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Amit Kumar

Publications and source records attributed to Amit Kumar.

At least 145 records · Page 8Linked to original sources
arXiv2023

Efficient Algorithms and Hardness Results for the Weighted $k$-Server Problem

In this paper, we study the weighted $k$-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) $k$-server problem which has a polynomial-time solution using min-cost flows, there are strong computational lower bounds for the weighted $k$-server problem, even on the uniform metric. Specifically, we show that assuming the unique games conjecture, there are no polynomial-time algorithms with a sub-polynomial approximation factor, even if we use $c$-resource augmentation for $c < 2$. Furthermore, if we consider the natural LP relaxation of the problem, then obtaining a bounded integrality gap requires us to use at least $\ell$ resource augmentation, where $\ell$ is the number of distinct server weights. We complement these results by obtaining a constant-approximation algorithm via LP rounding, with a resource augmentation of $(2+ε)\ell$ for any constant $ε> 0$. In the online setting, an $\exp(k)$ lower bound is known for the competitive ratio of any randomized algorithm for the weighted $k$-server problem on the uniform metric. In contrast, we show that $2\ell$-resource augmentation can bring the competitive ratio down by an exponential factor to only $O(\ell^2 \log \ell)$. Our online algorithm uses the two-stage approach of first obtaining a fractional solution using the online primal-dual framework, and then rounding it online.

cs.DS↗
arXiv2023

Computing Jet Transport Coefficients On The Lattice

The leading jet transport coefficients $\hat{q}$ or $\hat{e}_{2}$ encode transverse or longitudinal momentum broadening of a hard parton traversing a hot medium. Understanding their temperature dependence is key to appreciating the observed suppression of high-transverse momentum probes at RHIC or LHC collision energies. We present a first continuum extrapolated result of $\hat{q}$ computed on pure SU(3) lattices with non-trivial temperature dependence different from the weak-coupling expectation. We discuss our formalism and its challenges and status in view of obtaining $\hat{e}_{2}$ or of unquenching the calculation. We consider a hard quark subject to a single scattering on the plasma. The transport coefficients are factorized in terms of matrix elements given as integrals of non-local gauge-covariant gluon field-strength field-strength correlators. After the analytic continuation to the deep-Euclidean region, the hard scale permits to recast these as a series of local, gauge-invariant operators. The renormalized leading-twist term in this expansion is closely related to static quantities, and is computed on pure SU(3) lattices ($N_τ=4,~6,~8,$ and $10$) for a wide range of temperatures, ranging from 200MeV < T < 1GeV. Our estimate for the unquenched result in $2+1$-flavor QCD has very similar features.

hep-lat↗
arXiv2023

Data processing of Visible Emission Line Coronagraph Onboard ADITYA L1

ADITYA-L1 is India's first dedicated mission to observe the sun and its atmosphere from a halo orbit around L1 point. Visible emission line coronagraph (VELC) is the prime payload on board at Aditya-L1 to observe the sun's corona. VELC is designed as an internally occulted reflective coronagraph to meet the observational requirements of wide wavelength band and close to the solar limb (1.05 Ro). Images of the solar corona in continuum and spectra in three emission lines 5303Å [Fe xiv], 7892Å [Fe xi] and 10747 [Fe xiii] obtained with high cadence to be analyzed using software algorithms automatically. A reasonable part of observations will be made in synoptic mode, those, need to be analyzed and results made available for public use. The procedure involves the calibration of instrument and detectors, converting the images into fits format, correcting the images and spectra for the instrumental effects, align the images etc. Then, develop image processing algorithms to detect the occurrence of energetic events using continuum images. Also derive physical parameters, such as temperature and velocity structure of solar corona using emission line observations. Here, we describe the calibration of detectors and the development of software algorithms to detect the occurrence of CMEs and analyze the spectroscopic data.

astro-ph.SR↗
arXiv2023

Origin of magnetic ordering in half-Heusler RuMnGa

The half-Heusler alloy RuMnGa having valence electron count (VEC) 18 has recently been theoretically proposed to exhibit compensated ferrimagnetic (CFiM) character instead of the expected nonmagnetic ground state. On the other hand, a preliminary experimental study proposed ferromagnetic (FM) ordering. As no half-Heusler system with VEC 18 is known to exhibit magnetic ordering, we have investigated the details of crystal structure and magnetic properties of RuMnGa using a combination of experimental tools, viz., x-ray and neutron diffraction techniques, dc and ac susceptibility, isothermal magnetisation, heat capacity, resistivity and neutron depolarisation measurements. Rietveld refinements of x-ray and neutron diffraction data suggest single phase nature of the compound with elemental composition RuMn$_{0.86}$Ga$_{1.14}$. We have shown that the system exhibits FM-type ordering owing to the inherent presence of this minor off-stoichiometry, showing very low magnetic moment. The system also exhibits reentrant canonical spin-glass behaviour, which is rarely observed in half-Heusler alloys. The temperature coefficient of resistivity changes its sign from negative to positive and further to negative as the temperature decreases.

cond-mat.mtrl-sci↗
arXiv2023

4K$\times$4K CCD Imager for the 3.6m DOT: Recent up-gradations and results

The 4K$\times$4K CCD Imager is the first light instrument for the 3.6m Devasthal Optical Telescope and is producing broad-band imaging observations of many Galactic and extra-galactic sources since 2015-2016. Capabilities of the CCD Imager are demonstrated recently through several publications using the well-calibrated multi-band deep photometric results as expected from other similar facilities globally. In this article, we summarize some of the recent up-gradations made to improve the Imager, i.e., mounting the new filter wheel casing, replacing stray light baffles and discussing the fringe pattern corrections in redder filters. Some of the new science initiatives like galaxy-embedded faint point sources including WR stars and the observations of low surface brightness galaxy clusters are also discussed.

astro-ph.IM↗
arXiv2023

Nilpotency and Capability in multiplicative Lie algebras

This paper aims to introduce the concept of nilpotency and capability in multiplicative Lie algebras. Also, we see the existence of covers of a multiplicative Lie algebra and thoroughly examine their relationships with capable and perfect multiplicative Lie algebras.

math.GR↗
arXiv2023

Universal Weak Coreset

Coresets for $k$-means and $k$-median problems yield a small summary of the data, which preserve the clustering cost with respect to any set of $k$ centers. Recently coresets have also been constructed for constrained $k$-means and $k$-median problems. However, the notion of coresets has the drawback that (i) they can only be applied in settings where the input points are allowed to have weights, and (ii) in general metric spaces, the size of the coresets can depend logarithmically on the number of points. The notion of weak coresets, which have less stringent requirements than coresets, has been studied in the context of classical $k$-means and $k$-median problems. A weak coreset is a pair $(J,S)$ of subsets of points, where $S$ acts as a summary of the point set and $J$ as a set of potential centers. This pair satisfies the properties that (i) $S$ is a good summary of the data as long as the $k$ centers are chosen from $J$ only, and (ii) there is a good choice of $k$ centers in $J$ with cost close to the optimal cost. We develop this framework, which we call universal weak coresets, for constrained clustering settings. In conjunction with recent coreset constructions for constrained settings, our designs give greater data compression, are conceptually simpler, and apply to a wide range of constrained $k$-median and $k$-means problems.

cs.DS↗
arXiv2023

Dual Drazin generalized inverse for dual matrices

This manuscript proposes a generalized inverse for a dual matrix called dual Drazin generalized inverse (DDGI) which generalizes the notion of the dual group generalized inverse (DGGI). Under certain necessary and sufficient conditions, we establish the existence of the DDGI of a dual matrix of any index. Thereafter, we show that the DDGI is unique (whenever exists). The DDGI is then used to solve a linear dual system. We also establish reverse-order law and forward-order law for a particular form of the DGGI, dual Moore-Penrose generalized inverse (DMPGI), dual core generalized inverse (DCGI), and DDGI under certain suitable conditions. Finally, the partial-orders based on DCGI and DGGI are proposed.

math.RA↗
arXiv2023

Machine Translation by Projecting Text into the Same Phonetic-Orthographic Space Using a Common Encoding

The use of subword embedding has proved to be a major innovation in Neural Machine Translation (NMT). It helps NMT to learn better context vectors for Low Resource Languages (LRLs) so as to predict the target words by better modelling the morphologies of the two languages and also the morphosyntax transfer. Even so, their performance for translation in Indian language to Indian language scenario is still not as good as for resource-rich languages. One reason for this is the relative morphological richness of Indian languages, while another is that most of them fall into the extremely low resource or zero-shot categories. Since most major Indian languages use Indic or Brahmi origin scripts, the text written in them is highly phonetic in nature and phonetically similar in terms of abstract letters and their arrangements. We use these characteristics of Indian languages and their scripts to propose an approach based on common multilingual Latin-based encodings (WX notation) that take advantage of language similarity while addressing the morphological complexity issue in NMT. These multilingual Latin-based encodings in NMT, together with Byte Pair Embedding (BPE) allow us to better exploit their phonetic and orthographic as well as lexical similarities to improve the translation quality by projecting different but similar languages on the same orthographic-phonetic character space. We verify the proposed approach by demonstrating experiments on similar language pairs (Gujarati-Hindi, Marathi-Hindi, Nepali-Hindi, Maithili-Hindi, Punjabi-Hindi, and Urdu-Hindi) under low resource conditions. The proposed approach shows an improvement in a majority of cases, in one case as much as ~10 BLEU points compared to baseline techniques for similar language pairs. We also get up to ~1 BLEU points improvement on distant and zero-shot language pairs.

cs.CL↗
arXiv2023

Experimental observation of spin glass state in highly disordered quaternary Heusler alloy FeRuMnGa

The realization of spin-glass (S-G) state in Heusler alloys is very rare despite the presence of inherent structural and elemental disorder in those compounds. Although a few half and full Heusler alloys are known to exhibit S-G state, there is hardly any manifestation of the same in cases of quaternary Heusler compounds. Here we report the observation of S-G state in a highly disordered equiatomic quaternary Heusler compound: FeRuMnGa, where the S-G state is in between of canonical S-G and cluster glass. Different intricate features of S-G state including non-equilibrium magnetic dynamics at low temperature in the compound are unveiled through our comprehensive magnetic, heat capacity and neutron diffraction studies. The structural disorder in the sample is neither conventional \textit{A2}- nor \textit{B2}-type while those two types are commonly observed for Heusler compounds. The presence of disorder also plays a significant role in electron transport properties of the alloy, which is reflected in its exhibition of semi-metallic behavior and anomalous Hall effect at low temperature.

cond-mat.mtrl-sci↗
arXiv2023

4d-element induced improvement of structural disorder and development of weakly re-entrant spin-glass behaviour in NiRuMnSn

The pursuit of efficient spin-polarization in quaternary Heusler alloys with the general formula $XX'YZ$ (where X, $X'$, and Y are transition metals and Z is a p-block element), has been a subject of significant scientific interest. While previous studies shows that isoelectronic substitution of 4d element in place of 3d element in quaternary Heusler alloy, improves the half-metallic ferromagnetic characteristics, our research on the quaternary Heusler alloy NiRuMnSn reveals a strikingly different scenario. In this study, we present a detailed structural analysis of the material using X-ray absorption fine structure (EXAFS) and neutron diffraction (ND) techniques, which confirms the formation of a single-phase compound with 50:50 site disorder between Ni/Ru atoms at 4c/4d sites. Contrary to expectations, our DFT calculations suggests a considerable decrease in spin-polarization even in the ordered structure. Additionally, we report on the compound's exceptional behavior, displaying a rare re-entrant spin glass property below $\sim$60 K, a unique and intriguing feature for quaternary Heusler-type compounds.

cond-mat.mtrl-sci↗
arXiv2023

Exploiting Multilingualism in Low-resource Neural Machine Translation via Adversarial Learning

Generative Adversarial Networks (GAN) offer a promising approach for Neural Machine Translation (NMT). However, feeding multiple morphologically languages into a single model during training reduces the NMT's performance. In GAN, similar to bilingual models, multilingual NMT only considers one reference translation for each sentence during model training. This single reference translation limits the GAN model from learning sufficient information about the source sentence representation. Thus, in this article, we propose Denoising Adversarial Auto-encoder-based Sentence Interpolation (DAASI) approach to perform sentence interpolation by learning the intermediate latent representation of the source and target sentences of multilingual language pairs. Apart from latent representation, we also use the Wasserstein-GAN approach for the multilingual NMT model by incorporating the model generated sentences of multiple languages for reward computation. This computed reward optimizes the performance of the GAN-based multilingual model in an effective manner. We demonstrate the experiments on low-resource language pairs and find that our approach outperforms the existing state-of-the-art approaches for multilingual NMT with a performance gain of up to 4 BLEU points. Moreover, we use our trained model on zero-shot language pairs under an unsupervised scenario and show the robustness of the proposed approach.

cs.CL↗
arXiv2023

On WD and WDMP generalized inverses in rings

Motivated by the very recent work of Gao, Y., Chen, J., Wang, J., Zou, H. [Comm. Algebra, 49(8) (2021) 3241-3254; MR4283143], we introduce two new generalized inverses named weak Drazin (WD) and weak Drazin Moore-Penrose (WDMP) inverses for elements in rings. A few of their properties are then provided, and the fact that the proposed generalized inverses coincide with different well-known generalized inverses under certain assumptions is established. Further, we discuss additive properties, reverse-order law and forward-order law for WD and WDMP generalized inverses. Some examples are also provided in support of the theoretical results.

math.RA↗
arXiv2023

Exploiting Language Relatedness in Machine Translation Through Domain Adaptation Techniques

One of the significant challenges of Machine Translation (MT) is the scarcity of large amounts of data, mainly parallel sentence aligned corpora. If the evaluation is as rigorous as resource-rich languages, both Neural Machine Translation (NMT) and Statistical Machine Translation (SMT) can produce good results with such large amounts of data. However, it is challenging to improve the quality of MT output for low resource languages, especially in NMT and SMT. In order to tackle the challenges faced by MT, we present a novel approach of using a scaled similarity score of sentences, especially for related languages based on a 5-gram KenLM language model with Kneser-ney smoothing technique for filtering in-domain data from out-of-domain corpora that boost the translation quality of MT. Furthermore, we employ other domain adaptation techniques such as multi-domain, fine-tuning and iterative back-translation approach to compare our novel approach on the Hindi-Nepali language pair for NMT and SMT. Our approach succeeds in increasing ~2 BLEU point on multi-domain approach, ~3 BLEU point on fine-tuning for NMT and ~2 BLEU point on iterative back-translation approach.

cs.CL↗
arXiv2023

Electronic Transport Studies of Ag-doped Bi2Se3 Topological Insulator

The structural, magnetotransport, and angle-resolved photoemission spectroscopy (ARPES) of Ag-doped Bi2Se3 single crystals are presented. Temperature dependent resistivity exhibits metallic behavior with a slope change above 200 K for Ag-doped Bi2Se3. The magnetoresistance shows positive quadratic dependence at low fields satisfying Kohler's rule. Hall resistivity measurement shows that electrons are dominant charge carriers. Furthermore, these results agree well with the ARPES spectra observed at T = 20 K, where the Fermi level lies inside the bulk conduction band. The Dirac point of the topological surface states is shifted toward higher binding energy (~ 0.12 eV) for Ag-doped samples as compared to pristine Bi2Se3.

cond-mat.str-el↗
arXiv2023

Ordered normed spaces of functions of bounded variation

In this paper, we define and study the space of all the functions of bounded variation $f:[x,y]\to \mathbb{Y}$ denoted by $\mathcal{BV}[x,y],$ where $[x,y]$ is an ordered interval and $\mathbb{Y}$ is an absolute order unit space having vector lattice structure. By default, under the order structure of $\mathbb{Y},$ the space $\mathcal{BV}[x,y]$ forms a nearer absolute order unit space structure and in some cases it turns out to be an absolute order unit space (in fact, a unital $AM$-space). By help of variation function, we also define a different kind of order structure on the space $\mathcal{BV}[x,y]$ that also makes $\mathcal{BV}[x,y]$ a nearer absolute order unit space structure. Later, we also show that under certain conditions this ordering induces a complete norm on $\mathcal{BV}[x,y].$

math.FA↗
arXiv2023

On generalized-Drazin inverses and GD-star matrices

Motivated by the works of Wang and Liu [Linear Algebra Appl., 488 (2016) 235-248; MR3419784] and Mosic [Results Math., 75(2) (2020) 1-21; MR4079761], we provide further results on GD inverses and introduce two new classes for square matrices called GD-star (generalized-Drazin-star) and GD-star-one (generalized-Drazin-star-one) using a GD inverse of a matrix. We then exploit their various properties and characterize them in terms of various generalized inverses. We establish a representation of a GD-star matrix by using the core-nilpotent decomposition and Hartwig-Spindelbock decomposition. We also define a binary relation called GD-star order using this class of matrices. Further, we obtain some analogous results for the class of star-GD matrices. Moreover, the reverse-order law and forward-order law for GD inverse along with its monotonicity criteria are obtained.

math.RA↗