arXiv subjects

Anirban Chatterjee

Publications and source records attributed to Anirban Chatterjee.

48 records · Page 3Linked to original sources

arXiv2022

Dynamical analysis of $k$-essence cosmology in the light of Supernova Ia observations

In this paper, we analyse the JLA data on Supernova observations in the context of $k-$essence dark energy model with Lagrangian $L=VF(X)$, with a constant potential $V$ and the dynamical term $X = (1/2)\nabla_μϕ\nabla_νϕ= \dotϕ^2/2$ for a homogeneous scalar field $ϕ(t)$, in a flat FRW spacetime background. Scaling relations are used to extract temporal behaviour of different cosmological quantities and the form of the function $F(X)$ from the data. We explore how the parameters of the model, viz. value of the constant potential $V$ and a constant $C$ appearing in the emergent scaling relation, control the dynamics of the model in the context of JLA data, by setting up and analysing an equivalent dynamical system described by a set of autonomous equations.

gr-qc↗

arXiv2022

Fluctuations of Subgraph Counts in Graphon Based Random Graphs

Given a graphon $W$ and a finite simple graph $H$, with vertex set $V(H)$, denote by $X_n(H, W)$ the number of copies of $H$ in a $W$-random graph on $n$ vertices. The asymptotic distribution of $X_n(H, W)$ was recently obtained by Hladký, Pelekis, and Šileikis (2021) in the case where $H$ is a clique. In this paper, we extend this result to any fixed graph $H$. Towards this we introduce a notion of $H$-regularity of graphons and show that if the graphon $W$ is not $H$-regular, then $X_n(H, W)$ has Gaussian fluctuations with scaling $n^{|V(H)|-\frac{1}{2}}$. On the other hand, if $W$ is $H$-regular, then the fluctuations are of order $n^{|V(H)|-1}$ and the limiting distribution of $X_n(H, W)$ can have both Gaussian and non-Gaussian components, where the non-Gaussian component is a (possibly) infinite weighted sum of centered chi-squared random variables with the weights determined by the spectral properties of a graphon derived from $W$. Our proofs use the asymptotic theory of generalized $U$-statistics developed by Janson and Nowicki (1991). We also investigate the structure of $H$-regular graphons for which either the Gaussian or the non-Gaussian component of the limiting distribution (but not both) is degenerate. Interestingly, there are also $H$-regular graphons $W$ for which both the Gaussian or the non-Gaussian components are degenerate, that is, $X_n(H, W)$ has a degenerate limit even under the scaling $n^{|V(H)|-1}$. We give an example of this degeneracy with $H=K_{1, 3}$ (the 3-star) and also establish non-degeneracy in a few examples. This naturally leads to interesting open questions on higher-order degeneracies.

math.PR↗

arXiv2021

Dynamical stability of K-essence field interacting non-minimally with a perfect fluid

We study models of non-minimally coupled relativistic fluid and $k$-essence scalar field in the background of a flat Friedmann-Lemaitre-Robertson-Walker universe. The non-minimal coupling term is introduced in the Lagrangian level. We employ the variational approach with respect to independent variables that produce modified $k-$essence field equations and the Friedmann equations. We have analyzed the coupled field-fluid framework explicitly using the dynamical system technique considering two different models based on inverse power-law potential. After examining these models it is seen that both models are capable of producing accelerating attractor solutions satisfying adiabatic sound speed conditions.

gr-qc↗

arXiv2021

Look Before You Leap! Designing a Human-Centered AI System for Change Risk Assessment

Reducing the number of failures in a production system is one of the most challenging problems in technology driven industries, such as, the online retail industry. To address this challenge, change management has emerged as a promising sub-field in operations that manages and reviews the changes to be deployed in production in a systematic manner. However, it is practically impossible to manually review a large number of changes on a daily basis and assess the risk associated with them. This warrants the development of an automated system to assess the risk associated with a large number of changes. There are a few commercial solutions available to address this problem but those solutions lack the ability to incorporate domain knowledge and continuous feedback from domain experts into the risk assessment process. As part of this work, we aim to bridge the gap between model-driven risk assessment of change requests and the assessment of domain experts by building a continuous feedback loop into the risk assessment process. Here we present our work to build an end-to-end machine learning system along with the discussion of some of practical challenges we faced related to extreme skewness in class distribution, concept drift, estimation of the uncertainty associated with the model's prediction and the overall scalability of the system.

cs.LG↗

arXiv2021

Spectral properties of the Laplacian of a generalized Wigner matrix

In this article we consider the spectrum of a Laplacian matrix, also known as the Markov matrix, under the independence assumption. We assume that the entries have a variance profile. Motivated by recent works on generalized Wigner matrices we assume that variance profile gives rise to a sequence of graphons. Under the assumption that these graphons converge, we show that the limiting spectral distribution of the scaled Laplacian converge. We give an expression for the moments of the limiting measure in terms of graph homomorphisms. In some special cases we identify the limit explicitly. We also study the spectral norm and derive the order of the maximum eigenvalue. We show that our results cover Laplacian of various random graphs include inhomogeneous Erdős- R\' enyi random graph, sparse W-random graphs, stochastic block matrices and constrained random graphs.

math.PR↗

arXiv2020

Time-dependent diffusive interactions between dark matter and dark energy in the context of $k-$essence cosmology

We investigated the scenario of time-dependent diffusive interaction between dark matter and dark energy and showed that such a model can be accommodated within the observations of luminosity distance - redshift data in Supernova Ia (SNe Ia) observations. We obtain constrains on different relevant parameters of this model from the observational data. We consider a homogeneous scalar field $ϕ(t)$ driven by a $k-$essence Lagrangian of the from $L = V(ϕ)F(X)$ with constant potential $V(ϕ) = V$, to describe the dynamics of dark energy in this model. Using the temporal behaviour of the FRW scale factor, the equation of state and total energy density of the dark fluid, extracted from the analysis of SNe Ia (JLA) data, we have obtained the time-dependence of the $k-$essence scalar field and also reconstructed form of the function $F(X)$ in the $k-$essence Lagrangian.

gr-qc↗

arXiv2020

Drift-Adjusted And Arbitrated Ensemble Framework For Time Series Forecasting

Time Series Forecasting is at the core of many practical applications such as sales forecasting for business, rainfall forecasting for agriculture and many others. Though this problem has been extensively studied for years, it is still considered a challenging problem due to complex and evolving nature of time series data. Typical methods proposed for time series forecasting modeled linear or non-linear dependencies between data observations. However it is a generally accepted notion that no one method is universally effective for all kinds of time series data. Attempts have been made to use dynamic and weighted combination of heterogeneous and independent forecasting models and it has been found to be a promising direction to tackle this problem. This method is based on the assumption that different forecasters have different specialization and varying performance for different distribution of data and weights are dynamically assigned to multiple forecasters accordingly. However in many practical time series data-set, the distribution of data slowly evolves with time. We propose to employ a re-weighting based method to adjust the assigned weights to various forecasters in order to account for such distribution-drift. An exhaustive testing was performed against both real-world and synthesized time-series. Experimental results show the competitiveness of the method in comparison to state-of-the-art approaches for combining forecasters and handling drift.

cs.LG↗

arXiv2019

Implications of JLA data for $k-$essence model of dark energy with given equation of state

We investigated implications of recently released `Joint Light-curve Analysis' (JLA) supernova Ia (SNe Ia) data for dark energy models with time varying equation of state of dark energy, usually expressed as $w(z)$ in terms of variation with corresponding redshift $z$. From a comprehensive analysis of the JLA data, we obtain the observational constraints on the different functional forms of $w(z)$, corresponding to different varying dark energy models often considered in literature, \textit{viz.} CPL, JBP, BA and Logarithmic models. The constraints are expressed in terms of parameters ($w_a, w_b$) appearing in the chosen functional form for $w(z)$, corresponding to each of the above mentioned models. Realising dark energy with varying equation of state in terms of a homogeneous scalar field $ϕ$, with its dynamics driven by a $k-$essence Lagrangian $L=VF(X)$ with a constant potential $V$ and a dynamical term $F(X)$ with $X=(1/2)\nabla^μϕ\nabla_μϕ$ we reconstructed form of the function $F(X)$. This reconstruction has been performed for different varying dark energy models at best-fit values of parameters ($w_a, w_b$) obtained from analysis of JLA data. In the context of $k-$essence model, we also investigate the variation of adiabatic sound speed squared, $c_s^2(z)$, and obtained the domains in ($w_a, w_b$) parameter space corresponding to the physical bound $ c_s^2>0$ implying stability of density perturbations.

gr-qc↗

arXiv2019

Probing Dark-ALP Portals at Future $e^+e^-$ Colliders

We study portal interactions connecting visible and dark sectors, and involving local interactions of a photon, a dark photon and a axion-like particle (ALP) at future $e^+e^-$ colliders. These interactions, mediated by higher-dimensional effective operators, may arise at one-loop by kinetic mixing between dark and ordinary photons, or, for massless dark photons, by direct short-distance contributions. We explore these portal interactions for a heavy ALP with masses between about 10 GeV and 230 GeV by investigating the sensitivity of the production $e^+e^- \to γγ\barγ$ to the effective couplings, where the dark photon $\barγ$ gives rise to missing momentum in the final state. We will show how an appropriate choice of missing-energy and missing-mass cuts can optimize the signal to standard-model background ratio. Exclusion regions for the effective photon-dark-photon-ALP couplings versus the ALP mass are worked out for a few representative values of the collision energy and integrated luminosity, as presently envisaged by future $e^+e^-$ projects.

hep-ph↗

arXiv2019

Realising Interactions Between Dark Matter and Dark Energy Using $k$-essence Cosmology

In this paper we exploit dynamics of a $k-$essence scalar field to realise interactions between dark components of universe resulting in a evolution consistent with observed features of late time phase of cosmic evolution. Stress energy tensor corresponding to a $k-$essence Lagrangian $L=V( ϕ)F(X)$ (where $X=\frac{1}{2}g^{μν}\nabla_μϕ\nabla_νϕ$) is shown to be equivalent to an ideal fluid with two components having same equation of state. Stress energy tensor of one of the components may be generated from a constant potential $k-$essence Lagrangian of form $L_1=V_0F(X)$ ($V_0$ constant) and that of other from another Lagrangian of form $L_2=V_1(ϕ)F(X)$ with $V=V_0 + V_1(ϕ)$. We have shown that, the unified dynamics of dark matter and dark energy described by a single scalar field $ϕ$ driven by a $k-$essence Lagrangian $L= V(ϕ)F(X)$ may be viewed in terms of diffusive interactions between the two hypothetical fluid components `1' and `2' with stress energy tensors equivalent to that of Lagrangians $L_1$ and $L_2$ respectively. The energy transfer between the fluid components is determined by functions $V(ϕ)$, $F(X)$ and their derivatives. Such a realisation is shown to be consistent with the Supernova Ia data with certain constraints on the temporal behaviour of $k-$essence potential $V(ϕ)$. We have described a methodology to obtain such constraints.

gr-qc↗

arXiv2019

Semi-Bagging Based Deep Neural Architecture to Extract Text from High Entropy Images

Extracting texts of various size and shape from images containing multiple objects is an important problem in many contexts, especially, in connection to e-commerce, augmented reality assistance system in natural scene, etc. The existing works (based on only CNN) often perform sub-optimally when the image contains regions of high entropy having multiple objects. This paper presents an end-to-end text detection strategy combining a segmentation algorithm and an ensemble of multiple text detectors of different types to detect text in every individual image segments independently. The proposed strategy involves a super-pixel based image segmenter which splits an image into multiple regions. A convolutional deep neural architecture is developed which works on each of the segments and detects texts of multiple shapes, sizes, and structures. It outperforms the competing methods in terms of coverage in detecting texts in images especially the ones where the text of various types and sizes are compacted in a small region along with various other objects. Furthermore, the proposed text detection method along with a text recognizer outperforms the existing state-of-the-art approaches in extracting text from high entropy images. We validate the results on a dataset consisting of product images on an e-commerce website.

cs.CV↗

arXiv2018

Diffusive dark matter and dark energy scenario and $k-$essence in the context of Supernova Ia observations

We consider a unified model of interacting dark matter and dark energy to account for coincidence of present day dark energy and dark matter densities. We assume dark energy to be represented by a homogeneous scalar field $ϕ$ whose dynamics is driven by a (non-canonical) $k$-essence Lagrangian with constant potential and the particles of dark matter fluid undergoing velocity diffusion in background medium of the $k-$essence scalar field $ϕ$. This results in a transfer of energy from the fluid of dark matter to that of dark energy. This effect shows up as a source term in the continuity equation for dark matter and dark energy fluids. The source term involves a diffusion coefficient which is a measure of average energy transferred per unit time due to diffusion. We use time evolutions of the scale factor of background FRW spacetime, energy density and pressure of the dark fluid obtained from analysis of Supernova Ia data to obtain bounds on the diffusion parameter. For a constant potential in the $k$-essence Lagrangian, the temporal behaviour of a homogeneous $k$-essence field $ϕ$ is obtained for different values of the diffusion parameter. The obtained temporal behaviour may be expressed as $ϕ(t/t_0) = ϕ_0 + \varepsilon_1 (t/t_0 - 1) + \varepsilon_2 (t/t_0 -1)^2$, where $t_0$ is the time corresponding to present epoch. The coefficients $\varepsilon_1$ and $\varepsilon_2$ have been found and obtained as linear functions of diffusion parameter.

gr-qc↗