arXiv subjects

Saurabh Singh

Publications and source records attributed to Saurabh Singh.

At least 37 records · Page 2Linked to original sources

arXiv2025

A demonstration of the effect of fringe-rate filtering in the Hydrogen Epoch of Reionization Array delay power spectrum pipeline

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding.

astro-ph.CO↗

arXiv2025

Global 21 cm signal: a promising probe of primordial features

Inflationary models that involve bursts of particle production generate bump-like features in the primordial power spectrum of density perturbations. These features influence the evolution of density fluctuations, leaving their unique signatures in cosmological observations. A detailed investigation of such signatures would help constrain physical processes during inflation. With this motivation, the goal of this paper is two-fold. First, we conduct a detailed analysis of the effects of bump-like primordial features on the sky-averaged 21 cm signal. Using semi-numerical simulations, we demonstrate that the primordial features can significantly alter the ionization history and the global 21 cm profile, making them a promising probe of inflationary models. We found a special scale (namely, the turnover wavenumber, $k^{\rm turn}$) at which the effect of primordial bump-like features on the global 21 cm profile vanishes. Also, we found that the behaviour of the primordial features on the global profile and ionization history are quite opposite for $k > k^{\rm turn}$ and $k < k^{\rm turn}$. We trace the root cause of these behaviours to the effects of primordial features on the halo mass function at high redshifts. Furthermore, we discuss the degeneracy between the astrophysical parameters and the primordial features in detail. Secondly, for a fixed set of astrophysical parameters, we derive upper limits on the amplitude of bump-like features in the range $10^{-1} < k\,[{\rm Mpc}^{-1}] < 10^2$ using current limits on optical depth to reionization from CMB data by Planck.

astro-ph.CO↗

arXiv2025

Discretized Approximate Ancestral Sampling

The Fourier Basis Density Model (FBM) was recently introduced as a flexible probability model for band-limited distributions, i.e. ones which are smooth in the sense of having a characteristic function with limited support around the origin. Its density and cumulative distribution functions can be efficiently evaluated and trained with stochastic optimization methods, which makes the model suitable for deep learning applications. However, the model lacked support for sampling. Here, we introduce a method inspired by discretization--interpolation methods common in Digital Signal Processing, which directly take advantage of the band-limited property. We review mathematical properties of the FBM, and prove quality bounds of the sampled distribution in terms of the total variation (TV) and Wasserstein--1 divergences from the model. These bounds can be used to inform the choice of hyperparameters to reach any desired sample quality. We discuss these results in comparison to a variety of other sampling techniques, highlighting tradeoffs between computational complexity and sampling quality.

cs.IT↗

arXiv2025

Direction-dependent effects on global 21-cm detection

Cosmic dawn represents critical juncture in cosmic history when the first population of stars emerged. The astrophysical processes that govern this transformation need to be better understood. The detection of redshifted 21-cm radiation emitted from neutral hydrogen during this era offers a direct window into the thermal and ionization state of the universe. This emission manifests as differential brightness between spin temperature and the cosmic microwave background (CMB). SARAS experiment aims to detect the sky-averaged signal in the frequency range 40-200 MHz. SARAS's unique design and operation strategy to float the antenna over a water body minimizes spectral features that may arise due to stratified ground beneath the antenna. However, the antenna environment can be prone to configuration changes due to variations in critical design parameters such as conductivity and antenna tilts. In this paper, we connect the variations in antenna properties to signal detection prospects. By using realistic simulations of a direction and frequency-dependent radiation pattern of the SARAS antenna and its transfer function, we establish critical parameters and estimate bias in the detectability of different models of the global 21-cm signal. We find a correlation between the nature of chromaticity in antenna properties and the bias in the recovered spectral profiles of 21-cm signals. We also find stringent requirements for transfer function corrections, which can otherwise make detection prospects prohibitive. We finally explore a range of critical parameters that allow robust signal detection.

astro-ph.CO↗

arXiv2025

Fourier Head: Helping Large Language Models Learn Complex Probability Distributions

As the quality of large language models has improved, there has been increased interest in using them to model non-linguistic tokens. For example, the Decision Transformer recasts agentic decision making as a sequence modeling problem, using a decoder-only LLM to model the distribution over the discrete action space for an Atari agent. However, when adapting LLMs to non-linguistic domains, it remains unclear if softmax over discrete bins captures the continuous structure of the tokens and the potentially complex distributions needed for high quality token generation. We introduce a neural network layer, constructed using Fourier series, which we can easily substitute for any linear layer if we want the outputs to have a more continuous structure. We perform extensive analysis on synthetic datasets, as well as on large-scale decision making and time series forecasting tasks. We also provide theoretical evidence that this layer can better learn signal from data while ignoring high-frequency noise. All of our results support the effectiveness of our proposed Fourier head in scenarios where the underlying data distribution has a natural continuous structure. For example, the Fourier head improves a Decision Transformer agent's returns across four benchmark Atari games by as much as 377%, and increases a state-of-the-art times series foundation model's forecasting performance by 3.5% across 20 benchmarks unseen during training.

cs.LG↗

arXiv2025

Weyl and Dirac Semimetals for Thermoelectric Applications

Weyl and Dirac semimetals, characterized by their unique band structures with linear energy dispersion (E vs k) near the Fermi level (EF), have emerged as promising candidates for next-generation technology based on thermoelectric materials. Their exceptional electronic properties, notably high carrier mobility and substantial Berry curvature, offer the potential to surmount the limitations inherent in conventional thermoelectric materials. A comprehensive understanding of the fundamental physics underlying these materials is essential. This chapter mainly focused into the topological properties and distinctive electronic band structures of Weyl and Dirac semimetals, providing a theoretical framework for comprehending their thermoelectric transport properties such as Seebeck coefficients, electrical and thermal conductivity. The pivotal role of Berry curvature in enhancing Seebeck coefficients while reducing thermal conductivity is a key focus. Experimental advancements in synthesizing single crystals and characterizing these materials have been significant. Recent development in material growth and characterization techniques have propelled research forward. The intricate relationship between material properties, such as carrier concentration, electronic bandgap, and crystal structure, and thermoelectric performance is explored. Realizing the potential of Weyl and Dirac semimetals for practical thermoelectric applications necessitates overcoming specific challenges. This chapter outlines strategies to optimize thermoelectric figures of merit (ZT) through band engineering, carrier doping, and nanostructuring. Moreover, the exploration of hybrid materials and heterostructures offers promising avenues for enhancing thermoelectric performance for renewable energy applications.

cond-mat.mtrl-sci↗

arXiv2025

matvis: A matrix-based visibility simulator for fast forward modelling of many-element 21 cm arrays

Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch of Reionisation will require not only exquisite control over instrumental calibration and systematics to achieve the necessary dynamic range of observations but also validation of analysis techniques to demonstrate their statistical properties and signal loss characteristics. A key ingredient in achieving this is the ability to perform high-fidelity simulations of the kinds of data that are produced by the large, many-element, radio interferometric arrays that have been purpose-built for these studies. The large scale of these arrays presents a computational challenge, as one must simulate a detailed sky and instrumental model across many hundreds of frequency channels, thousands of time samples, and tens of thousands of baselines for arrays with hundreds of antennas. In this paper, we present a fast matrix-based method for simulating radio interferometric measurements (visibilities) at the necessary scale. We achieve this through judicious use of primary beam interpolation, fast approximations for coordinate transforms, and a vectorised outer product to expand per-antenna quantities to per-baseline visibilities, coupled with standard parallelisation techniques. We validate the results of this method, implemented in the publicly-available matvis code, against a high-precision reference simulator, and explore its computational scaling on a variety of problems.

astro-ph.IM↗

arXiv2024

Impacts and Statistical Mitigation of Missing Data on the 21cm Power Spectrum: A Case Study with the Hydrogen Epoch of Reionization Array

The precise characterization and mitigation of systematic effects is one of the biggest roadblocks impeding the detection of the fluctuations of cosmological 21cm signals. Missing data in radio cosmological experiments, often due to radio frequency interference (RFI), poses a particular challenge to power spectrum analysis as it could lead to the ringing of bright foreground modes in Fourier space, heavily contaminating the cosmological signals. Here we show that the problem of missing data becomes even more arduous in the presence of systematic effects. Using a realistic numerical simulation, we demonstrate that partially flagged data combined with systematic effects can introduce significant foreground ringing. We show that such an effect can be mitigated through inpainting the missing data. We present a rigorous statistical framework that incorporates the process of inpainting missing data into a quadratic estimator of the 21cm power spectrum. Under this framework, the uncertainties associated with our inpainting method and its impact on power spectrum statistics can be understood. These results are applied to the latest Phase II observations taken by the Hydrogen Epoch of Reionization Array, forming a crucial component in power spectrum analyses as we move toward detecting 21cm signals in the ever more noisy RFI environment.

astro-ph.CO↗

arXiv2024

Stochastic Sampling from Deterministic Flow Models

Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are sensitive to model estimation and discretization errors and do not permit different samples conditioned on an intermediate state, limiting their application. We present a general method to turn the underlying ODE of such flow models into a family of stochastic differential equations (SDEs) that have the same marginal distributions. This method permits us to derive families of \emph{stochastic samplers}, for fixed (e.g., previously trained) \emph{deterministic} flow models, that continuously span the spectrum of deterministic and stochastic sampling, given access to the flow field and the score function. Our method provides additional degrees of freedom that help alleviate the issues with the deterministic samplers and empirically outperforms them. We empirically demonstrate advantages of our method on a toy Gaussian setup and on the large scale ImageNet generation task. Further, our family of stochastic samplers provide an additional knob for controlling the diversity of generation, which we qualitatively demonstrate in our experiments.

cs.LG↗

arXiv2024

Coupling of magnetism and transport properties to the lattice degrees of freedom in NdBaCo$_2$O$_{5+δ}$ ($δ\sim 0.65$)

We have studied the origin of zero volume expansion below the Curie temperature (Tc), variable range hopping (VRH) behaviour using structural, magnetic, transport and thermal studies on the oxygen deficient double perovskite NdBaCo$_2$O$_{5+δ}$ ($δ\sim 0.65$). The valence state of Co ions and the possible properties exhibited by such compound were studied using electronic structure calculations for $δ= 0.75$. Careful investigation of structure shows that the compound stabilizes in tetragonal structure (P4/mmm) having $2a_p \times 2a_p \times 2a_p$ (222) superstructure, where $a_p$ is the cubic perovskite lattice parameter. The compound exhibits a minimum in resistivity, ferromagnetic and ferrimagnetic transitions around 375 K, 120 K ($T_c$) and 60 K, respectively with signature of Griffiths phase above $T_c$. Our detailed structural analysis suggests signature of the onset of the above magnetic transitions at temperatures well above its stabilisation at long range level thereby leading to VRH behaviour. The observed zero thermal expansion in volume below Tc appears to be due to competing magnetic interactions within and between the magnetic sublattices. Our electronic structure calculations show (a) the importance of electron-electron correlation in Nd $4f$ and Co $3d$ states (b) Co ions stabilize in intermediate spin (IS) state, having oxidation state less than +3 (c) half metallicity. Our results show the possibility of coupling between magnetism and ferroelectricity. We believe that our results especially on the valence state of the Co ion, zero thermal expansion in volume, short range magnetic orderings and the connection between different degrees of freedom will be helpful in clearing the ambiguities existing in literature on the nature of magnetism and thereby aiding in designing new functionalities.

cond-mat.str-el↗

arXiv2024

Holographic Beam Measurements of the Canadian Hydrogen Intensity Mapping Experiment (CHIME)

We present the first results of the holographic beam mapping program for the Canadian Hydrogen Intensity Mapping Experiment (CHIME). We describe the implementation of the holographic technique as adapted for CHIME, and introduce the processing pipeline which prepares the raw holographic timestreams for analysis of beam features. We use data from six bright sources across the full 400-800\,MHz observing band of CHIME to provide measurements of the co-polar and cross-polar beam response of CHIME in both amplitude and phase for the 1024 dual-polarized feeds instrumented on CHIME. In addition, we present comparisons with independent probes of the CHIME beam which indicate the presence of polarized beam leakage in CHIME. Holographic measurements of the CHIME beam have already been applied in science with CHIME, e.g. in estimating detection significance of far sidelobe FRBs, and in validating the beam models used for CHIME's first detections of \tcm emission (in cross-correlation with measurements of large-scale structure from galaxy surveys and the Lyman-$α$ forest). Measurements presented in this paper, and future holographic results, will provide a unique data set to characterize the CHIME beam and improve the experiment's prospects for a detection of BAO.

astro-ph.IM↗

arXiv2024

Fourier Basis Density Model

We introduce a lightweight, flexible and end-to-end trainable probability density model parameterized by a constrained Fourier basis. We assess its performance at approximating a range of multi-modal 1D densities, which are generally difficult to fit. In comparison to the deep factorized model introduced in [1], our model achieves a lower cross entropy at a similar computational budget. In addition, we also evaluate our method on a toy compression task, demonstrating its utility in learned compression.

cs.LG↗

arXiv2024

Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties

In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid dualizing complexes have strong functorial properties, allowing us to construct the twisted induction pseudofunctor, which is our ring-theoretic version of the twisted inverse pseudofunctor $f^{!}$. This is the first article of a bigger project, whose final goal is establishing Grothendieck Duality, including global duality for proper maps, for Deligne-Mumford stacks.

math.AG↗

arXiv2024

Hydrogen Epoch of Reionization Array (HERA) Phase II Deployment and Commissioning

This paper presents the design and deployment of the Hydrogen Epoch of Reionization Array (HERA) phase II system. HERA is designed as a staged experiment targeting 21 cm emission measurements of the Epoch of Reionization. First results from the phase I array are published as of early 2022, and deployment of the phase II system is nearing completion. We describe the design of the phase II system and discuss progress on commissioning and future upgrades. As HERA is a designated Square Kilometer Array (SKA) pathfinder instrument, we also show a number of "case studies" that investigate systematics seen while commissioning the phase II system, which may be of use in the design and operation of future arrays. Common pathologies are likely to manifest in similar ways across instruments, and many of these sources of contamination can be mitigated once the source is identified.

astro-ph.IM↗

arXiv2023

Joint analysis constraints on the physics of the first galaxies with low frequency radio astronomy data

The first billion years of cosmic history remains largely unobserved. We demonstrate, using a novel machine learning technique, how combining upper limits on the spatial fluctuations in the 21-cm signal with observations of the sky-averaged 21-cm signal from neutral hydrogen can improve our understanding of this epoch. By jointly analysing data from SARAS3 (redshift $z\approx15-25$) and limits from HERA ($z\approx8$ and $10$), we show that such a synergetic analysis provides tighter constraints on the astrophysics of galaxies 200 million years after the Big Bang than can be achieved with the individual data sets. Although our constraints are weak, this is the first time data from a sky-averaged 21-cm experiment and power spectrum experiment have been analysed together. In synergy, the two experiments leave only $64.9^{+0.3}_{-0.1}$% of the explored broad theoretical parameter space to be consistent with the joint data set, in comparison to $92.3^{+0.3}_{-0.1}$% for SARAS3 and $79.0^{+0.5}_{-0.2}$% for HERA alone. We use the joint analysis to constrain star formation efficiency, minimum halo mass for star formation, X-ray luminosity of early emitters and the radio luminosity of early galaxies. The joint analysis disfavours at 68% confidence a combination of galaxies with X-ray emission that is $\lesssim 33$ and radio emission that is $\gtrsim 32$ times as efficient as present day galaxies. We disfavour at $95$% confidence scenarios in which power spectra are $\geq126$ mK$^{2}$ at $z=25$ and the sky-averaged signals are $\leq-277$ mK.

astro-ph.CO↗

arXiv2023

ssVERDICT: Self-Supervised VERDICT-MRI for Enhanced Prostate Tumour Characterisation

Purpose: Demonstrating and assessing self-supervised machine learning fitting of the VERDICT (Vascular, Extracellular and Restricted DIffusion for Cytometry in Tumours) model for prostate. Methods: We derive a self-supervised neural network for fitting VERDICT (ssVERDICT) that estimates parameter maps without training data. We compare the performance of ssVERDICT to two established baseline methods for fitting diffusion MRI models: conventional nonlinear least squares (NLLS) and supervised deep learning. We do this quantitatively on simulated data, by comparing the Pearson's correlation coefficient, mean-squared error (MSE), bias, and variance with respect to the simulated ground truth. We also calculate in vivo parameter maps on a cohort of 20 prostate cancer patients and compare the methods' performance in discriminating benign from cancerous tissue via Wilcoxon's signed-rank test. Results: In simulations, ssVERDICT outperforms the baseline methods (NLLS and supervised DL) in estimating all the parameters from the VERDICT prostate model in terms of Pearson's correlation coefficient, bias, and MSE. In vivo, ssVERDICT shows stronger lesion conspicuity across all parameter maps, and improves discrimination between benign and cancerous tissue over the baseline methods. Conclusion: ssVERDICT significantly outperforms state-of-the-art methods for VERDICT model fitting, and shows for the first time, fitting of a complex three-compartment biophysical model with machine learning without the requirement of explicit training labels.

eess.IV↗

arXiv2023

STARFIRE: An algorithm for estimating radio frequency interference in orbits around Earth

Ground-based 21-cm experiments targeting the global signal from the periods of Cosmic Dawn (CD) and Epoch of Reionization (EoR) are susceptible to adverse effects presented by i) the ionosphere ii) antenna chromaticity induced by objects in its vicinity iii) terrestrial radio frequency interference (RFI). Terrestrial RFI is particularly challenging as the FM radio band spanning over 88-108 MHz lies entirely within the frequency range of the CD/EoR experiments ($\sim 40-200$ MHz). Multiple space-based experiments have been proposed to operate in the radio-quiet zone on the lunar farside. An intermediate option in cost and complexity is an experiment operating in space in an orbit around Earth, which readily alleviates the first two challenges. However, the effect of RFI in Earth's orbit on the detection of global signal needs to be quantitatively evaluated. We present STARFIRE -- Simulation of TerrestriAl Radio Frequency Interference in oRbits around Earth -- an algorithm that provides an expectation of FM seeded RFI at different altitudes over Earth. Using a limited set of publicly available FM transmitter databases, which can be extended by the user community, we demonstrate the use of the STARFIRE framework to generate a three-dimensional spatio-spectral cube of RFI as would be measured in Earth orbit. Applications of STARFIRE include identifying minimum RFI orbits around Earth, producing RFI spectra over a particular location, and generating RFI heatmaps at specific frequencies for a range of altitudes. STARFIRE can be easily adapted for different frequencies, altitudes, antenna properties, RFI databases, and combined with astrophysical sky-models. This can be used to estimate the effect of RFI on the detection of global 21-cm signal from Earth-orbit, and hence for sensitivity estimates and experiment design of an Earth orbiting CD/EoR detection experiment.

astro-ph.IM↗

arXiv2023

Flux Calibration of CHIME/FRB Intensity Data

Fast radio bursts (FRBs) are bright radio transients of micro-to-millisecond duration and unknown extragalactic origin. Central to the mystery of FRBs are their extremely high characteristic energies, which surpass the typical energies of other radio transients of similar duration, like Galactic pulsar and magnetar bursts, by orders of magnitude. Calibration of FRB-detecting telescopes for burst flux and fluence determination is crucial for FRB science, as these measurements enable studies of the FRB energy and brightness distribution in comparison to progenitor theories. The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a radio interferometer of cylindrical design. This design leads to a high FRB detection rate but also leads to challenges for CHIME/FRB flux calibration. This paper presents a comprehensive review of these challenges, as well as the automated flux calibration software pipeline that was developed to calibrate bursts detected in the first CHIME/FRB catalog, consisting of 536 events detected between July 25th, 2018 and July 1st, 2019. We emphasize that, due to limitations in the localization of CHIME/FRB bursts, flux and fluence measurements produced by this pipeline are best interpreted as lower limits, with uncertainties on the limiting value.

astro-ph.IM↗