arXiv subjects

Shamik Ghosh

Publications and source records attributed to Shamik Ghosh.

At least 37 records · Page 2Linked to original sources

arXiv2022

On some subclasses of circular-arc catch digraphs

Catch digraphs was introduced by Hiroshi Maehara in 1984 as an analog of intersection graphs where a family of pointed sets represents a digraph. After that Prisner continued his research particularly on interval catch digraphs by characterizing them diasteroidal triple free. It has numerous applications in the field of real world problems like network technology and telecommunication operations. Recently, we characterized three important subclasses of interval catch digraphs. In this article we introduce a new class of catch digraphs, namely circular-arc catch digraphs. The definition is same as interval catch digraph, only the intervals are replaced by circular-arcs here. We present the characterization of proper circular-arc catch digraphs, which is a natural subclass of circular-arc catch digraphs where no circular-arc is contained in other properly. For this we introduce a concept, namely monotone circular ordering for the vertices of the augmented adjacency matrix of it. Next we find that underlying graph of a proper oriented circular-arc catch digraph is a proper circular-arc graph. Also we characterize proper oriented circular-arc catch digraphs by defining a certain kind of circular vertex ordering of its vertices. Another interesting result is to characterize oriented circular-arc catch digraphs which are tournaments in terms of forbidden subdigraphs. Further we study some properties of an oriented circular-arc catch digraph. In conclusion we discuss the relations between these subclasses of circular-arc catch digraphs.

math.CO↗

arXiv2022

Performance forecasts for the primordial gravitational wave detection pipelines for AliCPT-1

AliCPT is the first Chinese cosmic microwave background (CMB) experiment which will make the most precise measurements of the CMB polarization in the northern hemisphere. The key science goal for AliCPT is the detection of primordial gravitational waves (PGWs). It is well known that an epoch of cosmic inflation, in the very early universe, can produce PGWs, which leave an imprint on the CMB in form of odd parity $B$-mode polarization. In this work, we study the performance of the component separation and parameter estimation pipelines in context of constraining the value of the tensor-to-scalar ratio. Based on the simulated data for one observation season, we compare five different pipelines with different working principles. Three pipelines perform component separation at map or spectra level before estimating $r$ from the cleaned spectra, while the other two pipelines performs a global fit for both foreground parameters and $r$. We also test different methods to account for the effects of time stream filtering systematics. This work shows that our pipelines provide consistent and robust constraints on the tensor-to-scalar ratio and a consistent sensitivity $σ(r) \sim 0.02$. This showcases the potential of precise $B$-mode polarization measurement with AliCPT-1. AliCPT will provide a powerful opportunity to detect PGWs, which is complementary with various ground-based CMB experiments in the southern hemisphere.

astro-ph.CO↗

arXiv2022

Forecasts on CMB lensing observations with AliCPT-1

AliCPT-1 is the first Chinese CMB experiment aiming for high precision measurement of Cosmic Microwave Background B-mode polarization. The telescope, currently under deployment in Tibet, will observe in two frequency bands centered at 90 and 150 GHz. We forecast the CMB lensing reconstruction, lensing-galaxy as well as lensing-CIB (Cosmic Infrared Background) cross correlation signal-to-noise ratio (SNR) for AliCPT-1. We consider two stages with different integrated observation time, namely "4 module*yr" (first stage) and "48 module*yr" (final stage). For lensing reconstruction, we use three different quadratic estimators, namely temperature-only, polarization-only and minimum-variance estimators, using curved sky geometry. We take into account the impact of inhomogeneous hit counts as well as of the mean-field bias due to incomplete sky coverage. In the first stage, our results show that the 150 GHz channel is able to measure the lensing signal at $15σ$ significance with the minimum-variance estimator. In the final stage, the measurement significance will increase to $31σ$. We also combine the two frequency data in the harmonic domain to optimize the SNR. Our result show that the coadding procedure can significantly reduce the reconstruction bias in the multiple range l>800. Thanks to the high quality of the polarization data in the final stage of AliCPT-1, the EB estimator will dominate the lensing reconstruction in this stage. We also estimate the SNR of cross-correlations between AliCPT-1 CMB lensing and other tracers of the large scale structure of the universe. For its cross-correlation with DESI galaxies/quasars, we report the cross-correlation SNR = 10-20 for the 4 redshift bins at 0.05<z<2.1. In the first stage, the total SNR is about $32$. In the final stage, the lensing-galaxy cross-correlation can reach SNR=52.

astro-ph.CO↗

arXiv2022

Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum

Estimating the cross-correlation power spectra of cosmic microwave background (CMB), in particular, the T B and EB spectra, is important for testing parity symmetry in cosmology and diagnosing insidious instruments systematics. The Quadratic Maximum Likelihood (QML) estimator provides the optimal estimates of power spectra, but it is computationally very expensive. The hybrid pseudo-Cl estimator is computationally fast but performs poorly on large scales. As a natural extension of previous work (Chen et al. 2021), in this article, we present a new unbiased estimator based on the Smith-Zaldarriaga (SZ) approach of E-B separation and scalar QML approach to reconstruct the cross-correlation power spectrum, called QML-SZ estimator. Our new estimator relies on the ability to construct scalar maps, which allows us to use a scalar QML estimator to obtain the cross-correlation power spectrum. By reducing the pixel number and algorithm complexity, the computational cost is nearly one order of magnitude smaller and the running time is nearly two orders of magnitude faster in the test situations.

astro-ph.IM↗

arXiv2021

Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum

Constructing a fast and efficient estimator for the B-mode power spectrum of cosmic microwave background (CMB) is of critical importance for CMB science. For a general CMB survey, the Quadratic Maximum Likelihood (QML) estimator for CMB polarization has been proved to be the optimal estimator with minimal uncertainties, but it is computationally very expensive. In this article, we propose two new QML methods for B-mode power spectrum estimation. We use the Smith-Zaldarriaga approach to prepare pure-B mode map, and E-mode recycling method to obtain a leakage free B-mode map. We then use the scalar QML estimator to analyze the scalar pure-B map (QML-SZ) or B-mode map (QML-TC). The QML-SZ and QML-TC estimators have similar error bars as the standard QML estimators but their computational cost is nearly one order of magnitude smaller. The basic idea is that one can construct the pure B-mode CMB map by using the E-B separation method proposed by Smith-Zaldarriaga (SZ) or the one considering the template cleaning (TC) technique, then apply QML estimator to these scalar fields. By simulating potential observations of space-based and ground-based detectors, we test the reliability of these estimators by comparing them with the corresponding results of the traditional QML estimator and the pure B-mode pseudo-Cl estimator.

astro-ph.CO↗

arXiv2021

Reconstructing simulated CMB polarization power spectra with the Analytical Blind Separation method

Multi-frequency observations are needed to separate the CMB from foregrounds and accurately extract cosmological information from the data. The Analytical Blind Separation (ABS) method is dedicated to extracting the CMB power spectrum from multi-frequency observations in the presence of contamination from astrophysical foreground emission and instrumental noise. In this study, we apply the ABS method to simulated sky maps as could be observed with a future space-borne survey, in order to test the method's capability for determining the CMB polarization $E$- and $B$-mode power spectra. We present the ABS method performance on simulations for both a full-sky analysis and for an analysis concentrating on sky regions less impacted by Galactic foreground emission. We discuss the origin and minimization of biases in the estimated CMB polarization angular power spectra. We find that the ABS method performs quite well for the analysis of full-sky observations at intermediate and small angular scales, in spite of strong foreground contamination. On the largest scales, extra work is still required to reduce biases of various origins and the impact of confusion between CMB $E$ and $B$ polarization for partial-sky analyses.

astro-ph.CO↗

arXiv2021

Oriented Bipartite Graphs and the Goldbach Graph

In this paper, we study oriented bipartite graphs. In particular, we introduce "bitransitive" graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic bitournaments. As applications, we characterize acyclic bitournaments with Hamiltonian paths, determine number of non-isomorphic acyclic bitournaments of a given order, and solve the graph-isomorphism problem in linear time for acyclic bitournaments. Next, we prove the well-known Caccetta-H$\ddot{\textrm{a}}$ggkvist Conjecture for oriented bipartite graphs for some cases for which it is unsolved in general oriented graphs. We also introduce the concept of undirected as well as oriented "odd-even" graphs. We characterize bipartite graphs and acyclic oriented bipartite graphs in terms of them. In fact, we show that any bipartite graph (acyclic oriented bipartite graph) can be represented by some odd-even graph (oriented odd-even graph). We obtain some conditions for connectedness of odd-even graphs. This study of odd-even graphs and their connectedness is motivated by a special family of odd-even graphs which we call "Goldbach graphs". We show that the famous Goldbach's conjecture is equivalent to the connectedness of Goldbach graphs. Several other number theoretic conjectures (e.g., the twin prime conjecture) are related to various parameters of Goldbach graphs, motivating us to study the nature of vertex-degrees and independent sets of these graphs. Finally, we observe Hamiltonian properties of some odd-even graphs related to Goldbach graphs for small number of vertices.

math.CO↗

arXiv2021

The design of the Ali CMB Polarization Telescope receiver

Ali CMB Polarization Telescope (AliCPT-1) is the first CMB degree-scale polarimeter to be deployed on the Tibetan plateau at 5,250m above sea level. AliCPT-1 is a 90/150 GHz 72 cm aperture, two-lens refracting telescope cooled down to 4 K. Alumina lenses, 800mm in diameter, image the CMB in a 33.4° field of view on a 636mm wide focal plane. The modularized focal plane consists of dichroic polarization-sensitive Transition-Edge Sensors (TESes). Each module includes 1,704 optically active TESes fabricated on a 150mm diameter silicon wafer. Each TES array is read out with a microwave multiplexing readout system capable of a multiplexing factor up to 2,048. Such a large multiplexing factor has allowed the practical deployment of tens of thousands of detectors, enabling the design of a receiver that can operate up to 19 TES arrays for a total of 32,376 TESes. AliCPT-1 leverages the technological advancements in the detector design from multiple generations of previously successful feedhorn-coupled polarimeters, and in the instrument design from BICEP-3, but applied on a larger scale. The cryostat receiver is currently under integration and testing. During the first deployment year, the focal plane will be populated with up to 4 TES arrays. Further TES arrays will be deployed in the following years, fully populating the focal plane with 19 arrays on the fourth deployment year. Here we present the AliCPT-1 receiver design, and how the design has been optimized to meet the experimental requirements.

astro-ph.IM↗

arXiv2020

Towards ending the partial sky E-B ambiguity in CMB observations

A crucial problem for partial sky analysis of CMB polarization is the $E$-$B$ leakage problem. Such leakage arises from the presence of `ambiguous' modes that satisfy properties of both $E$ and $B$ modes. Solving this problem is critical for primordial polarization $B$ mode detection in partial sky CMB polarization experiments. In this work we introduce a new method for reducing the leakage. We demonstrate that if we complement the $E$-mode information outside the observation patch with ancillary data from full-sky CMB observations, we can reduce and even effectively remove the $E$-to-$B$ leakage. For this objective, we produce $E$-mode Stokes $QU$ maps from Wiener filtered full-sky intensity and polarization CMB observations. We use these maps to fill the sky region that is not observed by the ground-based experiment of interest, and thus complement the partial sky Stokes $QU$ maps. Since the $E$-mode information is now available on the full sky we see a significant reduction in the $E$-to-$B$ leakage. We evaluate on simulated data sets the performance of our method for a `shallow' $f_\text{sky}=8\%$, and a `deep' $f_\text{sky}=2\%$ northern hemisphere sky patch, with AliCPT-like properties, and a LSPE-like $f_\text{sky}=30\%$ sky patch, by combining those observations with Planck-like full sky polarization maps. We find that our method outperforms the standard and the pure-$B$ method pseudo-$C_\ell$ estimators for all of our simulations. Our new method gives unbiased estimates of the $B$-mode power spectrum through-out the entire multipole range with near-optimal pseudo-$C_\ell$ errors for $\ell>20$. We also study the application of our method to the CMB-S4 experiment combined with LiteBIRD-like full sky data, and show that using signal-dominated full sky $E$-mode data we can eliminate the $E$-to-$B$ leakage problem.

astro-ph.CO↗

arXiv2020

On central-max-point tolerance graphs and some subclasses of interval catch digraphs

Max-point-tolerance graphs (MPTG) were studied by Catanzaro et al. in 2017 and the same class of graphs were introduced in the name of p-BOX(1) graphs by Soto and Caro in 2015. In our paper we consider central-max-point tolerance graphs (central MPTG) by taking the points of MPTG as center points of their corresponding intervals. In course of study on this class of graphs we show that the class of central MPTG is same as the class of unit max-tolerance graphs. We prove the class of unit central max-point tolerance graphs is same as that of proper central max-point tolerance graphs and both of them are equivalent to the class of proper interval graphs. Next we introduce 50% max-tolerance graphs and separate this class from unit max-tolerance graph whereas for min-tolerance graphs 50% and unit denote the same graph class. Interval catch digraphs (ICD) was introduced by Maehera in 1984. In his introducing paper Maehera proposed a conjecture for the characterization of central interval catch digraph (central ICD) in terms of forbidden subdigraphs. In this paper, we disprove the conjecture by showing counter examples. We find close relation between a central MPTG and a central ICD. Also we characterize this digraph by defining a suitable mapping from the vertex set to the real line. Next we study oriented interval catch digraphs (oriented ICD). We characterize augmented adjacency matrix of an oriented ICD when it is a tournament. Also we characterize an oriented ICD whose underlying graph is a tree. Further we obtain characterization of the adjacency matrix of a proper interval catch digraph. Another important result is to provide forbidden subdigraph characterization of those proper oriented interval catch digraphs whose underlying undirected graph is chordal. In last section we discuss relationships between these classes of graphs and digraphs.

math.CO↗

arXiv2020

A Dynamic Reduction Network for Point Clouds

Classifying whole images is a classic problem in machine learning, and graph neural networks are a powerful methodology to learn highly irregular geometries. It is often the case that certain parts of a point cloud are more important than others when determining overall classification. On graph structures this started by pooling information at the end of convolutional filters, and has evolved to a variety of staged pooling techniques on static graphs. In this paper, a dynamic graph formulation of pooling is introduced that removes the need for predetermined graph structure. It achieves this by dynamically learning the most important relationships between data via an intermediate clustering. The network architecture yields interesting results considering representation size and efficiency. It also adapts easily to a large number of tasks from image classification to energy regression in high energy particle physics.

cs.CV↗

arXiv2020

hammurabi X: Simulating Galactic Synchrotron Emission with Random Magnetic Fields

We present version X of the hammurabi package, the HEALPix-based numeric simulator for Galactic polarized emission. Improving on its earlier design, we have fully renewed the framework with modern C++ standards and features. Multi-threading support has been built in to meet the growing computational workload in future research. For the first time, we present precision profiles of hammurabi line-of-sight integral kernel with multi-layer HEALPix shells. In addition to fundamental improvements, this report focuses on simulating polarized synchrotron emission with Gaussian random magnetic fields. Two fast methods are proposed for realizing divergence-free random magnetic fields either on the Galactic scale where a field alignment and strength modulation are imposed, or on a local scale where more physically motivated models like a parameterized magneto-hydrodynamic (MHD) turbulence can be applied. As an example application, we discuss the phenomenological implications of Gaussian random magnetic fields for high Galactic latitude synchrotron foregrounds. In this, we numerically find B/E polarization mode ratios lower than unity based on Gaussian realizations of either MHD turbulent spectra or in spatially aligned magnetic fields.

astro-ph.IM↗

arXiv2019

A Pixel Space Method for Testing Dipole Modulation in the CMB Polarization

We introduce a pixel space method to detect dipole modulation or hemispherical power asymmetry in the cosmic microwave background (CMB) polarization. The method relies on the use of squared total polarized flux whose ensemble average picks up a dipole due to the dipole modulation in the CMB polarization. The method is useful since it can be applied easily to partial sky. We define several statistics to characterize the amplitude of the detected signal. By simulations we show that the method can be used to reliably extract the signal at 2.7$σ$ level or higher in future CORE-like missions, assuming that the signal is present in the CMB polarization at the level detected by the Planck mission in the CMB temperature. An application of the method to the 2018 Planck data does not detect a significant effect, when taking into account the presence of correlated detector noise and residual systematics in data. Using the FFP10 we find the presence of a very strong bias which might be masking any real effect.

astro-ph.CO↗

arXiv2019

The galaxy power spectrum from TGSS ADR1 and the effect of flux calibration systematics

We explore the large to moderate scale anisotropy in distant radio sources using the TGSS ADR1 catalog. We use different measures, i.e. number counts, sky brightness and flux per source, for this study. In agreement with earlier results, we report a significant excess of clustering signal above the angular scale of roughly $10$ degrees (i.e. $l\lessapprox 20-30$). We find that some survey areas have a systematically low/high flux and argue this may be the cause of the observed signal of excess power at low multipoles. With mocks we demonstrate the effect of such large scale flux systematics and recover TGSS like excess clustering signal by assuming $20\%$ flux uncertainties over $\sim 10^\circ \times 10^\circ$ size patches. We argue that that TGSS at this stage, i.e. TGSS ADR1, is not suitable for large scale clustering measurements. We find that the measure, flux per source, shows evidence of isotropy for all multipoles $l > 2$ despite the presence of systematics in the data.

astro-ph.CO↗

arXiv2018

A simulation study to distinguish prompt photon from $π^0$ and beam halo in a granular calorimeter using deep networks

In a hadron collider environment identification of prompt photons originating in a hard partonic scattering process and rejection of non-prompt photons coming from hadronic jets or from beam related sources, is the first step for study of processes with photons in final state. Photons coming from decay of $π_0$'s produced inside a hadronic jet and photons produced in catastrophic bremsstrahlung by beam halo muons are two major sources of non-prompt photons. In this paper the potential of deep learning methods for separating the prompt photons from beam halo and $π^0$'s in the electromagnetic calorimeter of a collider detector is investigated, using an approximate description of the CMS detector. It is shown that, using only calorimetric information as images with a Convolutional Neural Network, beam halo (and $π^{0}$) can be separated from photon with 99.96\% (97.7\%) background rejection for 99.00\% (90.0\%) signal efficiency which is much better than traditionally employed variables.

physics.ins-det↗

arXiv2018

Characterization and recognition of proper tagged probe interval graphs

Interval graphs were used in the study of genomics by the famous molecular biologist Benzer. Later on probe interval graphs were introduced by Zhang as a generalization of interval graphs for the study of cosmid contig mapping of DNA. A tagged probe interval graph (briefly, TPIG) is motivated by similar applications to genomics, where the set of vertices is partitioned into two sets, namely, probes and nonprobes and there is an interval on the real line corresponding to each vertex. The graph has an edge between two probe vertices if their corresponding intervals intersect, has an edge between a probe vertex and a nonprobe vertex if the interval corresponding to a nonprobe vertex contains at least one end point of the interval corresponding to a probe vertex and the set of non-probe vertices is an independent set. This class of graphs have been defined nearly two decades ago, but till today there is no known recognition algorithm for it. In this paper, we consider a natural subclass of TPIG, namely, the class of proper tagged probe interval graphs (in short PTPIG). We present characterization and a linear time recognition algorithm for PTPIG. To obtain this characterization theorem we introduce a new concept called canonical sequence for proper interval graphs, which, we belief, has an independent interest in the study of proper interval graphs. Also to obtain the recognition algorithm for PTPIG, we introduce and solve a variation of consecutive $1$'s problem, namely, oriented consecutive $1$'s problem and some variations of PQ-tree algorithm. We also discuss the interrelations between the classes of PTPIG and TPIG with probe interval graphs and probe proper interval graphs.

math.CO↗

arXiv2018

Maximal and maximum transitive relation contained in a given binary relation

We study the problem of finding a \textit{maximal} transitive relation contained in a given binary relation. Given a binary relation of size $m$ defined on a set of size $n$, we present a polynomial time algorithm that finds a maximal transitive sub-relation in time $O(n^2 + nm)$. We also study the problem of finding a \textit{maximum} transitive relation contained in a binary relation. This is the problem of computing a maximum transitive subgraph in a given digraph. For the class of directed graphs with the underlying graph being triangle-free, we present a $0.874$-approximation algorithm. This is achieved via a simple connection to the problem of maximum directed cut. Further, we give an upper bound for the size of any maximum transitive relation to be $m/4 + cm^{4/5}$, where $c > 0$ and $m$ is the number of edges in the digraph.

cs.DS↗

arXiv2017

Dipole Modulation of Cosmic Microwave Background Temperature and Polarization

We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l+1 multipoles, exactly as in the case of temperature. We obtain results for the case of TE, EE and BB correlations. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. We analyze the CMBR temperature and polarization data in order to extract the signal of these correlation between l and l+1 multipoles. Our results for the case of temperature using the latest PLANCK data agree with those obtained by an earlier analysis. A detailed study of the correlation in the polarization data is not possible at present. Hence we restrict ourselves to a preliminary investigation in this case.

astro-ph.CO↗