatory will be to search for optical counterparts to fast radio bursts (FRB) that can be used to identify the origins of FRB and probe the epoch of reionization and baryonic matter in the interstellar and intergalactic mediums. The UFA camera will consist of two single-photon resolution fast-response detector 16x16 arrays operated in coincidence mounted on the 0.7 meter Nazarbayev University Transient Telescope at the Assy-Turgen Astrophysical Observatory (NUTTelA-TAO) located near Almaty, Kazakhstan. We are currently developing two readout systems that can measure down to the microsecond and nanosecond timescales and characterizing two silicon photomultipliers (SiPM) and one photomultiplier tube (PMT) to compare the detectors for the UFA observatory and astrophysical observations in general., Comment: 9 pages, 7 figures, 1 table

Cosmic Microwave Background temperature and polarization anisotropies from Planck have estimated a lower value of the optical depth to reionization ($\tau$) compared to WMAP. A significant period in the reionization history would then fall within $6

Microlenses with typical stellar masses (a few ${\rm M}_{\odot}$) have traditionally been disregarded as potential sources of gravitational lensing effects at LIGO/Virgo frequencies, since the time delays are often much smaller than the inverse of the frequencies probed by LIGO/Virgo, resulting in negligible interference effects at LIGO/Virgo frequencies. While this is true for isolated microlenses in this mass regime, we show how, under certain circumstances and for realistic scenarios, a population of microlenses (for instance stars and remnants from a galaxy halo or from the intracluster medium) embedded in a macromodel potential (galaxy or cluster) can conspire together to produce time delays of order one millisecond which would produce significant interference distortions in the observed strains. At sufficiently large magnification factors (of several hundred), microlensing effects should be common in gravitationally lensed gravitational waves. We explore the regime where the predicted signal falls in the frequency range probed by LIGO/Virgo. We find that stellar mass microlenses, permeating the lens plane, and near critical curves, can introduce interference distortions in strongly lensed gravitational waves. For those lensed events with negative parity, (or saddle points, never studied before in the context of gravitational waves), and that take place near caustics of macromodels, they are more likely to produce measurable interference effects at LIGO/Virgo frequencies. This is the first study that explores the effect of a realistic population of microlenses, plus a macromodel, on strongly lensed gravitational waves., Comment: 16 pages