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Interacting supernovae provide key insights into the mass-loss processes of massive stars and their circumstellar environments. By analyzing their photometric and spectroscopic properties, we can study the complex interactions between ejected material and circumstellar material (CSM). This paper highlights the diversity of interacting SNe, including Types IIn, Ibn, and Icn, and explores the challenges in understanding progenitor systems, CSM structures, and late-time evolution. Advances in high-cadence observations and modeling are crucial for improving our knowledge of these stellar explosions., Comment: 4 pages, 4 figures, published in the International Astronomical Union Proceedings Series for the IAU GA 2024 (Astronomy in Focus, Focus Meeting 4 "Bridging the final stages of massive stars to supernovae and transients)"

In \href{https://link.aps.org/doi/10.1103/PhysRevD.92.103004}{Phys. Rev. D 92 (2015) 103004}, simple analytical solutions of the Friedman equations were obtained for a universe having stiff matter component in the early universe together with a dark matter, and a dark energy component. In this analysis, the universe is considered to be made of a dark fluid which behaves as a stiff matter in the early phase of the universe (when the internal energy dominates). It is also more logical to consider quantum gravitational effects in the early phase of the cosmological evolution. In this analysis, following \href{https://link.aps.org/doi/10.1103/PhysRevD.65.043508}{Phys. Rev. D 65 (2002) 043508}, we consider renormalization group improved modified Friedmann equations where the Newton's gravitational constant ($G$) and the cosmological constant ($\Lambda$) flows with the momentum scale $k$ of the universe. It is observed that for a universe undergoing a stiff matter era, radiation era, and matter era, inflation is absent in the early time regime of the universe when the flow of the Newton's gravitational constant and cosmological constant is under consideration. Using the identification of the momentum scale with the scale factor of the universe, we then explore the era $t>t_{\text{Pl}}$ which indicates a primarily matter dominated era with accelerated expansion due to the presence of dark energy. Finally, considering the total equation of state as a combination of linear equation of state along with a polytropic equation of state, we observe that after the Planck-time the universe can undergo an inflationary phase and we find out that the inflation is enhanced by quantum gravitational effects arising due to the consideration of renormalization group approach to quantum gravity., Comment: 17 pages LATEX, comments are welcome. OTM

We investigate relativistic effects on the performance of a quantum battery in an open quantum framework. We consider an Unruh-DeWitt detector driven by a coherent classical pulse as a quantum battery that is interacting with a massless scalar field through a quadratic coupling. The battery follows a trajectory composed of uniform acceleration along one direction, combined with constant four-velocity components in the orthogonal plane to the acceleration. Accelerated motion degrades the performance of the quantum battery rapidly in the absence of the orthogonal velocity component. We show that the quadratic scalar field coupling enhances coherence and stability in the presence of orthogonal velocity. We observe that decoherence is mitigated significantly, resulting in remarkable improvement in the battery capacity and efficiency compared to the case of the usual linear field coupling. This opens up the possibility of nonlinear environmental coupling enabling stored energy to be retained over longer durations, leading to more efficient operation of quantum devices., Comment: 15 pages LaTeX; Comments are welcome

An undeniable signature scheme is type of digital signature where the signer retains control over the signature's verifiability. Therefore with the approval of the signer, only an authenticated verifier can verify the signature. In this work, we develop a module lattice-based post-quantum undeniable signature system. Our method is based on the GPV framework utilizing module lattices, with the security assured by the hardness of the SIS and LWE problems. We have thoroughly proved all the desired securities for the proposed scheme. Finally, we have implemented our protocol for different sets of parameters. The purpose of opting a module variant rather than a ring variant is to provide greater flexibility in selecting parameters.

We propose UnCLe, a standardized benchmark for Unsupervised Continual Learning of a multimodal depth estimation task: Depth completion aims to infer a dense depth map from a pair of synchronized RGB image and sparse depth map. We benchmark depth completion models under the practical scenario of unsupervised learning over continuous streams of data. Existing methods are typically trained on a static, or stationary, dataset. However, when adapting to novel non-stationary distributions, they "catastrophically forget" previously learned information. UnCLe simulates these non-stationary distributions by adapting depth completion models to sequences of datasets containing diverse scenes captured from distinct domains using different visual and range sensors. We adopt representative methods from continual learning paradigms and translate them to enable unsupervised continual learning of depth completion. We benchmark these models for indoor and outdoor and investigate the degree of catastrophic forgetting through standard quantitative metrics. Furthermore, we introduce model inversion quality as an additional measure of forgetting. We find that unsupervised continual learning of depth completion is an open problem, and we invite researchers to leverage UnCLe as a development platform., Comment: Preprint

Quantum computing presents a double-edged sword: while it has the potential to revolutionize fields such as artificial intelligence, optimization, healthcare, and so on, it simultaneously poses a threat to current cryptographic systems, such as public-key encryption. To address this threat, post-quantum cryptography (PQC) has been identified as the solution to secure existing software systems, promoting a national initiative to prepare the next generation with the necessary knowledge and skills. However, PQC is an emerging interdisciplinary topic, presenting significant challenges for educators and learners. This research proposes a novel active learning approach and assesses the best practices for teaching PQC to undergraduate and graduate students in the discipline of information systems. Our contributions are two-fold. First, we compare two instructional methods: 1) traditional faculty-led lectures and 2) student-led seminars, both integrated with active learning techniques such as hands-on coding exercises and Kahoot games. The effectiveness of these methods is evaluated through student assessments and surveys. Second, we have published our lecture video, slides, and findings so that other researchers and educators can reuse the courseware and materials to develop their own PQC learning modules. We employ statistical analysis (e.g., t-test and chi-square test) to compare the learning outcomes and students' feedback between the two learning methods in each course. Our findings suggest that student-led seminars significantly enhance learning outcomes, particularly for graduate students, where a notable improvement in comprehension and engagement is observed. Moving forward, we aim to scale these modules to diverse educational contexts and explore additional active learning and experiential learning strategies for teaching complex concepts of quantum information science., Comment: 23 pages, 8 figures

Given two nonincreasing $n$-tuples of real numbers $\lambda_n$, $\mu_n$, the Horn problem asks for a description of all nonincreasing $n$-tuples of real numbers $\nu_n$ such that there exist Hermitian matrices $X_n$, $Y_n$ and $Z_n$ respectively with these spectra such that $X_n + Y_n = Z_n$. There is also a randomized version of this problem where $X_n$ and $Y_n$ are sampled uniformly at random from orbits of Hermitian matrices arising from the conjugacy action by elements of the unitary group. One then asks for a description of the probability measure of the spectrum of the sum $Z_n$. Both the original Horn problem and its randomized version have solutions using the hives introduced by Knutson and Tao. In an asymptotic sense, as $n \rightarrow \infty$, large deviations for the randomized Horn problem were given by Narayanan and Sheffield in terms of the surface tension of hives. In this paper, we provide upper and lower bounds on this surface tension function. We also obtain a closed-form expression for the total entropy of a surface tension minimizing continuum hive with boundary conditions arising from GUE eigenspectra. Finally, we give several empirical results for random hives and lozenge tilings arising from an application of the octahedron recurrence for large $n$ and a numerical approximation of the surface tension function.

The effect of noise induced by gravitons on a Bose-Einstein condensate has been explored in (Phys. Rev. D 110 (2024) 026014; https://link.aps.org/doi/10.1103/PhysRevD.110.026014). In the previous paper, we investigated the effects of graviton while detecting a gravitational wave using a Bose-Einstein condensate. In this work we shall explicitly calculate the decoherence due to the noise of gravitons between two momentum states of the Bose-Einstein condensate. This decoherence happens due to Bremsstrahlung from the Bose-Einstein condensates due to the effect of the noise induced by gravitons. It is also observed that the two states become entangled because of the existence of a surrounding graviton field which degrades over time via means of this gravitational Bremsstrahlung. Using this property of the Bose-Einstein condensate in a quantum gravity background, we propose an experimental test via the use of atom lasers (generated from the condensate) which would, in principle, help to detect gravitons in future generations of very advanced ultra-cold temperature experiments., Comment: 18 pages LATEX. Comments are welcome. Om Thakur Ma

We present photometric and spectroscopic observations of SN2020xga and SN2022xgc, two hydrogen-poor superluminous supernovae (SLSNe-I) at $z = 0.4296$ and $z = 0.3103$ respectively, that show an additional set of broad Mg II absorption lines, blueshifted by a few thousand km s$^{-1}$ with respect to the host galaxy absorption system. Previous work interpreted this as due to resonance line scattering of the SLSN continuum by rapidly expanding CSM expelled shortly before the explosion. The peak rest-frame $g$-band magnitude of SN2020xga is $-22.30 \pm 0.04$ mag and of SN2022xgc is $-21.97 \pm 0.05$ mag, placing them among the brightest SLSNe-I. We use high-quality spectra from ultraviolet to near-infrared wavelengths to model the Mg II line profiles and infer the properties of the CSM shells. We find that the CSM shell of SN2020xga resides at $\sim 1.3 \times 10^{16} \rm cm$ moving with a maximum velocity of $4275~\rm km~s^{-1}$, and the shell of SN2022xgc is located at $\sim 0.8 \times 10^{16} \rm cm$ reaching up to $4400~\rm km~s^{-1}$. These shells were expelled $\sim 11$ and $\sim 5$ months before explosion for SN2020xga and SN2022xgc respectively, possibly as a result of Luminous Blue Variable-like eruptions or pulsational pair instability (PPI) mass loss. We also analyze optical photometric data and model the light curves considering powering from the magnetar spin-down mechanism. The results support very energetic magnetars, approaching the mass-shedding limit, powering these SNe with ejecta masses of $\sim 7-9 \rm~M_\odot$. The ejecta masses inferred from the magnetar modeling are not consistent with the PPI scenario pointing towards stars $> 50~\rm M_\odot$ He-core, hence alternative scenarios such as fallback accretion are discussed., Comment: 25 pages text, 8 pages appendix, 21 figures. Submitted to A&A

Coherent control of single photon sources is a key requirement for the advancement of photonic quantum technologies. Among them, nanowire-based quantum dot sources are popular due to their potential for on-chip hybrid integration. Here we demonstrate on-demand single-photon generation ($g^{(2)}(0)(X^{*}) =0.078$ and $g^{(2)}(0)(X)= 0.03$) from resonantly excited InAsP/InP nanowire quantum dots and observe Rabi oscillations in the dot emission, indicating successful coherent manipulation of the excitonic states in the nanowire. We also measure a low emission time jitter for resonant excitation as compared to above-band excitation. This work addresses the long-standing challenge of resonantly exciting nanowire-quantum dots. It paves the way for hybrid quantum photonic integration, enabling spin-photon entanglement and matter memories on-chip.

The global surge in the cases of gastric cancer has prompted an investigation into the potential of gut microbiota as a predictive marker for the disease. The alterations in gut diversity are suspected to be associated with an elevated risk of gastric cancer. This paper delves into finding the correlation between gut microbiota and gastric cancer, focusing on patients who have undergone total and subtotal gastrectomy. Utilizing data mining and statistical learning methods, an analysis was conducted on 16S-RNA sequenced genes obtained from 96 participants with the aim of identifying specific genera of gut microbiota associated with gastric cancer. The study reveals several prominent bacterial genera that could potentially serve as biomarkers assessing the risk of gastric cancer. These findings offer a pathway for early risk assessment and precautionary measures in the diagnosis of gastric cancer. The intricate mechanisms through which these gut microbiotas influence gastric cancer progression warrant further investigation. This research significantly aims to contribute to the growing understanding of the gut-cancer axis and its implications in disease prediction and prevention.

We investigate the thermodynamics of a Schwarzschild black hole, surrounded by the quintessence energy-matter in the linear and quadratic generalized uncertainty principle framework. Considering the variance in the position to be of the order of the event horizon radius and equating the variance in the momentum to the Hawking temperature of the black hole, we substitute these variances in the deformed algebra. From there we obtained the generalized uncertainty principle-modified black hole temperature and eventually the specific heat of the black hole. Then we calculate the critical as well as the remnant mass and obtain the entropy relation. We observe that the entropy relation includes the usual leading order ``\textit{area divided by four}" term, sub-leading logarithmic term, and higher order inverse of the area corrections. Finally, calculating the energy output as a function of time, we obtain the evaporation time of the black hole. The results show the dependence of the quintessence parameter on the thermodynamic quantities in the framework of linear and quadratic generalized uncertainty principle., Comment: 17 pages LATEX; Comments are welcome

Recently, the construction of cryptographic schemes based on hard lattice problems has gained immense popularity. Apart from being quantum resistant, lattice-based cryptography allows a wide range of variations in the underlying hard problem. As cryptographic schemes can work in different environments under different operational constraints such as memory footprint, silicon area, efficiency, power requirement, etc., such variations in the underlying hard problem are very useful for designers to construct different cryptographic schemes. In this work, we explore various design choices of lattice-based cryptography and their impact on performance in the real world. In particular, we propose a suite of key-encapsulation mechanisms based on the learning with rounding problem with a focus on improving different performance aspects of lattice-based cryptography. Our suite consists of three schemes. Our first scheme is Florete, which is designed for efficiency. The second scheme is Espada, which is aimed at improving parallelization, flexibility, and memory footprint. The last scheme is Sable, which can be considered an improved version in terms of key sizes and parameters of the Saber key-encapsulation mechanism, one of the finalists in the National Institute of Standards and Technology's post-quantum standardization procedure. In this work, we have described our design rationale behind each scheme. Further, to demonstrate the justification of our design decisions, we have provided software and hardware implementations. Our results show Florete is faster than most state-of-the-art KEMs on software and hardware platforms. The scheme Espada requires less memory and area than the implementation of most state-of-the-art schemes. The implementations of Sable maintain a trade-off between Florete and Espada regarding performance and memory requirements on the hardware and software platform.

Let $C$ be an irreducible smooth complex projective curve of genus $g$, with $g_C \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$, with $r\geqslant 2$. Let $\mc Q:=\mc Q(E,\,d)$ be the Quot Scheme parameterizing torsion quotients of $E$ of degree $d$. We explicitly describe all deformations of $\mc Q$., Comment: Final version; Revista Matem\'atica Complutense (to appear)

We present the long-term photometric and spectroscopic analysis of a transitioning SN~IIn/Ibn from $-$10.8 d to 150.7 d post $V$-band maximum. SN~2021foa shows prominent He {\sc i} lines comparable in strength to the H$\alpha$ line around peak, placing SN~2021foa between the SN~IIn and SN~Ibn populations. The spectral comparison shows that it resembles the SN~IIn population at pre-maximum, becomes intermediate between SNe~IIn/Ibn and at post-maximum matches with SN~IIn 1996al. The photometric evolution shows a precursor at $-$50 d and a light curve shoulder around 17d. The peak luminosity and color evolution of SN 2021foa are consistent with most SNe~IIn and Ibn in our comparison sample. SN~2021foa shows the unique case of a SN~IIn where the narrow P-Cygni in H$\alpha$ appear at later stages. The H$\alpha$ profile consists of a narrow (500 -- 1200 km s$^{-1}$) component, intermediate width (3000 -- 8000 km s$^{-1}$) and broad component in absorption. Temporal evolution of the H$\alpha$ profile favours a disk-like CSM geometry. Hydrodynamical modelling of the lightcurve well reproduces a two-component CSM structure with different densities ($\rho$ $\propto$ r$^{-2}$ -- $\rho$ $\propto$ r$^{-5}$), mass-loss rates (10$^{-3}$ -- 10$^{-1}$ M$_{\odot}$ yr$^{-1}$) assuming a wind velocity of 1000 km s$^{-1}$ and having a CSM mass of 0.18 M$_{\odot}$. The overall evolution indicates that SN~2021foa most likely originated from a LBV star transitioning to a WR star with the mass-loss rate increasing in the period from 5 to 0.5 years before the explosion or it could be due to a binary interaction., Comment: Submitted to MNRAS; 20 pages, 16 figures, 4 tables

The cores of stars are the cosmic furnaces where light elements are fused into heavier nuclei. The fusion of hydrogen to helium initially powers all stars. The ashes of the fusion reactions are then predicted to serve as fuel in a series of stages, eventually transforming massive stars into a structure of concentric shells. These are composed of natal hydrogen on the outside, and consecutively heavier compositions inside, predicted to be dominated by helium, carbon/oxygen, oxygen/neon/magnesium, and oxygen/silicon/sulphur. Silicon and sulphur are fused into inert iron, leading to the collapse of the core and either a supernova explosion or the direct formation of a black hole. Stripped stars, where the outer hydrogen layer has been removed and the internal He-rich layer (in Wolf-Rayet WN stars) or even the C/O layer below it (in Wolf-Rayet WC/WO stars) are exposed, provide evidence for this shell structure, and the cosmic element production mechanism it reflects. The types of supernova explosions that arise from stripped stars embedded in shells of circumstellar material (most notably Type Ibn supernovae from stars with outer He layers, and Type Icn supernovae from stars with outer C/O layers) confirm this scenario. However, direct evidence for the most interior shells, which are responsible for the production of elements heavier than oxygen, is lacking. Here, we report the discovery of the first-of-its-kind supernova arising from a star peculiarly stripped all the way to the silicon and sulphur-rich internal layer. Whereas the concentric shell structure of massive stars is not under debate, it is the first time that such a thick, massive silicon and sulphur-rich shell, expelled by the progenitor shortly before the SN explosion, has been directly revealed., Comment: 48 pages, 12 figures and 10 tables. Submitted to a high-impact journal. The reduced spectra and photometry will be made available via the journal webpage and the WISeREP archive after the acceptance of the paper

In this paper we study the Minkowskian product Finsler manifolds. More precisely, we prove that if the Minkowskian product Finsler manifold is Einstein then either the product manifold is Ricci flat or both the quotient manifolds are Einstein with same scalar functions.

Hydrogen-rich superluminous supernovae (SLSNe II) are rare. The exact mechanism producing their extreme light curve peaks is not understood. Analysis of single events and small samples suggest that CSM interaction is the main responsible for their features. However, other mechanisms can not be discarded. Large sample analysis can provide clarification. We aim to characterize the light curves of a sample of 107 SLSNe II to provide valuable information that can be used to validate theoretical models. We analyze the gri light curves of SLSNe II obtained through ZTF. We study peak absolute magnitudes and characteristic timescales. When possible we compute g-r colors, pseudo-bolometric light curves, and estimate lower limits for their total radiated energy. We also study the luminosity distribution of our sample and estimate the percentage of them that would be observable by the LSST. Finally, we compare our sample to other H-rich SNe and to H-poor SLSNe I. SLSNe II are heterogeneous. Their median peak absolute magnitude is -20.3 mag in optical bands. Their rise can take from two weeks to over three months, and their decline from twenty days to over a year. We found no significant correlations between peak magnitude and timescales. SLSNe II tend to show fainter peaks, longer declines and redder colors than SLSNe I. We present the largest sample of SLSNe II light curves to date, comprising of 107 events. Their diversity could be explained by considering different CSM morphologies. Although, theoretical analysis is needed to explore alternative scenarios. Other luminous transients, such as Active Galactic Nuclei, Tidal Disruption Events or SNe Ia-CSM, can easily become contaminants. Thus, good multi-wavelength light curve coverage becomes paramount. LSST could miss 30 percent of the ZTF events in the its footprint in gri bands. Redder bands become important to construct complete samples., Comment: 35 pages. 27 figures. 9 tables

We study a magnitude-limited sample of 36 Broad-lined Type Ic Supernovae (SNe Ic-BL) from the Zwicky Transient Facility Bright Transient Survey (detected between March 2018 and August 2021), which is the largest systematic study of SNe Ic-BL done in literature thus far. We present the light curves (LCs) for each of the SNe, and analyze the shape of the LCs to derive empirical parameters, along with the explosion epochs for every event. The sample has an average absolute peak magnitude in the r band of $M_r^{max}$ = -18.51 $\pm$ 0.15 mag. Using spectra obtained around peak light, we compute expansion velocities from the Fe II 5169 Angstrom line for each event with high enough signal-to-noise ratio spectra, and find an average value of $v_{ph}$ = 16,100 $\pm$ 1,100 km $s^{-1}$. We also compute bolometric LCs, study the blackbody temperature and radii evolution over time, and derive the explosion properties of the SNe. The explosion properties of the sample have average values of $M_{Ni}$ = $0.37_{-0.06}^{+0.08}$ solar masses, $M_{ej}$ = $2.45_{-0.41}^{+0.47}$ solar masses, and $E_K$= $4.02_{-1.00}^{+1.37} \times 10^{51}$ erg. Thirteen events have radio observations from the Very Large Array, with 8 detections and 5 non-detections. We find that the populations that have radio detections and radio non-detections are indistinct from one another with respect to their optically-inferred explosion properties, and there are no statistically significant correlations present between the events' radio luminosities and optically-inferred explosion properties. This provides evidence that the explosion properties derived from optical data alone cannot give inferences about the radio properties of SNe Ic-BL, and likely their relativistic jet formation mechanisms., Comment: 52 pages, 34 Figures, 8 Tables; Accepted to ApJ

We present optical and near-infrared observations of two Type Ibn supernovae (SNe), SN 2018jmt and SN 2019cj. Their light curves have rise times of about 10 days, reaching an absolute peak magnitude of $M_g$(SN 2018jmt) = $-$19.07 $\pm$ 0.37 and $M_V$(SN 2019cj) = $-$18.94 $\pm$ 0.19 mag, respectively. The early-time spectra of SN 2018jmt are dominated by a blue continuum, accompanied by narrow (600$-$1000 km~s$^{-1}$) He I lines with P-Cygni profile. At later epochs, the spectra become more similar to those of the prototypical SN Ibn 2006jc. At early phases, the spectra of SN 2019cj show flash ionisation emission lines of C III, N III and He II superposed on a blue continuum. These features disappear after a few days, and then the spectra of SN 2019cj evolve similarly to those of SN 2018jmt. The spectra indicate that the two SNe exploded within a He-rich circumstellar medium (CSM) lost by the progenitors a short time before the explosion. We model the light curves of the two SNe Ibn to constrain the progenitor and the explosion parameters. The ejecta masses are consistent with either that expected for a canonical SN Ib ($\sim$ 2 M$_{\odot}$) or those from a massive WR star ($>$ $\sim$ 4 M$_{\odot}$), with the kinetic energy on the order of $10^{51}$ erg. The lower limit on the ejecta mass ($>$ $\sim$ 2 M$_{\odot}$) argues against a scenario involving a relatively low-mass progenitor (e.g., $M_{ZAMS}$ $\sim$ 10 M$_{\odot}$). We set a conservative upper limit of $\sim$0.1 M$_{\odot}$ for the $^{56}$Ni masses in both SNe. From the light curve modelling, we determine a two-zone CSM distribution, with an inner, flat CSM component, and an outer CSM with a steeper density profile. The physical properties of SN 2018jmt and SN 2019cj are consistent with those expected from the core collapse of relatively massive, stripped-envelope (SE) stars., Comment: 28 pages, 19 figures, Accepted for publication in Astronomy & Astrophysics

We present ultraviolet, optical and near-infrared photometric and optical spectroscopic observations of the luminous, fast blue optical transient (LFBOT), CSS161010:045834-081803 (CSS161010). The transient was found in a low-redshift (z=0.033) dwarf galaxy. The light curves of CSS161010 are characterized by an extremely fast evolution and blue colours. The V-band light curve shows that CSS161010 reaches an absolute peak of M$_{V}^{max}=-20.66\pm0.06$ mag in 3.8 days from the start of the outburst. After maximum, CSS161010 follows a power-law decline $\propto t^{-2.8\pm0.1}$ in all optical bands. These photometric properties are comparable to those of well-observed LFBOTs such as AT 2018cow, AT 2020mrf and AT 2020xnd. However, unlike these objects, the spectra of CSS161010 show a remarkable transformation from a blue and featureless continuum to spectra dominated by very broad, entirely blueshifted hydrogen emission lines of velocities of up to 10% of the speed of light. The persistent blueshifted emission and the lack of any emission at the rest wavelength of CSS161010 are unique features not seen in any transient before CSS161010. The combined observational properties of CSS161010 and its M$_{*}\sim10^{8}$ M$_\odot$ dwarf galaxy host favour the tidal disruption of a star by an intermediate-mass black hole as its origin., Comment: 29 pages (including the appendix); 8 figures in the main text, 4 figures and 8 tables in the appendix. Accepted for publication in ApJ

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in $3+1$-dimensions. This geometry is the gravity dual to a class of $2+1$-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent ($z$) present in the Lifshitz field theory., Comment: v1: 51 pages LaTex, multiple figures, v2: matches with the published version

Based on the Schmidt decomposition new convenient thumbrules are obtained to test entanglement of wavefunctions for bipartite qubit and qutrit systems. For the qubit system there is an underlying SU(2) algebra , while the same for a qutrit system is SU(3)., Comment: 8 pages, latex, research article

The Cosmic Microwave Background (CMB) observations results reported by {\it Planck} satellite suggest a plateau characteristic in the flat potential of the inflaton field is favored to drive the Universe's early acceleration. On that note, Power Law Plateau (PLP) potential has gained a lot of attention. In this study, we demonstrate that implementing this inflationary model in an Einstein-Gauss-Bonnet(EGB) gravity background makes the model compatible with observations while avoiding late-stage thermal inflation which is otherwise unavoidable in a standard scenario. More importantly, we have taken the PLP model as a case study to check the new slow-roll approximations method proposed in \cite{Pozdeeva:2024ihc}. Then we take one step further to check the consequence of generalized reheating in this scenario. Thus opening a new promising window to study inflationary dynamics in EGB gravity., Comment: 23 pages, 4 figures

In loop quantum cosmology, the slow-roll inflation is generic, and when the kinetic energy of the scalar field dominates at the bounce, the evolution of the Friedmann-Lema\^itre-Robertson-Walker universe will go through three distinguishable epochs, bouncing, transition, and finally slow-roll inflation, before the reheating commences. The bouncing dynamics are insensitive of the potential and initial conditions, so that the expansion factor and the scalar field can be described uniquely by a universal solution during this epoch. After about $10^5$ Planck time, the epoch of transition starts and the universe rapidly turns over from the kinetic energy dominated state to the potential energy dominated one, whereby the slow-roll inflationary phase begins. In this paper, we consider the power law plateau potential and study the pre-inflationary cosmology for different sets of initial conditions, so that during the slow-roll inflation epoch enough e-folds will be produced. Considering the generalized reheating and comparing with the recent Planck 2018 data, we are able to constrain the total number of e-folds ($N_T$) from the bounce till today to be consistent with the current observable universe. Depending on the matter driving the reheating (subject to the different dominant equations of states), we report the observationally allowed $N_T$ and reheating temperature and find in particular $N_T \simeq 127$, which is significantly different from the one $N_T \gtrsim 141$ obtained previously without considering the reheating phase., Comment: 13 pages, 6 figures

We investigate the spectroscopic characteristics of Intermediate Luminosity Red Transients (ILRTs), a class of elusive objects with peak luminosity between that of classical novae and standard supernovae. We present the extensive optical and near-infrared (NIR) spectroscopic monitoring of four ILRTs, namely NGC 300 2008OT-1, AT 2019abn, AT 2019ahd and AT 2019udc. First we focus on the evolution of the most prominent spectral features observed in the low resolution spectra, then we discuss more in detail the high resolution spectrum collected for NGC 300 2008OT-1 with the Very Large Telescope equipped with UVES. Finally we analyse late time spectra of NGC 300 2008OT-1 and AT 2019ahd through comparisons with both synthetic and observed spectra. Balmer and Ca lines dominate the optical spectra, revealing the presence of slowly moving circumstellar medium (CSM) around the objects. The line luminosity of H$\alpha$, H$\beta$ and Ca II NIR triplet presents a double peaked evolution with time, possibly indicative of interaction between fast ejecta and the slow CSM. The high resolution spectrum of NGC 300 2008OT-1 reveals a complex circumstellar environment, with the transient being surrounded by a slow ($\sim$30 km s$^{-1}$) progenitor wind. At late epochs, optical spectra of NGC 300 2008OT-1 and AT 2019ahd show broad ($\sim$2500 km s$^{-1}$) emission features at $\sim$6170 A and $\sim$7000 A which are unprecedented for ILRTs. We find that these lines originate most likely from the blending of several narrow lines, possibly of iron-peak elements., Comment: 28 pages, 19 figures. Submitted to A&A

We investigate the photometric characteristics of a sample of Intermediate Luminosity Red Transients (ILRTs), a class of elusive objects with peak luminosity between that of classical novae and standard supernovae. We present the multi-wavelength photometric follow-up of four ILRTs, namely NGC 300 2008OT-1, AT 2019abn, AT 2019ahd and AT 2019udc. Through the analysis and modelling of their spectral energy distribution and bolometric light curves we infer the physical parameters associated with these transients. All four objects display a single peaked light curve which ends in a linear decline in magnitudes at late phases. A flux excess with respect to a single black body emission is detected in the infrared domain for three objects in our sample, a few months after maximum. This feature, commonly found in ILRTs, is interpreted as a sign of dust formation. Mid infrared monitoring of NGC 300 2008OT-1 761 days after maximum allows us to infer the presence of $\sim$10$^{-3}$-10$^{-5}$ M$_{\odot}$ of dust, depending on the chemical composition and the grain size adopted. The late time decline of the bolometric light curves of the considered ILRTs is shallower than expected for $^{56}$Ni decay, hence requiring an additional powering mechanism. James Webb Space Telescope observations of AT 2019abn prove that the object has faded below its progenitor luminosity in the mid-infrared domain, five years after its peak. Together with the disappearance of NGC 300 2008OT-1 in Spitzer images seven years after its discovery, this supports the terminal explosion scenario for ILRTs. With a simple semi-analytical model we try to reproduce the observed bolometric light curves in the context of few M$_{\odot}$ of material ejected at few 10$^{3}$ km s$^{-1}$ and enshrouded in an optically thick circumstellar medium., Comment: 21 pages, 15 figures plus 20 additional pages of data in appendix. Submitted to A&A

In this paper we consider a single particle, apin-momentum entangled state and measure the effect of relativistic boost on quantum coherence. The effect of the relativistic boost on single-particle generalized Gaussian wave packets is studied. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence, it is shown that in general the coherence decays with the increase in momentum of the state, as well as the boost applied to it. A more prominent loss of coherence due to relativistic boost is observed for a single particle electron than that of a neutron. The analysis is carried out with generalized Gaussian wave packet of the form $\sim p^n \exp(-\frac{p^2}{\sigma^2})$. We also obtain a bound on the unknown parameter $n$ appearing in the wave packet. It is found to have a dependence on the mass of the particle and the width of the Gaussian wave packet., Comment: 10 pages LATEX. Comments are welcome

We present the results of a nation-wide baseline survey, conducted by us, for the status of Astronomy education among secondary school students in India. The survey was administered in 10 different languages to over 2000 students from diverse backgrounds, and it explored multiple facets of their perspectives on astronomy. The topics included students' views on the incorporation of astronomy in curricula, their grasp of fundamental astronomical concepts, access to educational resources, cultural connections to astronomy, and their levels of interest and aspirations in the subject. We find notable deficiencies in students' knowledge of basic astronomical principles, with only a minority demonstrating proficiency in key areas such as celestial sizes, distances, and lunar phases. Furthermore, access to resources such as telescopes and planetariums remain limited across the country. Despite these challenges, a significant majority of students expressed a keen interest in astronomy. We further analyze the data along socioeconomic and gender lines. Particularly striking were the socioeconomic disparities, with students from resource-poor backgrounds often having lower levels of access and proficiency. Some differences were observed between genders, although not very pronounced. The insights gleaned from this study hold valuable implications for the development of a more robust astronomy curriculum and the design of effective teacher training programs in the future., Comment: 15 pages, 19 figures

Recent advancements in offline Reinforcement Learning (Offline RL) have led to an increased focus on methods based on conservative policy updates to address the Out-of-Distribution (OOD) issue. These methods typically involve adding behavior regularization or modifying the critic learning objective, focusing primarily on states or actions with substantial dataset support. However, we challenge this prevailing notion by asserting that the absence of an action or state from a dataset does not necessarily imply its suboptimality. In this paper, we propose a novel approach to tackle the OOD problem. We introduce an offline RL teacher-student framework, complemented by a policy similarity measure. This framework enables the student policy to gain insights not only from the offline RL dataset but also from the knowledge transferred by a teacher policy. The teacher policy is trained using another dataset consisting of state-action pairs, which can be viewed as practical domain knowledge acquired without direct interaction with the environment. We believe this additional knowledge is key to effectively solving the OOD issue. This research represents a significant advancement in integrating a teacher-student network into the actor-critic framework, opening new avenues for studies on knowledge transfer in offline RL and effectively addressing the OOD challenge.

With the ability to learn from static datasets, Offline Reinforcement Learning (RL) emerges as a compelling avenue for real-world applications. However, state-of-the-art offline RL algorithms perform sub-optimally when confronted with limited data confined to specific regions within the state space. The performance degradation is attributed to the inability of offline RL algorithms to learn appropriate actions for rare or unseen observations. This paper proposes a novel domain knowledge-based regularization technique and adaptively refines the initial domain knowledge to considerably boost performance in limited data with partially omitted states. The key insight is that the regularization term mitigates erroneous actions for sparse samples and unobserved states covered by domain knowledge. Empirical evaluations on standard discrete environment datasets demonstrate a substantial average performance increase of at least 27% compared to existing offline RL algorithms operating on limited data.

We give a combinatorial classification of torus equivariant vector bundles on a (normal) projective T-variety of complexity-one. This extends the classification of equivariant line bundles on complexity-one T-varieties by Petersen-S\"uss on one hand, and Klyachko's classification of equivariant vector bundles on toric varieties on the other hand. A main ingredient in our classification is the classification of torus equivariant vector bundles on toric schemes over a DVR in terms of piecewise affine maps to the (extended) Bruhat-Tits building of the general linear group., Comment: 29 pages, 1 figure. arXiv admin note: text overlap with arXiv:2402.18712

This paper investigates the dynamics of current and efficiency in a bosonic system consisting of a central system interacting with two reservoirs at different temperatures. We derive a master equation describing the time evolution of the density matrix of the system, accounting for the interactions and energy transfer between the components. We quantify the current, representing the flow of bosons through the system and analyse its dependence on the system's parameters and temperatures of the thermal reservoirs. In the steady state regime, we derived an expression for the efficiency of the energy transfer process. Our analysis show that quantum effects, such as the dependence on temperature and the quantum correction factor, can significantly impact energy transfer efficiency. In particular, we observe that at high temperatures, the efficiency of the quantum system is greater than the Carnot efficiency. The insights gained from this analysis may have implications in various fields, including quantum computing and energy harvesting, where optimising energy utilisation is crucial.

We present a detailed investigation of photometric, spectroscopic, and polarimetric observations of the Type II SN 2023ixf. Earlier studies have provided compelling evidence for a delayed shock breakout from a confined dense circumstellar matter (CSM) enveloping the progenitor star. The temporal evolution of polarization in SN~2023ixf revealed three distinct peaks in polarization evolution at 1.4 d, 6.4 d, and 79.2 d, indicating an asymmetric dense CSM, an aspherical shock front and clumpiness in the low-density extended CSM, and an aspherical inner ejecta/He-core. SN 2023ixf displayed two dominant axes, one along the CSM-outer ejecta and the other along the inner ejecta/He-core, showcasing the independent origin of asymmetry in the early and late evolution. The argument for an aspherical shock front is further strengthened by the presence of a high-velocity broad absorption feature in the blue wing of the Balmer features in addition to the P-Cygni absorption post 16 d. Hydrodynamical light curve modeling indicated a progenitor of 10 solar mass with a radius of 470 solar radii and explosion energy of 2e51 erg, along with 0.06 solar mass of 56-Ni, though these properties are not unique due to modeling degeneracies. The modeling also indicated a two-zone CSM: a confined dense CSM extending up to 5e14 cm, with a mass-loss rate of 1e-2 solar mass per year, and an extended CSM spanning from 5e14 cm to at least 1e16cm with a mass-loss rate of 1e-4 solar mass per year, both assuming a wind-velocity of 10 km/s. The early nebular phase observations display an axisymmetric line profile of [OI], red-ward attenuation of the emission of Halpha post 125 days, and flattening in the Ks-band, marking the onset of dust formation., Comment: 32 pages, 15 figures, 1 Table, Accepted in the Astrophysical Journal

In this work, we consider a general gravitational wave detector of gravitational wave interacting with an incoming gravitational wave carrying plus polarization only placed inside a harmonic trap. This model can be well acquainted with the description of a resonant detector of gravitational wave as well. The well known detector-gravitational wave interaction scenario uses the method of a semi classical approach where the detector is treated quantum mechanically but the gravitational wave is considered at a classical level. In our analysis, we use a discrete mode decomposition of the gravitational wave perturbation which results in a Hamiltonian involving the position and momentum operators corresponding to the gravitational wave and the harmonic oscillator. We have then calculated the transition probability for the harmonic oscillator-gravitational wave tensor product state for going from an initial state to some unknown final state. Using the energy flux relation of the gravitational waves, we observe that if we consider the total energy as a combination of the number of gravitons in the initial state of the detector then the transition probability for the resonant absorption case scenario takes the analytical form which is exactly similar to the semi-classical absorption case. In case of the emission scenario, we observe a spontaneous emission of a single graviton which was completely absent in the semi-classical analouge of this model. This therefore gives a direct signature of linearized quantum gravity., Comment: 8 pages LATEX; Comments are welcome. Om Thakur Ma

We present high-cadence photometric and spectroscopic observations of supernova (SN) 2024ggi, a Type II SN with flash spectroscopy features which exploded in the nearby galaxy NGC 3621 at $\sim$7 Mpc. The light-curve evolution over the first 30 hours can be fit by two power law indices with a break after 22 hours, rising from $M_V \approx -12.95$ mag at +0.66 days to $M_V \approx -17.91$ mag after 7 days. In addition, the densely sampled color curve shows a strong blueward evolution over the first few days and then behaves as a normal SN II with a redward evolution as the ejecta cool. Such deviations could be due to interaction with circumstellar material (CSM). Early high- and low-resolution spectra clearly show high-ionization flash features from the first spectrum to +3.42 days after the explosion. From the high-resolution spectra, we calculate the CSM velocity to be 37 $\pm~4~\mathrm{km\,s^{-1}} $. We also see the line strength evolve rapidly from 1.22 to 1.49 days in the earliest high-resolution spectra. Comparison of the low-resolution spectra with CMFGEN models suggests that the pre-explosion mass-loss rate of SN 2024ggi falls in a range of $10^{-3}$ to $10^{-2}$ M$_{\odot}$ yr$^{-1}$, which is similar to that derived for SN 2023ixf. However, the rapid temporal evolution of the narrow lines in the spectra of SN 2024ggi ($R_\mathrm{CSM} \sim 2.7 \times 10^{14} \mathrm{cm}$) could indicate a smaller spatial extent of the CSM than in SN 2023ixf ($R_\mathrm{CSM} \sim 5.4 \times 10^{14} \mathrm{cm}$) which in turn implies lower total CSM mass for SN 2024ggi., Comment: 23 pages, 15 figures, 4 tables, accepted for publication in ApJL

In an earlier analysis \href{https://link.aps.org/doi/10.1103/PhysRevD.105.085007}{Phys. Rev. D 105 (2022) 085007}, we have explored the event of acceleration radiation for an atom freely falling into the event horizon of a quantum-corrected Schwarzschild black hole. We want to explore the acceleration-radiation when the atom is freely falling into the event horizon of a charged quantum-corrected black hole. We consider the quantum effects of the electromagnetic field along with the gravitational field in an asymptotic safety regime. Introducing the quantum improved Reisner-Nordstr\"{o}m metric, we have calculated the excitation probability of a two-level atom freely falling into the event horizon of quantum improved charged black hole. Recently, in the case of the braneworld black hole (where the tidal charge has the same dimension as the square of the charge of a Reissner-Nordstr\"{o}m black hole in natural units), we have observed from the form of the transition probability that the temperature will have no contribution in the first order of the tidal charge. We observe that for a quantum corrected Reissner-Nordstr\"{o}m black hole, there is a second-order contribution in the charge parameter in the temperature that can be read off from the transition probability. Next, we calculate the HBAR entropy in this thought experiment and show that this entropy has a leading order Bekenstein-Hawking entropy term along with some higher order correction terms involving logarithmic as well as fractional terms of the black hole area due to infalling photons. We have finally investigated the validity of Wien's displacement law and compared the critical value of the field wavelength with the general Schwarzschild black hole and its corresponding quantum-corrected case., Comment: 12 pages LATEX, comments are welcome

Let $C$ be a smooth projective curve over $\mathbb{C}$ of genus $g(C)\geqslant 3$ (respectively, $g(C)=2$). Fix integers $r,k$ such that $2\leqslant k\leqslant r-2$, (respectively, $3\leqslant k\leqslant r-2$). Let $\mathcal{Q}:={\rm Quot}_{C/\mathbb{C}}(\mathcal{O}^{\oplus r}_C, k, d)$ be the Quot scheme parametrizing rank $k$ and degree $d$ quotients of the trivial bundle of rank $r$. Let $\mathcal{Q}_L$ denote the closed subscheme of the Quot scheme parametrizing quotients such that the quotient sheaf has determinant $L$. It is known that $\mathcal{Q}_L$ is an integral, normal, local complete intersection, locally factorial scheme of Picard rank 2, when $d\gg0$. In this article we compute the nef cone, effective cone and canonical divisor of this variety when $d\gg0$. We show this variety is Fano iff $r=2k+1$., Comment: Added section on effective cones in v2. Minor modifications to exposition. Comments are welcome

We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fields $\phi$ whose Lagrangian is non-canonical and of the form $\mathcal{L}(X,\phi)=-V(\phi)F(X)$, with $X=\frac{1}{2} g_{\mu\nu} \nabla^{\mu}\phi \nabla^{\nu} \phi$ and $V(\phi)$ the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus our results are in sync with the latest observations. So the Raychaudhuri equation can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios., Comment: 6 pages

We consider a Bose-Einstein condensate interacting with a gravitational wave for the case when the gravitational fluctuations are quantized in order to incorporate quantum gravity effects into the theory. We observe that the solution of the time-dependent part of the pseudo-Goldstone boson has infusions from the noise induced by gravitons and the corresponding differential equation of motion is Langevin-like. Using this result, we obtain the quantum gravity modified Fisher information which has been termed as the quantum gravitational Fisher information (QGFI). The inverse square root of the stochastic average of the QGFI gives the minimum uncertainty in the measurement of the gravitational wave amplitude. The minimum uncertainty does not go to infinity as the measurement time approaches zero in a quantum gravity setup rather it has a measurable finite value for gravitons with high squeezing. Finally, we observe the effect of decoherence due to interacting phonon modes in the QGFI and observe a less obvious decoherence effect for higher squeezing of the initial graviton., Comment: 8 pages LATEX. This is a letter version of arXiv:2403.18460 [hep-th]. OTM

We present long-term photometric and spectroscopic studies of Circumstellar Material (CSM)-Ejecta interacting supernova (SN) ASASSN-14il in the galaxy PGC 3093694. The SN reaches a peak $r$-band magnitude of $\sim$ $-20.3 \pm 0.2$ mag rivaling SN 2006tf and SN 2010jl. The multiband and the pseudo-bolometric lightcurve show a plateau lasting $\sim 50$ days. Semi-analytical CSM interaction models can match the high luminosity and decline rates of the lightcurves but fail to faithfully represent the plateau region and the bumps in the lightcurves. The spectral evolution resembles the typical SNe IIn dominated by CSM interaction, showing blue-continuum and narrow Balmer lines. The lines are dominated by electron scattering at early epochs. The signatures of the underlying ejecta are visible as the broad component in the H$\alpha$ profile from as early as day 50, hinting at asymmetry in the CSM. A narrow component is persistent throughout the evolution. The SN shows remarkable photometric and spectroscopic similarity with SN 2015da. However, the different polarization in ASASSN-14il compared to SN 2015da suggests an alternative viewing angle. The late-time blueshift in the H$\alpha$ profiles supports dust formation in the post-shock CSM or ejecta. The mass-loss rate of 2-7 M$_{\odot} \mathrm{yr}^{-1}$ suggests a Luminous Blue Variable (LBV) progenitor in an eruptive phase for ASASSN-14il., Comment: 26 pages, 12 figures, 9 tables, submitted in ApJ

Traditional machine learning models often require powerful hardware, making them unsuitable for deployment on resource-limited devices. Tiny Machine Learning (tinyML) has emerged as a promising approach for running machine learning models on these devices, but integrating multiple data modalities into tinyML models still remains a challenge due to increased complexity, latency, and power consumption. This paper proposes TinyVQA, a novel multimodal deep neural network for visual question answering tasks that can be deployed on resource-constrained tinyML hardware. TinyVQA leverages a supervised attention-based model to learn how to answer questions about images using both vision and language modalities. Distilled knowledge from the supervised attention-based VQA model trains the memory aware compact TinyVQA model and low bit-width quantization technique is employed to further compress the model for deployment on tinyML devices. The TinyVQA model was evaluated on the FloodNet dataset, which is used for post-disaster damage assessment. The compact model achieved an accuracy of 79.5%, demonstrating the effectiveness of TinyVQA for real-world applications. Additionally, the model was deployed on a Crazyflie 2.0 drone, equipped with an AI deck and GAP8 microprocessor. The TinyVQA model achieved low latencies of 56 ms and consumes 693 mW power while deployed on the tiny drone, showcasing its suitability for resource-constrained embedded systems., Comment: Accepted as a full paper by the tinyML Research Symposium 2024

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The gravitational wave perturbation is then considerd as a sum of discrete Fourier modes in the momentum space. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonincal commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in the decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing., Comment: 26 pages LATEX. Om Thakur Ma

Let $\Gamma$ be a finite set of Jordan curves in the plane. For any curve $\gamma \in \Gamma$, we denote the bounded region enclosed by $\gamma$ as $\tilde{\gamma}$. We say that $\Gamma$ is a non-piercing family if for any two curves $\alpha , \beta \in \Gamma$, $\tilde{\alpha} \setminus \tilde{\beta}$ is a connected region. A non-piercing family of curves generalizes a family of $2$-intersecting curves in which each pair of curves intersect in at most two points. Snoeyink and Hershberger (``Sweeping Arrangements of Curves'', SoCG '89) proved that if we are given a family $\mathcal{C}$ of $2$-intersecting curves and a fixed curve $C\in\mathcal{C}$, then the arrangement can be \emph{swept} by $C$, i.e., $C$ can be continuously shrunk to any point $p \in \tilde{C}$ in such a way that the we have a family of $2$-intersecting curves throughout the process. In this paper, we generalize the result of Snoeyink and Hershberger to the setting of non-piercing curves. We show that given an arrangement of non-piercing curves $\Gamma$, and a fixed curve $\gamma\in \Gamma$, the arrangement can be swept by $\gamma$ so that the arrangement remains non-piercing throughout the process. We also give a shorter and simpler proof of the result of Snoeyink and Hershberger and cite applications of their result, where our result leads to a generalization.

In this work, we extend the study in \href{https://link.springer.com/article/10.1007/JHEP11(2022)013}{JHEP11(2022)013} incorporating the AdS/CFT duality to establish a relationship between the local temperatures (Tolman temperatures) of a large (AdS) spherical and a (AdS) planar Schwarzschild black hole near the AdS boundary considering Gauss-Bonnet curvature correction in the gravitational action. We have shown that the higher curvature corrections appear in the local temperature relationship due to the inclusion of Gauss-Bonnet term in the bulk. By transforming the metric into Fefferman-Graham form, we have calculated the energy density of the conformal fluid at the boundary. The obtained result contains finite coupling corrections which are holographically induced by the Gauss-Bonnet curvature correction in the bulk theory. Following the well known approach of fluid/gravity duality, the energy density of the conformal fluid at the boundary is then compared with the black body radiation energy density. This comparison shows that the energy density is proportional to the temperature of the conformal fluid. The temperature of the conformal fluid is then shown to be related to the Tolman temperature of the black hole which then eventually helps us to establish both the Hawking temperature and Tolman temperature relationship between large spherically symmetric and planar Schwarzschild black holes in Gauss-Bonnet gravity near the AdS boundary., Comment: v1: 17 pages LaTex, v2: 23 pages & multiple new figures, to appear in Classical and Quantum Gravity

We present an optical photometric and spectroscopic analysis of the fast-declining hydrogen-rich Type II supernova (SN) 2019nyk. The light curve properties of SN 2019nyk align well with those of other fast-declining Type II SNe, such as SNe 2013by and 2014G. SN 2019nyk exhibits a peak absolute magnitude of -18.09 $\pm$ 0.17 mag in the V band, followed by a rapid decline at 2.84 $\pm$ 0.03 mag (100 d)$^{-1}$ during the recombination phase. The early spectra of SN 2019nyk exhibit high-ionisation emission features as well as narrow H Balmer lines, persisting until 4.1 d since explosion, indicating the presence of circumstellar material (CSM) in close proximity. A comparison of these features with other Type II SNe displaying an early interaction reveals similarities between these features and those observed in SNe 2014G and 2023ixf. We also compared the early spectra to literature models, estimating a mass-loss rate of the order of 10$^{-3}$ M$_\odot$ yr$^{-1}$. Radiation hydrodynamical modelling of the light curve also suggests the mass loss from the progenitor within a short period prior to explosion, totalling 0.16 M$_\odot$ of material within 2900 R$_\odot$ of the progenitor. Furthermore, light curve modelling infers a zero-age main sequence mass of 15 M$_\odot$ for the progenitor, a progenitor radius of 1031 R$_\odot$, and an explosion energy of 1.1 $\times$ 10$^{51}$ erg., Comment: 18 pages, 23 figures, accepted in A&A