arXiv subjects

Hitesh Kumar

Publications and source records attributed to Hitesh Kumar.

30 records · Page 2Linked to original sources

arXiv2025

Vibration-assisted tunneling through single Au adatoms on two-dimensional WSe2

Scanning tunneling microscopy (STM) at 5 K was used to study individual Au atoms adsorbed on the surface of a WSe2 layer grown on epitaxial graphene. In line with theoretical predictions, scanning tunneling spectroscopy measurements reveal that the weakly bound adatom gives rise to an electronic state within the energy band gap of the WSe2 layer. Adatoms in different surface locations show different gap-state energy values that follow a random distribution around the Fermi level of the sample with a standard deviation of ~50 meV. The location-dependent shift is attributed to spatial variations in disorder potential. Tunneling via the gap state is accompanied by vibrational excitations as apparent from pronounced sideband peaks in the conductance spectra with Poisson-distributed intensities indicating significant electron-phonon coupling with a Huang-Rhys factor of S=2.8. STM tunneling through single Au adatoms on two-dimensional WSe2 constitutes a model case of resonant double-barrier tunneling accompanied by strong coupling to vibrational degrees of freedom.

cond-mat.mes-hall↗

arXiv2025

Vertex Partitioning and $p$-Energy of Graphs

For a Hermitian matrix $A$ of order $n$ with eigenvalues $λ_1(A)\ge \cdots\ge λ_n(A)$, define \[ \mathcal{E}_p^+(A)=\sum_{λ_i > 0} λ_i^p(A), \quad \mathcal{E}_p^-(A)=\sum_{λ_i<0} |λ_i(A)|^p,\] to be the positive and the negative $p$-energy of $A$, respectively. In this note, first we show that if $A=[A_{ij}]_{i,j=1}^k$, where $A_{ii}$ are square matrices, then \[ \mathcal{E}_p^+(A)\geq \sum_{i=1}^{k} \mathcal{E}_p^+(A_{ii}), \quad \mathcal{E}_p^-(A)\geq \sum_{i=1}^{k} \mathcal{E}_p^-(A_{ii}),\] for any real number $p\geq 1$. We then apply the previous inequality to establish lower bounds for $p$-energy of the adjacency matrix of graphs.

math.CO↗

arXiv2025

Refinement of a conjecture on positive square energy of graphs

Let $G$ be a simple graph of order $n$ with eigenvalues $λ_1(G)\geq \cdots \geq λ_n(G)$. Define \[s^+(G)=\sum_{λ_i >0} λ_i^2(G), \quad s^-(G)=\sum_{λ_i<0} λ_i^2(G).\] It was conjectured by Elphick, Farber, Goldberg and Wocjan that for every connected graph $G$ of order $n$, $s^+(G) \ge n-1.$ We verify this conjecture for graphs with domination number at most 2. We then strengthen the conjecture as follows: if $G$ is a connected graph of order $n$ and size $m \geq n+1$, then $s^+(G) \geq n$. We prove this conjecture for claw-free graphs and graphs with diameter 2.

math.CO↗

arXiv2025

The 4m International Liquid Mirror Telescope: Construction, operation, and science

The International Liquid Mirror Telescope (ILMT) project was motivated by the need for an inexpensive 4 metre diameter optical telescope that could be devoted entirely to astronomical surveys. Its scientific programmes include the detection and study of transients, variable objects, asteroids, comets, space debris and low surface brightness galaxies. To this end, a collaboration was formed between the Institute of Astrophysics and Geophysics (Liège University, Belgium), several Canadian universities (University of British Columbia, Laval University, University of Montreal, University of Toronto, York University, University of Victoria) and the Aryabhatta Research Institute of Observational Sciences (ARIES, India). After several years of design work in Belgium and construction in India on the ARIES Devasthal site, the telescope saw its first light on 29 April 2022. Its commissioning phase lasted from May 2022 until June 2023 (beginning of the monsoon). The ILMT was inaugurated on 21 March 2023 and has been in regular operation since October 2023. The telescope continuously observes the sky passing at the zenith using the SDSS g', r', and i' filters. This paper describes the ILMT, its operation, performance and shows some initial results.

astro-ph.IM↗

arXiv2024

A Linear Lower Bound for the Square Energy of Graphs

Let $G$ be a graph of order $n$ with eigenvalues $λ_1 \geq \cdots \geqλ_n$. Let \[s^+(G)=\sum_{λ_i>0} λ_i^2, \qquad s^-(G)=\sum_{λ_i<0} λ_i^2.\] The smaller value, $s(G)=\min\{s^+(G), s^-(G)\}$ is called the \emph{square energy} of $G$. In 2016, Elphick, Farber, Goldberg and Wocjan conjectured that for every connected graph $G$ of order $n$, $s(G)\geq n-1.$ No linear bound for $s(G)$ in terms of $n$ is known. Let $H_1, \ldots, H_k$ be disjoint vertex-induced subgraphs of $G$. In this note, we prove that \[s^+(G)\geq\sum_{i=1}^{k} s^+(H_i) \quad \text{ and } \quad s^-(G)\geq\sum_{i=1}^{k} s^-(H_i),\] which implies that $s(G)\geq \frac{3n}{4}$ for every connected graph $G$ of order $n\ge 4$.

math.CO↗

arXiv2024

On the second largest adjacency eigenvalue of trees with given diameter

For a graph $G$, let $λ_2(G)$ denote the second largest eigenvalue of the adjacency matrix of $G$. We determine the extremal trees with maximum/minimum adjacency eigenvalue $λ_2$ in the class $\mathcal{T}(n,d)$ of $n$-vertex trees with diameter $d$. This contributes to the literature on $λ_2$-extremization over different graph families. We also revisit the notion of the spectral center of a tree and the proof of $λ_2$ maximization over trees.

math.CO↗

arXiv2024

Bollobás-Nikiforov Conjecture for graphs with not so many triangles

Bollobás and Nikiforov conjectured that for any graph $G \neq K_n$ with $m$ edges \[ λ_1^2+λ_2^2\le \bigg( 1-\frac{1}{ω(G)}\bigg)2m\] where $λ_1$ and $λ_2$ denote the two largest eigenvalues of the adjacency matrix $A(G)$, and $ω$ denotes the clique number of $G$. This conjecture was recently verified for triangle-free graphs by Lin, Ning and Wu and for regular graphs by Zhang. Elphick, Wocjan and Linz proposed a generalization of this conjecture. In this note, we verify this generalized conjecture for the family of graphs on $m$ edges, which contain at most $O(m^{1.5-\varepsilon})$ triangles for some $\varepsilon > 0$. In particular, we show that the conjecture is true for planar graphs, book-free graphs and cycle-free graphs.

math.CO↗

arXiv2023

Subdivision and Graph Eigenvalues

This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the $k$-th largest and $k$-th smallest eigenvalues for any fixed $k$. It is expected that after subdivision, most eigenvalues of the new graph will lie in the interval $[-2,2]$. We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.

math.CO↗

arXiv2022

First light preparations of the 4m ILMT

The 4m International Liquid Mirror Telescope (ILMT) is a zenith-pointing optical observing facility at ARIES Devasthal observatory (Uttarakhand, India). The first light preparatory activities of the ILMT were accomplished in April 2022 followed by on-sky tests that were carried out at the beginning of May 2022. This telescope will perform a multi-band optical (SDSS $g'$, $r'$ and $i'$) imaging of a narrow strip (~$22'$) of sky utilizing the time-delayed integration technique. Single-scan ILMT images have an integration time of 102 sec and consecutive-night images can be co-added to further improve the signal-to-noise ratio. An image subtraction technique will also be applied to the nightly recorded observations in order to detect transients, objects exhibiting variations in flux or position. Presently, the facility is in the commissioning phase and regular operation will commence in October 2022, after the monsoon. This paper presents a discussion of the main preparation activities before first light, along with preliminary results obtained.

astro-ph.IM↗

arXiv2020

Proper divisor graph of a positive integer

The proper divisor graph $Υ_n$ of a positive integer $n$ is the simple graph whose vertices are the proper divisors of $n$, and in which two distinct vertices $u, v$ are adjacent if and only if $n$ divides $uv$. The graph $Υ_n$ plays an important role in the study of the zero divisor graph of the ring $\mathbb{Z}_n$. In this paper, we study some graph theoretic properties of $Υ_n$ and determine the graph parameters such as clique number, chromatic number, chromatic index, independence number, matching number, domination number, vertex and edge covering numbers of $Υ_n$. We also determine the automorphism group of $Υ_n$.

math.CO↗

arXiv2020

Robotic Grasp Manipulation Using Evolutionary Computing and Deep Reinforcement Learning

Intelligent Object manipulation for grasping is a challenging problem for robots. Unlike robots, humans almost immediately know how to manipulate objects for grasping due to learning over the years. A grown woman can grasp objects more skilfully than a child because of learning skills developed over years, the absence of which in the present day robotic grasping compels it to perform well below the human object grasping benchmarks. In this paper we have taken up the challenge of developing learning based pose estimation by decomposing the problem into both position and orientation learning. More specifically, for grasp position estimation, we explore three different methods - a Genetic Algorithm (GA) based optimization method to minimize error between calculated image points and predicted end-effector (EE) position, a regression based method (RM) where collected data points of robot EE and image points have been regressed with a linear model, a PseudoInverse (PI) model which has been formulated in the form of a mapping matrix with robot EE position and image points for several observations. Further for grasp orientation learning, we develop a deep reinforcement learning (DRL) model which we name as Grasp Deep Q-Network (GDQN) and benchmarked our results with Modified VGG16 (MVGG16). Rigorous experimentations show that due to inherent capability of producing very high-quality solutions for optimization problems and search problems, GA based predictor performs much better than the other two models for position estimation. For orientation learning results indicate that off policy learning through GDQN outperforms MVGG16, since GDQN architecture is specially made suitable for the reinforcement learning. Based on our proposed architectures and algorithms, the robot is capable of grasping all rigid body objects having regular shapes.

cs.LG↗

arXiv2017

Development and characterization of Brassica juncea fruticulosa introgression lines exhibiting resistance to mustard aphid

Background: Mustard aphid is a major pest of Brassica oilseeds. No source for aphid resistance is presently available in Brassica juncea . A wild crucifer, Brassica fruticulosa is known to be resistant to mustard aphid. An artificially synthesized amphiploid, AD-4 (B. fruticulosa x B. rapa var. brown sarson) was developed for use as a bridge species to transfer fruticulosa resistance to B. juncea. Using the selfed backcross we could select a large number of lines with resistance to mustard aphid. This paper reports cytogenetic stability of introgression lines, molecular evidence for alien introgression and their reaction to mustard aphid infestation. Results: Majority of introgression lines had expected euploid chromosome number(2n= 36), showed normal meiosis and high pollen grain fertility. Well-distributed and transferable simple-sequence repeats (SSR) markers for all the 18 B. juncea chromosomes helped to characterize introgression events. Average proportions of recipient and donor genome in the substitution lines were 49.72 and 35.06%, respectively. Minimum alien parent genome presence (27.29%) was observed in the introgression line, Ad3K-280 . Introgressed genotypes also varied for their resistance responses to mustard aphid infestations under artificial release conditions for two continuous seasons. Some of the test genotypes showed consistent resistant reaction. Conclusions: B.juncea-fruticulosa introgression set may prove to be a very powerful breeding tool for aphid resistance related QTL/gene discovery and fine mapping of the desired genes/QTLs to facilitate marker assisted transfer of identified gene(s) for mustard aphid resistance in the background of commercial mustard genotypes.

q-bio.GN↗