arXiv subjects

Sayan Mandal

Publications and source records attributed to Sayan Mandal.

28 records · Page 2Linked to original sources

arXiv2020

End-to-End Bengali Speech Recognition

Bengali is a prominent language of the Indian subcontinent. However, while many state-of-the-art acoustic models exist for prominent languages spoken in the region, research and resources for Bengali are few and far between. In this work, we apply CTC based CNN-RNN networks, a prominent deep learning based end-to-end automatic speech recognition technique, to the Bengali ASR task. We also propose and evaluate the applicability and efficacy of small 7x3 and 3x3 convolution kernels which are prominently used in the computer vision domain primarily because of their FLOPs and parameter efficient nature. We propose two CNN blocks, 2-layer Block A and 4-layer Block B, with the first layer comprising of 7x3 kernel and the subsequent layers comprising solely of 3x3 kernels. Using the publicly available Large Bengali ASR Training data set, we benchmark and evaluate the performance of seven deep neural network configurations of varying complexities and depth on the Bengali ASR task. Our best model, with Block B, has a WER of 13.67, having an absolute reduction of 1.39% over comparable model with larger convolution kernels of size 41x11 and 21x11.

eess.AS↗

arXiv2020

Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation

Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions -- (i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in a sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic felicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe.

astro-ph.CO↗

arXiv2020

Computing Minimal Persistent Cycles: Polynomial and Hard Cases

Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing minimal 1-dimensional persistent cycles (persistent 1-cycles) for finite intervals is NP-hard while the same for infinite intervals is polynomially tractable. In this paper, we address this problem for general dimensions with $\mathbb{Z}_2$ coefficients. In addition to proving that it is NP-hard to compute minimal persistent d-cycles (d>1) for both types of intervals given arbitrary simplicial complexes, we identify two interesting cases which are polynomially tractable. These two cases assume the complex to be a certain generalization of manifolds which we term as weak pseudomanifolds. For finite intervals from the d-th persistence diagram of a weak (d+1)-pseudomanifold, we utilize the fact that persistent cycles of such intervals are null-homologous and reduce the problem to a minimal cut problem. Since the same problem for infinite intervals is NP-hard, we further assume the weak (d+1)-pseudomanifold to be embedded in $\mathbb{R}^{d+1}$ so that the complex has a natural dual graph structure and the problem reduces to a minimal cut problem. Experiments with both algorithms on scientific data indicate that the minimal persistent cycles capture various significant features of the data.

cs.CG↗

arXiv2019

Observationally inferred dark matter phase-space distribution and direct detection experiments

We present a detailed analysis of the effect of an observationally determined dark matter (DM) velocity distribution function (VDF) of the Milky Way (MW) on DM direct detection rates. We go beyond local kinematic tracers and use rotation curve data up to 200 kpc to construct a MW mass model and self-consistently determine the local phase-space distribution of DM. This approach mitigates any incomplete understanding of local dark matter-visible matter degeneracies that can affect the determination of the VDF. Comparing with the oft used Standard Halo Model (SHM), which assumes an isothermal VDF, we look at how the tail of the empirically determined VDF alters our interpretation of the present direct detection WIMP DM cross section exclusion limits. While previous studies have suggested a very large difference (of more than an order of magnitude) in the bounds at low DM masses, we show that accounting for the detector response at low threshold energies, the difference is still significant although less extreme. The change in the number of signal events, when using the empirically determined DM VDF in contrast to the SHM VDF, is most prominent for low DM masses for which the shape of the recoil energy spectrum depends sensitively on the detector threshold energy as well as detector response near the threshold. We demonstrate that these trends carry over to the respective DM exclusion limits, modulo detailed understanding of the experimental backgrounds. With the unprecedented precision of astrometric data in the GAIA era, use of observationally determined DM phase-space will become a critical and necessary ingredient for DM searches. We provide an accurate fit to the current best observationally determined DM VDF (and self-consistent local DM density) for use in analyzing current DM direct detection data by the experimental community.

hep-ph↗

arXiv2019

The dynamo effect in decaying helical turbulence

We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity, is approximately constant. This scaling of magnetic energy persists over long time scales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a cross-over to the t^{-2/3} decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe.

physics.flu-dyn↗

arXiv2018

E and B polarizations from inhomogeneous and solar surface turbulence

Gradient- and curl-type or E- and B-type polarizations have been routinely analyzed to study the physics contributing to the cosmic microwave background polarization and galactic foregrounds. They characterize the parity-even and parity-odd properties of the underlying physical mechanisms, for example hydromagnetic turbulence in the case of dust polarization. Here we study spectral correlation functions characterizing the parity-even and parity-odd parts of linear polarization for homogeneous and inhomogeneous turbulence to show that only the inhomogeneous helical case can give rise to a parity-odd polarization signal. We also study nonhelical turbulence and suggest that a strong nonvanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both helical and nonhelical cases. This could explain the enhanced EE/BB ratio observed recently for dust polarization. We close with a preliminary assessment of using linear polarization of the Sun to characterize its helical turbulence without being subjected to the pi ambiguity that magnetic inversion techniques have to address.

astro-ph.SR↗

arXiv2018

Magnetism in the Early Universe

Blazar observations point toward the possible presence of magnetic fields over intergalactic scales of the order of up to $\sim1\,$Mpc, with strengths of at least $\sim10^{-16}\,$G. Understanding the origin of these large-scale magnetic fields is a challenge for modern astrophysics. Here we discuss the cosmological scenario, focussing on the following questions: (i) How and when was this magnetic field generated? (ii) How does it evolve during the expansion of the universe? (iii) Are the amplitude and statistical properties of this field such that they can explain the strengths and correlation lengths of observed magnetic fields? We also discuss the possibility of observing primordial turbulence through direct detection of stochastic gravitational waves in the mHz range accessible to LISA.

astro-ph.CO↗

arXiv2018

Persistent 1-Cycles: Definition, Computation, and Its Application

Persistence diagrams, which summarize the birth and death of homological features extracted from data, are employed as stable signatures for applications in image analysis and other areas. Besides simply considering the multiset of intervals included in a persistence diagram, some applications need to find representative cycles for the intervals. In this paper, we address the problem of computing these representative cycles, termed as persistent 1-cycles, for $\text{H}_1$-persistent homology with $\mathbb{Z}_2$ coefficients. The definition of persistent cycles is based on the interval module decomposition of persistence modules, which reveals the structure of persistent homology. After showing that the computation of the optimal persistent 1-cycles is NP-hard, we propose an alternative set of meaningful persistent 1-cycles that can be computed with an efficient polynomial time algorithm. We also inspect the stability issues of the optimal persistent 1-cycles and the persistent 1-cycles computed by our algorithm with the observation that the perturbations of both cannot be properly bounded. We design a software which applies our algorithm to various datasets. Experiments on 3D point clouds, mineral structures, and images show the effectiveness of our algorithm in practice.

cs.CG↗

arXiv2018

Statistical Properties of Scale-Invariant Helical Magnetic Fields and Applications to Cosmology

We investigate the statistical properties of isotropic, stochastic, Gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. We discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. We are particularly interested in scale-invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. We determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. We show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. At smaller scales, the scale-invariant spectrum changes with time. It becomes a steeper weak-turbulence spectrum at progressively larger scales. We show numerically that the critical length scale where this happens is the turbulent-diffusive scale, which increases with the square root of time.

astro-ph.CO↗

arXiv2017

Evolution of hydromagnetic turbulence from the electroweak phase transition

We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today.

astro-ph.CO↗