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It is shown theoretically how to use the EPR (Electron Paramagnetic Resonance) technique, using electron spins as qubits, coupled with each other by the exchange interaction, to set the configuration of n qubits (n=1,2,3,4) at resonance, in conjunction with pulses, to construct the NOT (one qubit), CNOT (two qubits), CCNOT (three qubits), CCCNOT (four qubits) Toffoli gates, which can be exploited to build a quantum computer. This is unique to EPR, wherein exchange-coupled electron spins are used. This is not possible with NMR (Nuclear Magnetic Resonance), that uses nuclear spins as qubits, which do not couple with each other by the exchange interaction.

Nonlinear interactions between single quantum particles are at the heart of any quantum information system, including analog quantum simulation and fault-tolerant quantum computing. This remains a particularly difficult problem for photonic qubits, as photons do not interact with each other. While engineering light-matter interaction can effectively create photon-photon interaction, the required photon number to observe any nonlinearity is very high, where any quantum mechanical signature disappears. However, with emerging low-dimensional materials, and engineered photonic resonators, the photon number can be potentially reduced to reach the quantum nonlinear optical regime. In this review paper, we discuss different mechanisms exploited in solid-state platforms to attain quantum nonlinear optics. We review emerging materials and optical resonator architecture with different dimensionalities. We also present new research directions and open problems in this field.

The study of complex organic molecules containing thiol ($-$SH) groups is essential in interstellar media because $-$SH plays an important role in the polymerization of amino acids (R-CH(NH$_{2}$)-COOH). Some quantum chemical studies have shown that there is a high chance of detecting the emission lines of dithioformic acid (HC(S)SH) in the highly dense and warm-inner regions of hot molecular cores and hot corinos. Therefore, we attempted to search for the emission lines of HC(S)SH toward the highly dense hot corino object NGC 1333 IRAS 4A using the Atacama Large Millimeter/Submillimeter Array (ALMA) band 7. We present the first detection of the rotational emission lines of the trans-conformer of dithioformic acid (t-HC(S)SH) toward the NGC 1333 IRAS 4A2. The column density and excitation temperature of the t-HC(S)SH toward NGC 1333 IRAS 4A2 are (2.63$\pm$0.32)$\times$10$^{15}$ cm$^{-2}$ and 255$\pm$32 K, respectively. The fractional abundance of t-HC(S)SH with respect to H$_{2}$ is (2.53$\pm$0.68)$\times$10$^{-9}$. The column density ratio of t-HC(S)SH and t-HCOOH toward NGC 1333 IRAS 4A2 is 0.36$\pm$0.02. To understand the possible formation pathways of HC(S)SH, we computed a two-phase warm-up chemical model abundance of HC(S)SH using the gas-grain chemical code UCLCHEM. After chemical modeling, we claim that HC(S)SH is formed in NGC 1333 IRAS 4A2 via barrierless radical--radical reactions between CSSH and H on the grain surfaces., Comment: Published in ACS Earth and Space Chemistry

The atomic and molecular compounds of cometary ices serve as valuable knowledge into the chemical and physical properties of the outer solar nebula, where comets are formed. From the cometary atmospheres, the atoms and gas-phase molecules arise mainly in three ways: (i) the outgassing from the nucleus, (ii) the photochemical process, and (iii) the sublimation of icy grains from the nucleus. In this paper, we present the radio and millimeter wavelength observation results of Oort cloud non-periodic comet C/2022 E3 (ZTF) using the Giant Metrewave Radio Telescope (GMRT) band L and the Atacama Large Millimeter/Submillimeter Array (ALMA) band 6. We do not detect continuum emissions and an emission line of atomic hydrogen (HI) at rest frequency 1420 MHz from this comet using the GMRT. Based on ALMA observations, we detect the dust continuum emission and rotational emission lines of methanol (CH$_{3}$OH) from comet C/2022 E3 (ZTF). From the dust continuum emission, the activity of dust production (Af$\rho$) of comet ZTF is 2280$\pm$50 cm. Based on LTE spectral modelling, the column density and excitation temperature of CH$_{3}$OH towards C/2022 E3 (ZTF) are (4.50$\pm$0.25)$\times$10$^{14}$ cm$^{-2}$ and 70$\pm$3 K. The integrated emission maps show that CH$_{3}$OH was emitted from the coma region of the comet. The production rate of CH$_{3}$OH towards C/2022 E3 (ZTF) is (7.32$\pm$0.64)$\times$10$^{26}$ molecules s$^{-1}$. The fractional abundance of CH$_{3}$OH with respect to H$_{2}$O in the coma of the comet is 1.52%. We also compare our derived abundance of CH$_{3}$OH with the existence modelled value, and we see the observed and modelled values are nearly similar. We claim that CH$_{3}$OH is formed via the subsequential hydrogenation of formaldehyde (H$_{2}$CO) on the grain surface of comet C/2022 E3 (ZTF)., Comment: Accepted for publication in Research in Astronomy and Astrophysics (RAA)

We present the results of deep radio observations of 7 nearby large galaxies observed using the upgraded Giant Metrewave Radio Telescope (uGMRT) 0.3-0.5 GHz receivers with an angular resolution of $\sim$10 arcsec. The achieved sensitivities of these observations range from $\approx$15 to 50 $\mu$Jy/beam which is $\approx$3-4 factor lower than the previous observations at these frequencies. For 2 galaxies (NGC3344 and NGC3627) with moderate inclination angles, significant diffuse emissions are seen for the first time. Detected radio halos in the vertical direction are significantly larger in our 0.4 GHz maps than compared to the observations at $\sim$1.5 GHz for 4 nearly edge-on galaxies - NGC3623, NGC4096, NGC4594, and NGC4631. For these 4 galaxies, significantly larger halos are also detected along the galaxy disk. For NGC3623 and NGC4594, we could detect elongated radio disks which was not seen before. We also present new uGMRT images of NGC3344 and NGC3623 at 1.3 GHz and a new VLA image of NGC3627 at 1.5 GHz. We fitted an exponential function to the flux densities along different cross-cuts and found a significantly wider distribution at 0.4 GHz uGMRT images than compared to the high-frequency images at $\sim$1.5 GHz. Using maps at 0.144, 0.4, and $\sim$1.5 GHz, we made spectral index maps of the 7 sample galaxies and found steepening of the spectrum up to a value of $\sim$ -1.5 in the halo regions of the galaxies., Comment: 17 pages, Accepted for publication in ApJ

The upcoming Electron-Ion Collider (EIC), with its high luminosity, will offer an unprecedented opportunity to explore the internal structure of atomic nucleus over an extended energy range from $\sqrt{s_{ep}} =$ 45 GeV to $\sqrt{s_{ep}} =$ 140 GeV. A particularly promising aspect of this collider is the study of the partonic structure with quasi-real photons which can also be studied in inclusive ultra-peripheral collisions at the Large Hadron Collider (LHC). In this work, we present our validation of resolved photoproduction at fixed order for (next-to-)leading order using \texttt{MadGraph5\_aMC@NLO}, a widely adopted framework at the LHC., Comment: 6 pages. 4 figures, proceedings for the "31st International Workshop on Deep Inelastic Scattering (DIS2024)", 8-12 April 2024, Grenoble, France

In this work, we investigate the particle creation rate in a dynamical (Vaidya) spacetime using Feynman's path integral formalism within the framework of the effective action approach. We analyze particle production rates in the region of dynamical horizons, revealing an initial high rate followed by a rapid decline in all cases. Additionally, we explore the thermodynamic properties by calculating the surface gravity and corresponding Hayward-Kodama temperatures for each scenario. Graphical representations show the variation of surface gravity over time for the three cases, offering insights into the system's thermodynamic evolution. Our research investigates the connection between background geometry and the particle creation process, placing it within the broader context of quantum field theory in curved spacetime. The non-stationary nature of Vaidya geometry is highlighted as a valuable framework for examining the dynamic aspects of particle creation. This in-depth analysis enhances our understanding of quantum processes in curved spacetime and may offer insights relevant to thermodynamics and studies of gravitational collapse., Comment: 13 pages, 6 figures

Among the surprising features of quantum measurements, the problem of distinguishing and anti-distinguishing general quantum measurements is fundamentally appealing. Quantum theory offers four distinct scenarios for distinguishing (and anti-distinguishing) quantum measurements - (i) probing single systems and without access to the post-measurement states, (ii) probing entangled systems and without access to the post-measurement states, (iii) probing single systems with access to the post-measurement states, and (iv) probing entangled systems with access to the post-measurement states. In these scenarios, we consider the probability of distinguishing (and anti-distinguishing) quantum measurements sampled from a given set in the single-shot regime. For some scenarios, we derive analytical expressions for the distinguishability (and anti-distinguishability) of qubit projective measurements. Notably, we demonstrate that in scenario (iii), the distinguishability of any pair of qubit projective measurements is always higher than in scenario (ii). Interestingly, for some qubit non-projective measurements, the highest distinguishability in scenario (ii) is achieved using a non-maximally entangled state. It turns out that, for any set of measurements, the distinguishability (and anti-distinguishability) in scenario (i) is always less than or equal to that in any other scenario, while it reaches its highest possible value in scenario (iv). We establish that these relations form a strict hierarchy, and there is no hierarchical relation between scenarios (ii) and (iii). Specifically, we construct pairs (and triples) of qubit measurements that are perfectly distinguishable (and anti-distinguishable) in scenario (ii) but not in scenario (iii), and vice versa. Furthermore, we identify qubit measurements that achieve perfect distinguishability (and anti-distinguishability) only in scenario (iv)., Comment: 21 pages, 11 figures. Comments are welcome

Human movement analysis is crucial in health and sports biomechanics for understanding physical performance, guiding rehabilitation, and preventing injuries. However, existing tools are often proprietary, expensive, and function as "black boxes", limiting user control and customization. This paper introduces vail\'a-Versatile Anarcho Integrated Liberation \'Analysis in Multimodal Toolbox-an open-source, Python-based platform designed to enhance human movement analysis by integrating data from multiple biomechanical systems. vail\'a supports data from diverse sources, including retroreflective motion capture systems, inertial measurement units (IMUs), markerless video capture technology, electromyography (EMG), force plates, and GPS or GNSS systems, enabling comprehensive analysis of movement patterns. Developed entirely in Python 3.11.9, which offers improved efficiency and long-term support, and featuring a straightforward installation process, vail\'a is accessible to users without extensive programming experience. In this paper, we also present several workflow examples that demonstrate how vail\'a allows the rapid processing of large batches of data, independent of the type of collection method. This flexibility is especially valuable in research scenarios where unexpected data collection challenges arise, ensuring no valuable data point is lost. We demonstrate the application of vail\'a in analyzing sit-to-stand movements in pediatric disability, showcasing its capability to provide deeper insights even with unexpected movement patterns. By fostering a collaborative and open environment, vail\'a encourages users to innovate, customize, and freely explore their analysis needs, potentially contributing to the advancement of rehabilitation strategies and performance optimization., Comment: 21 pages, 13 figures, submitted to arXiv under cs.SE (Software Engineering)

Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite fermion framework used to explain fractional quantum Hall states (such as Laughlin states). Crucially, they hold promise for hosting non-Abelian excitations, which are essential for developing topological qubits - key components for fault-tolerant quantum computing. In this work, we show that these coveted half-quantized plateaus can appear in more than one unexpected way. We report the observation of fractional states with conductance quantization at $\nu_H = 5/2$ arising due to charge equilibration in the confined region of a quantum point contact in monolayer graphene., Comment: 30 pages, 18 figures, and 2 tables

This research explores refined boundary conditions for a traction-free surface in a non-local micropolar half-space, combining non-local and micropolar elasticity effects to study Rayleigh wave propagation in an isotropic, homogeneous medium. This study revisits the solution for Rayleigh waves obtained within the framework of Eringen's non-local differential model. It highlights that the equivalence between the non-local differential and integral formulations breaks down for a micropolar half-space and can only be restored under specific additional boundary conditions. For mathematical tractability, equivalence is assumed for a defined subset of stresses. Asymptotic analysis is further employed to capture the effects of the boundary layer within the non-local micropolar half-space. This technique finally derives the refined boundary conditions for micropolar media.

Self-supervised learning has developed rapidly over the last decade and has been applied in many areas of computer vision. Decorrelation-based self-supervised pretraining has shown great promise among non-contrastive algorithms, yielding performance at par with supervised and contrastive self-supervised baselines. In this work, we explore the decorrelation-based paradigm of self-supervised learning and apply the same to learning disentangled stroke features for writer identification. Here we propose a modified formulation of the decorrelation-based framework named SWIS which was proposed for signature verification by standardizing the features along each dimension on top of the existing framework. We show that the proposed framework outperforms the contemporary self-supervised learning framework on the writer identification benchmark and also outperforms several supervised methods as well. To the best of our knowledge, this work is the first of its kind to apply self-supervised learning for learning representations for writer verification tasks.

The Tweedie exponential dispersion family is a popular choice among many to model insurance losses that consist of zero-inflated semicontinuous data. In such data, it is often important to obtain credibility (inference) of the most important features that describe the endogenous variables. Post-selection inference is the standard procedure in statistics to obtain confidence intervals of model parameters after performing a feature extraction procedure. For a linear model, the lasso estimate often has non-negligible estimation bias for large coefficients corresponding to exogenous variables. To have valid inference on those coefficients, it is necessary to correct the bias of the lasso estimate. Traditional statistical methods, such as hypothesis testing or standard confidence interval construction might lead to incorrect conclusions during post-selection, as they are generally too optimistic. Here we discuss a few methodologies for constructing confidence intervals of the coefficients after feature selection in the Generalized Linear Model (GLM) family with application to insurance data.

Accurately predicting water table dynamics is vital for sustaining groundwater resources that support ecological functions and anthropogenic activities. This study evaluates a statistical model (BigVAR) that handles three major flexibilities: (a) prediction under a sparsity assumption in coefficients, (b) consideration of a time series autoregression framework, and (c) allowance for lags in both dependent and independent variables for estimating water table depth using daily hydroclimatic data from the USDA Forest Service Santee Experimental Forest (SC) and a site in NC. Data from 2006--2019 (SC) and 1988--2008 (NC) were used, with key predictors including soil and air temperature, precipitation, wind, and radiation. For WS80, RMSE during the dormant season was 10.09 cm, with a daily testing phase RMSE of 14.94 cm. The model achieved an R^2 of 0.93 for 2019 (a dry year) and 0.96 for 2016 (a wet year). Solar radiation, rainfall, and wind direction were among the most influential variables. This predictive model aids in managing wetland hydrology and supports decision-making for forest managers and hydrologists., Comment: Autoregressive, Hydrology, time series modeling, variable selection, water table depth, hydrology

Phonons in solid-state quantum emitters play a crucial role in their performance as photon sources in quantum technology. For resonant driving, phonons dampen the Rabi oscillations resulting in reduced preparation fidelities. The phonon spectral density, which quantifies the strength of the carrier-phonon interaction, is non-monotonous as a function of energy. As one of the most prominent consequences, this leads to the reappearance of Rabi rotations for increasing pulse power, which was theoretically predicted in Phys. Rev. Lett. 98, 227403 (2007). In this paper we present the experimental demonstration of the reappearance of Rabi rotations.

Faithfulness is arguably the most critical metric to assess the reliability of explainable AI. In NLP, current methods for faithfulness evaluation are fraught with discrepancies and biases, often failing to capture the true reasoning of models. We introduce Adversarial Sensitivity as a novel approach to faithfulness evaluation, focusing on the explainer's response when the model is under adversarial attack. Our method accounts for the faithfulness of explainers by capturing sensitivity to adversarial input changes. This work addresses significant limitations in existing evaluation techniques, and furthermore, quantifies faithfulness from a crucial yet underexplored paradigm., Comment: Accepted as a Full Paper at EMNLP 2024 Workshop BlackBoxNLP

The recent emergence of quantum confined nanomaterials in the field of radiation detection, in particular lead halide perovskite nanocrystals, offers potentially revolutionary scalability and performance advantages over conventional materials. This development raises fundamental questions about the mechanism of scintillation itself at the nanoscale and the role of particle size, arguably the most defining parameter of quantum dots. Understanding this is crucial for the design and optimisation of future nanotechnology scintillators. In this work, we address these open questions by theoretically and experimentally studying the size-dependent scintillation of CsPbBr3 nanocrystals using a combination of Monte Carlo simulations, spectroscopic, and radiometric techniques. The results reveal and unravel a complex parametric space where the fine balance between the simultaneous effects of size-dependent energy deposition, (multi-)exciton population, and light emission under ionizing excitation, typical of confined particles, combine to maximize the scintillation efficiency and time performance of larger nanocrystals due to greater stopping power and reduced Auger decay. The remarkable agreement between theory and experiment produces a fully validated descriptive model that unprecedentedly predicts the scintillation yield and kinetics of nanocrystals without free parameters, providing the first fundamental guide for the rational design of nanoscale scintillators.

Signatures of chaos can be understood by studying quantum systems whose classical counterpart is chaotic. However, the concepts of integrability, non-integrability and chaos extend to systems without a classical analogue. Here, we first review the classical route from order into chaos. Since nature is fundamentally quantum, we discuss how chaos manifests in the quantum domain. We briefly describe semi-classical methods, and discuss the consequences of chaos in quantum information processing. We review the quantum version of Lyapunov exponents, as quantified by the out-of-time ordered correlators (OTOC), Kolmogorov-Sinai (KS) entropy and sensitivity to errors. We then review the study of signatures of quantum chaos using quantum tomography. Classically, if we know the dynamics exactly, as we maintain a constant coarse-grained tracking of the trajectory, we gain exponentially fine-grained information about the initial condition. In the quantum setting,as we track the measurement record with fixed signal-to-noise, we gain increasing information about the initial condition. In the process, we have given a new quantification of operator spreading in Krylov subspaces with quantum state reconstruction. The study of these signatures is not only of theoretical interest but also of practical importance., Comment: 22 pages. This is a review article. arXiv admin note: text overlap with arXiv:2409.10182

Present works discusses the efficient structural analysis and weight optimization of the cable-stiffened deployable structures. The stiffening effect of cables is incorporated through a matrix analysis based iterative strategy to identify the active and passive cables. The structural form can be easily deployed to cartesian as well as polar coordinates through the arrangement of duplet members. The large span utility of cable stiffened bar members can pose challenges to the deployability due to increased weight. A novel teaching-learning based optimization (TLBO) algorithm is utilized to optimize the overall weight of the structure through efficient section designs with proper constraint on the yield criteria. The penalty function approach is adopted to identify the unfeasible designs. A number of example cases are analysed and comparison is presented with the existing literature to show the suitability of the proposed approach. Finally, a new form of three-dimensional deployable structure is proposed. It is seen that such deployable structure can be accurately analysed using the iterative matrix analysis approach and efficiently optimized using the present algorithm., Comment: 33 pages, 21 figures

Phosphorus (P) is an important element for the chemical evolution of galaxies and many kinds of biochemical reactions. Phosphorus is one of the crucial chemical compounds in the formation of life on our planet. In an interstellar medium, phosphine (PH$_{3}$) is a crucial biomolecule that plays a major role in understanding the chemistry of phosphorus-bearing molecules, particularly phosphorus nitride (PN) and phosphorus monoxide (PO), in the gas phase or interstellar grains. We present the first confirmed detection of phosphine (PH$_{3}$) in the asymptotic giant branch (AGB) carbon-rich star IRC+10216 using the Atacama Large Millimeter/Submillimeter Array (ALMA) band 6. We detect the $J$ = 1$_{0}$$-$0$_{0}$ rotational transition line of PH$_{3}$ with a signal-to-noise ratio (SNR) of $\geq$3.5$\sigma$. This is the first confirmed detection of phosphine (PH$_{3}$) in the ISM. Based on LTE spectral modelling, the column density of PH$_{3}$ is (3.15$\pm$0.20)$\times$10$^{15}$ cm$^{-2}$ at an excitation temperature of 52$\pm$5 K. The fractional abundance of PH$_{3}$ with respect to H$_{2}$ is (8.29$\pm$1.37)$\times$10$^{-8}$. We also discuss the possible formation pathways of PH$_{3}$ and we claim that PH$_{3}$ may be created via the hydrogenation of PH$_{2}$ on the grain surface of IRC+10216., Comment: Accepted for publication in Journal of Astrophysics and Astronomy

Gravitational waveforms capturing binary's evolution through the early-inspiral phase play a critical role in extracting orbital features that nearly disappear during the late-inspiral and subsequent merger phase due to radiation reaction forces; for instance, the effect of orbital eccentricity. Phenomenological approaches that model compact binary mergers rely heavily on combining inputs from both analytical and numerical approaches to reduce the computational cost of generating templates for data analysis purposes. In a recent work, Chattaraj et al., Phys. Rev. D 106, 124008 (2022) arXiv:2204.02377(gr-qc), we demonstrated construction of a dominant (quadrupole) mode inspiral-merger-ringdown (IMR) model for binary black holes (BBHs) on elliptical orbits. The model was constructed in time-domain and is fully analytical. The current work is an attempt to improve this model by making a few important changes in our approach. The most significant of those involves identifying initial values of orbital parameters with which the inspiral part of the model is evolved. While the ingredients remain the same as in arXiv:2204.02377(gr-qc), resulting waveforms at each stage seem to have improved as a consequence of new considerations proposed here. The updated model is validated also against an independent waveform family resulting overlaps better than $\sim 96.5\%$ within the calibrated range of binary parameters. Further, we use the prescription of the dominant mode model presented here to provide an alternate (but equivalent) model for the (dominant) quadrupole mode and extend the same to a model including the effect of selected non-quadrupole modes. Finally, while this model assumes non-spinning components, we show that this could also be used for mildly spinning systems with component spins (anti-) aligned w.r.t the orbital angular momentum., Comment: 17 pages, 12 figures. arXiv admin note: text overlap with arXiv:2204.02377

Current carrying steady states of interacting spins chains exhibit rich structures generated through an interplay of current induced correlations and energetic constraints from the Hamiltonian. The XXZ spin chain when coupled to maximally polarizing Lindblad terms admits an exact solution in a matrix product state (MPS) form. We use this exact solution to study the correlations and distributions of simple local spin observables in the non equilibrium steady state (NESS). We present exact expressions for spin correlators, entropy per site, cumulant generating functions for distributions of local observables in the XX limit (Ising anisotropy $\Delta=0$). Further, we use the exact MPS solution in systems with $\Delta>0$, to numerically exactly calculate the entropy, correlations, as well as distributions of spin observables in blocks as large as $n\sim 200$ sites allowing an estimation of the rate functions. The $z$ magnetization distribution is consistant with short range spin correlations in the $z$ direction while the $x$-magnetization shows a double peak structure at larger $\Delta$ suggesting short range ferromagnetic ordering. We find that the distribution of $z$-magnetization sharpens for parameters where the current is maximized.

Transition-metal-based carbides (TMCs), renowned for their exceptional hardness, mechanical strength, and thermal properties, have recently emerged as promising candidates for topological superconductivity. In this study, we synthesized ReC in the NaCl structure at ambient pressure by substituting Mo or W at the Re-site. We investigated the superconducting properties of Re$_{1-x}$T$_{x}$C (where T = Mo, W) for $x = 0.5$ using magnetization, resistivity and specific heat measurements. These compounds display type-II, fully gapped, weakly coupled superconductivity with high critical fields, establishing them as new members of superconducting ultra-hard materials at ambient pressure and paving the way for superconducting device applications under extreme conditions., Comment: 6 pages, 4 figures

High-quality (Q)-factor optical resonators with extreme temporal coherence are of both technological and fundamental importance in optical metrology, continuous-wave lasing, and semiconductor quantum optics. Despite extensive efforts in designing high-Q resonators across different spectral regimes, the experimental realization of very large Q-factors at visible wavelengths remains challenging due to the small feature size that is sensitive to fabrication imperfections, and thus is typically implemented in integrated photonics. In the pursuit of free-space optics with the benefits of large space-bandwidth product and massive parallel operations, here we design and fabricate a visible-wavelength etch-free metasurface with minimized fabrication defects and experimentally demonstrate a million-scale ultrahigh-Q resonance. A new laser-scanning momentum-space-resolved spectroscopy technique with extremely high spectral and angular resolution is developed to characterize the record-high Q-factor as well as the dispersion of the million-Q resonance in free space. By integrating monolayer WSe2 into our ultrahigh-Q meta-resonator, we further demonstrate laser-like highly unidirectional and narrow-linewidth exciton emission, albeit without any operating power density threshold. Under continuous-wave laser pumping, we observe pump-power-dependent linewidth narrowing at room temperature, indicating the potential of our meta-optics platform in controlling coherent quantum light-sources. Our result also holds great promise for applications like optical sensing, spectral filtering, and few-photon nonlinear optics.

We search for gamma-ray emission from the galaxy cluster SPT-CL J2012-5649 in the energy range from 3 GeV to 1 TeV using the DArk Matter Particle Explorer (DAMPE) telescope. For our analysis, we use three different templates: point source, radial disk, and radial Gaussian. We do not detect a signal with significance $>3\sigma$ for any of these templates at any location within $R_{200}$ of the cluster center. We obtain 95\% C.L. upper limit on the energy flux ranging between $\sim 10^{-6}$ and $10^{-4} \rm{MeV~cm^{-2}~s^{-1}}$ depending on the energy range. These upper limits are consistent with a previously reported non-zero flux detected by Fermi-LAT at $6\sigma$ significance. This work represents the first proof of principle search for gamma-ray emission from a single galaxy cluster using DAMPE data., Comment: 12 pages, 4 figures. Accepted for publication in JHEAP

Optical trapping is having ever-increasing impact in science $-$ particularly biophysics, photonics and most recently in quantum optomechanics $-$ owing to its superior capability for manipulating nanoscale structures and materials. However, essentially all experimental optical trapping studies in the optical dipole regime have, to date, been dominated by the interaction between a material's electric polarizability, $\alpha_{e}$, and the electric part of the incident electromagnetic field, and therefore described by electric field intensity gradient forces. Optical trapping based on optical magnetic light-matter interactions has not been experimentally addressed despite it's immediate extension of the boundaries of optical trapping research and applications. This paper addresses this long-standing deficiency through the realization of optical magnetic trapping of large index of refraction (i.e., Si) nanoparticles and also presents a formalism for quantitative understanding of the experimental findings. Our experimental optical trapping results require including optical magnetic polarizability, $\alpha_{m}$, and electric-magnetic scattering forces associated with the Photonic Hall effect that are qualitatively and quantitatively validated by Maxwell stress tensor calculations. Our findings bring new opportunities for nanoparticle manipulation, potentially relax the limitations Ashkin claimed based on the optical Earnshaw's theorem, motivate optical matter formation by optical magnetic interactions, and suggest new N-body effects and symmetry breaking to drive dynamics of optical matter systems.

Medical image segmentation is one of the domains where sufficient annotated data is not available. This necessitates the application of low-data frameworks like few-shot learning. Contemporary prototype-based frameworks often do not account for the variation in features within the support and query images, giving rise to a large variance in prototype alignment. In this work, we adopt a prototype-based self-supervised one-way one-shot learning framework using pseudo-labels generated from superpixels to learn the semantic segmentation task itself. We use a correlation-based probability score to generate a dynamic prototype for each query pixel from the bag of prototypes obtained from the support feature map. This weighting scheme helps to give a higher weightage to contextually related prototypes. We also propose a quadrant masking strategy in the downstream segmentation task by utilizing prior domain information to discard unwanted false positives. We present extensive experimentations and evaluations on abdominal CT and MR datasets to show that the proposed simple but potent framework performs at par with the state-of-the-art methods., Comment: Accepted to ICPR 2024

We consider the free boundary problem for a 3-dimensional, incompressible, irrotational liquid drop of nearly spherical shape with capillarity. We study the problem from scratch, extending some classical results from the flat case (capillary water waves) to the spherical geometry: the reduction to a problem on the boundary, its Hamiltonian structure, the analyticity and tame estimates for the Dirichlet-Neumann operator in Sobolev class, and a linearization formula for it, both with the method of the good unknown of Alinhac and by a differential geometry approach. Then we prove the bifurcation of traveling waves, which are nontrivial (i.e., nonspherical) fixed profiles rotating with constant angular velocity.

Modern Education is not \textit{Modern} without AI. However, AI's complex nature makes understanding and fixing problems challenging. Research worldwide shows that a parent's income greatly influences a child's education. This led us to explore how AI, especially complex models, makes important decisions using Explainable AI tools. Our research uncovered many complexities linked to parental income and offered reasonable explanations for these decisions. However, we also found biases in AI that go against what we want from AI in education: clear transparency and equal access for everyone. These biases can impact families and children's schooling, highlighting the need for better AI solutions that offer fair opportunities to all. This chapter tries to shed light on the complex ways AI operates, especially concerning biases. These are the foundational steps towards better educational policies, which include using AI in ways that are more reliable, accountable, and beneficial for everyone involved., Comment: Technical Report, UROP-2023

The identification of complex prebiotic molecules using millimeter and submillimeter telescopes allows us to understand how the basic building blocks of life are formed in the universe. In the interstellar medium (ISM), ethylene glycol ((CH$_{2}$OH)$_{2}$) is the simplest sugar alcohol molecule, and it is the reduced alcohol of the simplest sugar-like molecule, glycolaldehyde (CH$_{2}$OHCHO). We present the first detection of the rotational emission lines of $aGg^{\prime}$ conformer of ethylene glycol ((CH$_{2}$OH)$_{2}$) towards the hot molecular core G358.93$-$0.03 MM1 using the Atacama Large Millimeter/Submillimeter Array (ALMA). The estimated column density of $aGg^{\prime}$-(CH$_{2}$OH)$_{2}$ towards the G358.93$-$0.03 MM1 is (4.5$\pm$0.1)$\times$10$^{16}$ cm$^{-2}$ with an excitation temperature of 155$\pm$35 K. The abundance of $aGg^{\prime}$-(CH$_{2}$OH)$_{2}$ with respect to H$_{2}$ is (1.4$\pm$0.5)$\times$10$^{-8}$. Similarly, the abundances of $aGg^{\prime}$-(CH$_{2}$OH)$_{2}$ with respect to CH$_{2}$OHCHO and CH$_{3}$OH are 3.1$\pm$0.5 and (6.1$\pm$0.3)$\times$10$^{-3}$. We compare the estimated abundance of $aGg^{\prime}$-(CH$_{2}$OH)$_{2}$ with the existing three-phase warm-up chemical model abundance of (CH$_{2}$OH)$_{2}$, and we notice the observed abundance and modelled abundance are nearly similar. We discuss the possible formation pathways of $aGg^{\prime}$-(CH$_{2}$OH)$_{2}$ towards the hot molecular cores, and we find that $aGg^{\prime}$-(CH$_{2}$OH)$_{2}$ is probably created via the recombination of two CH$_{2}$OH radicals on the grain surface of G358.93$-$0.03 MM1., Comment: Published in Monthly Notices of the Royal Astronomical Society (MNRAS)

A graph is called claw-free if it contains no induced subgraph isomorphic to the complete bipartite graph $K_{1, 3}$. The undirected power graph of a group $G$ has vertices the elements of $G$, with an edge between $g_1$ and $g_2$ if one of the two cyclic subgroups $\langle g_1\rangle, \langle g_2\rangle$ is contained in the other. It is denoted by $P(G)$. The reduced power graph, denoted by $P^*(G),$ is the subgraph of $P(G)$ induced by the non-identity elements. The main purpose of this paper is to explore the finite groups whose reduced power graph is claw-free. In particular we prove that if $P^*(G)$ is claw-free, then either $G$ is solvable or $G$ is an almost simple group. In the second case the socle of $G$ is isomorphic to $PSL(2,q)$ for suitable choices of $q$. Finally we prove that if $P^*(G)$ is claw-free, then the order of $G$ is divisible by at most 5 different primes.

When subject to a non-local unitary evolution, qubits in a quantum circuit become increasingly entangled. Conversely, measurements applied to individual qubits lead to their disentanglement from the collective system. The extent of entanglement reduction depends on the frequency of local projective measurements. A delicate balance emerges between unitary evolution, which enhances entanglement, and measurements which diminish it. In the thermodynamic limit, there is a phase transition from volume law entanglement to area law entanglement at a critical value of measurement frequency. This phenomenon, occurring in hybrid quantum circuits with both unitary gates and measurements, is termed as measurement-induced phase transition (MIPT). We study the behavior of MIPT in circuits comprising of two qubit unitary gates parameterized by Cartan decomposition. We show that the entangling power and gate typicality of the two-qubit local unitaries employed in the circuit can be used to explain the behavior of global bipartite entanglement the circuit can sustain. When the two qubit gate throughout the circuit is the identity and measurements are the sole driver of the entanglement behavior, we obtain analytical estimate for the entanglement entropy that shows remarkable agreement with numerical simulations. We also find that the entangling power and gate typicality enable the classification of the two-qubit unitaries by different universality classes of phase transitions that can occur in the hybrid circuit. For all unitaries in a particular universality class, the transition from volume to area law of entanglement occurs with same exponent that characterizes the phase transition., Comment: 14 page, 14 figures

We search for dark matter annihilation from galaxy clusters in the energy range from 1-300 GeV using nearly 16 years of Fermi-LAT data. For this purpose, we use 350 galaxy clusters selected from the 2500 $\rm{deg^2}$ SPT-SZ survey. We model the dark matter distribution using the NFW profile for the main halo along with the Einasto profile for the substructure. The largest signal is seen for the cluster SPT-CL J2021-5257 with a significance of around $3\sigma$. The best-fit dark matter mass and annihilation cross-section for this cluster are equal to $(60.0 \pm 11.8)$ GeV and $\langle \sigma v \rangle= (6.0 \pm 0.6) \times 10^{-25} \rm{cm^3 s^{-1}}$ for the $\bar{b} b$ annihilation channel. However, this central estimate is in conflict with the limits on annihilation cross-section from dwarf spheroidal galaxies, and hence cannot be attributed to dark matter annihilation. Three other clusters show significance between $2-2.5\sigma$, whereas all the remaining clusters show null results. The most stringent 95\% c.l. upper limit for the WIMP annihilation cross-section among all the clusters is from SPT-CL J0455-4159, viz. $\langle \sigma v \rangle = 6.44 \times 10^{-26} \text{cm}^3 \text{s}^{-1}$ for $m_{\chi} = 10$ GeV and $b\bar{b}$ annihilation channel., Comment: 27 pages, 10 figures. Accepted for publication in JCAP

We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of the concerned spaces. In particular, it is shown that such a study is related to the preservation of k-smoothness and the extremal properties of the unit ball of a Banach space. As an application of the results obtained in this direction, we obtain a refinement of the well-known Blanco-Koldobsky-Turnsek characterization of isometries on some polyhedral Banach spaces, including $ \ell_{\infty}^n, \ell_1^n. $

The $^{246}$Cm(n,$\gamma$) and $^{248}$Cm(n,$\gamma$) cross-sections have been measured at the Experimental Area 2 (EAR2) of the n_TOF facility at CERN with three C$_6$D$_6$ detectors. This measurement is part of a collective effort to improve the capture cross-section data for Minor Actinides (MAs), which are required to estimate the production and transmutation rates of these isotopes in light water reactors and innovative reactor systems. In particular, the neutron capture in $^{246}$Cm and $^{248}$Cm open the path for the formation of other Cm isotopes and heavier elements such as Bk and Cf and the knowledge of (n,$\gamma$) cross-sections of these Cm isotopes plays an important role in the transport, transmutation and storage of the spent nuclear fuel. The reactions $^{246}$Cm(n,$\gamma$) and $^{248}$Cm(n,$\gamma$) have been the two first capture measurements analyzed at n_TOF EAR2. Until this experiment and two recent measurements performed at J-PARC, there was only one set of data of the capture cross-sections of $^{246}$Cm and $^{248}$Cm, that was obtained in 1969 in an underground nuclear explosion experiment. In the measurement at n_TOF a total of 13 resonances of $^{246}$Cm between 4 and 400 eV and 5 of $^{248}$Cm between 7 and 100 eV have been identified and fitted. The radiative kernels obtained for $^{246}$Cm are compatible with JENDL-5, but some of them are not with JENDL-4, which has been adopted by JEFF-3.3 and ENDF/B-VIII.0. The radiative kernels obtained for the first three $^{248}$Cm resonances are compatible with JENDL-5, however, the other two are not compatible with any other evaluation and are 20% and 60% larger than JENDL-5.

This article exploits group-IV germanium (Ge) quantum dots (QDs) on Silicon-on-Insulator (SOI) grown by molecular beam epitaxy (MBE) in order to explore its optical behaviour in the Terahertz (THz) regime. In this work, Ge QDs, pumped by an above bandgap near infrared wavelength, exhibit THz amplitude modulation in the frequency range of 0.1-1.0 THz. The epitaxial Ge QDs outperform reference SOI substrate in THz amplitude modulation owing to higher carrier generation in weakly confined dots compared to its bulk counterpart. This is further corroborated using theoretical model based on the non-equilibrium Green's function (NEGF) method. This model enables the calculation of photo carriers generated (PCG) and their confinement in the Ge QD region. Our model also reroutes the calculation from PCG to corresponding plasma frequency and hence to refractive index and THz photo-conductivity. Moreover, the photo-generated confined holes accumulation at the Ge QDs-Si interface is elevated after optical illumination, leading to a decreased THz photo-conductivity. This augmentation in THz photo-conductivity contributes to a significant enhancement of THz modulation depth ~77% at Ge QDs-Si interfaces compared to bare SOI at 0.1 THz., Comment: 15 pages, 5 figures

In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during emergencies such as earthquakes. However, previous approaches often assume that individuals are separable and identical, which does not adequately account for the fact that some groups of people, such as families, need to move together and that some groups may be more important than others. To address these limitations, we modify the minsum flow problem to support flows represented as discrete and weighted sets. We also propose a 2-approximation pseudo-polynomial time algorithm to solve this modified problem for path networks with uniform capacity.

The numba-mpi package offers access to the Message Passing Interface (MPI) routines from Python code that uses the Numba just-in-time (JIT) compiler. As a result, high-performance and multi-threaded Python code may utilize MPI communication facilities without leaving the JIT-compiled code blocks, which is not possible with the mpi4py package, a higher-level Python interface to MPI. For debugging purposes, numba-mpi retains full functionality of the code even if the JIT compilation is disabled. The numba-mpi API constitutes a thin wrapper around the C API of MPI and is built around Numpy arrays including handling of non-contiguous views over array slices. Project development is hosted at GitHub leveraging the mpi4py/setup-mpi workflow enabling continuous integration tests on Linux (MPICH, OpenMPI & Intel MPI), macOS (MPICH & OpenMPI) and Windows (MS MPI). The paper covers an overview of the package features, architecture and performance. As of v1.0, the following MPI routines are exposed and covered by unit tests: size/rank, [i]send/[i]recv, wait[all|any], test[all|any], allreduce, bcast, barrier, scatter/[all]gather & wtime. The package is implemented in pure Python and depends on numpy, numba and mpi4py (the latter used at initialization and as a source of utility routines only). The performance advantage of using numba-mpi compared to mpi4py is depicted with a simple example, with entirety of the code included in listings discussed in the text. Application of numba-mpi for handling domain decomposition in numerical solvers for partial differential equations is presented using two external packages that depend on numba-mpi: py-pde and PyMPDATA-MPI.

The SHALON atmospheric Cherenkov telescope has detected very high energy gamma-ray emission at TeV energies from eight red dwarfs, namely, V388 Cas, V547 Cas, V780 Tau, V962 Tau, V1589 Cyg, GJ 1078, GJ 3684 and GL 851.1. Consequently, these red dwarfs have been suggested as sources of ultra-high energy cosmic rays. In this work, we search for soft gamma-ray emission from these TeV bright red dwarfs between 0.75-30 MeV using archival data from the COMPTEL gamma-ray imaging telescope, as a follow-up to a similar search for GeV gamma-ray emission using the Fermi-LAT telescope. Although, prima-facie, we detect non-zero photon flux from three red dwarfs with high significance, these signals can attributed to contamination from nearby sources such as Crab and Cygnus, which are within the angular resolution of COMPTEL, and have been previously detected as very bright point sources at MeV energies. Therefore, we could not detect any statistically significant signal ($>3\sigma$) from any of these eight red dwarfs from 0.75-30 MeV. We then report the 95% confidence level upper limits on the differential photon flux (at 30 MeV), integral photon flux and integral energy flux for all of the eight red dwarfs. The integral energy flux limits range between $10^{-11}-10^{-10} \rm{ergs/cm^2/s}$., Comment: 10 pages, 12 figures. Accepted for publication in JCAP

This work comprises a study of the thermodynamic behavior of modified $f(\bar{R},\bar{T})$ gravity, which had been developed based on a non-canonical theory known as K-essence theory. In this development, we use the Dirac-Born-Infeld (DBI) type of non-standard Lagrangian. We develop a modified first law and generalized second law of thermodynamics (GSLT) within the modified $f(\bar{R},\bar{T})$ gravity, where we consider the background metric to be the usual Friedmann-Lema$\hat{\text{i}}$tre-Robertson-Walker (FLRW) type. A graphical analysis of surface gravity has been performed for the modified FLRW metric via the $f(\bar{R},\bar{T})$ theory, which is different from the usual FLRW gravity through the usual $f(R,T)$ gravity. Exponential and power law scale factors are used to analyze cosmic surface gravity. Through the investigation of the modified GSLT, using the relation of scale factor with the scalar field, we have seen that during the initial phase of the universe, the entropy's rate of change may be either negative or positive, contingent upon the value of the curvature constant. The negativity of the entropy change indicates that the modified GSLT is not feasible in that particular area for a particular curvature constant. These traits suggest that during the inflationary period, entropy might have been either negative or positive. It has also been seen that entropy saturates every curvature value at different time ranges, which indicates the heat death of the universe., Comment: 20 pages, 10 figures

In this paper we provide a characterization of sets of finite local and non local perimeter via a $\Gamma-$convergence result. As an application we give a proof of the isoperimetric inequality, both in the local and in the non local case.

This work is an analytical investigation of the evolution of surface water waves in Miles and Jeffreys theories of wind wave interaction in water of finite depth. The present review is divided into two major parts. The first corresponds to the surface water waves in a linear regime and its nonlinear extensions. In this part, Miles theory of wave amplification by wind is extended to the case of finite depth. The dispersion relation provides a wave growth rate depending on depth. Our theoretical results are in good agreement with the data from the Australian Shallow Water Experiment and the data from the Lake George experiment. In the second part of this study, Jeffreys theory of wave amplification by wind is extended to the case of finite depth, where the Serre-Green-Naghdi is derived. We find the solitary wave solution of the system, with an increasing amplitude under the action of the wind. This continuous increase in amplitude leads to the soliton breaking and blow-up of the surface wave in finite time. The theoretical blow-up time is calculated based on actual experimental data. By applying an appropriate perturbation method, the SGN equation yields Korteweg de Vries Burger equation (KdVB). We show that the continuous transfer of energy from wind to water results in the growth of the KdVB soliton amplitude, velocity, acceleration, and energy over time while its effective wavelength decreases. This phenomenon differs from the classical results of Jeffreys approach due to finite depth. Again, blow-up and breaking occur in finite time. These times are calculated and expressed for soliton- and wind-appropriate parameters and values. These values are measurable in usual experimental facilities. The kinematics of the breaking is studied, and a detailed analysis of the breaking time is conducted using various criteria. Finally, some integrability perspectives are presented.

We report a colloidal synthesis of blue emissive, stable cube-shaped CsPbBr3 quantum dots (QDs) in the strong quantum confinement regime via a dissolution-recrystallization starting from pre-synthesized (KxCs1-x)4PbBr6 nanocrystals which are then reacted with PbBr2. This is markedly different from the known case of Cs4PbBr6 nanocrystals that react within seconds with PbBr2 and get transformed into much larger, green emitting CsPbBr3 nanocrystals. Here, instead, the conversion of (KxCs1-x)4PbBr6 nanocrystals to CsPbBr3 QDs occurs in a time span of hours, and tuning of the QDs size is achieved by adjusting the concentration of precursors. The QDs exhibit excitonic features in optical absorption that are tunable in the 420 - 452 nm range, accompanied by blue photoluminescence with quantum yield around 60%. Detailed spectroscopic investigations in both the single and multi-exciton regime reveal the exciton fine structure and the effect of Auger recombination of these CsPbBr3 QDs, confirming theoretical predictions for this system.

We search for a redshift dependence of $\sigma_8^0$ using 23 growth rate measurements from redshift space distortions and peculiar velocity measurements as a consistency check of $\Lambda$CDM. For this purpose we use the dataset from arXiv:1806.10822 consisting of 22 measurements, which has been vetted for internal consistencies. Eighteen of these measurements have been obtained from the Gold-2017 sample, collated from multiple redshift space distortion surveys between 2009 and 2016, whereas the remaining four have been obtained from the eBOSS DR14 quasar survey. We also added one additional data point from the BOSS DR12 CMASS galaxy sample. We find that for this dataset the $\sigma_8^0$ values are consistent between the low redshift and high redshift samples using three different redshift cuts. This implies that the growth rate measurements are consistent with a constant $\sigma_8^0$ in accord with $\Lambda$CDM, assuming there are no uncontrolled systematics in this dataset., Comment: 6 pages, 3 figures. Accepted for publication in EPJC

It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in $\mathbb{P}^4 (\mathbb{F}_{q^2})$ has at most $d(q^5+q^2) + q^3 + 1$ points in common with a threefold of degree $d$ defined over $\mathbb{F}_{q^2}$. He proved the conjecture for $d=2$. In this paper, we show that the conjecture is true for $d = 3$ and $q \ge 7$.

In star formation regions, the complex organic molecules (COMs) that contain peptide bonds ($-$NH$-$C(=O)$-$) play a major role in the metabolic process because $-$NH$-$C(=O)$-$ is connected to amino acids (R-CHNH$_{2}$$-$COOH). Over the past few decades, many COMs containing peptide-like bonds have been detected in hot molecular cores (HMCs), hot corinos, and cold molecular clouds, however, their prebiotic chemistry is poorly understood. We present the first detection of the rotational emission lines of formamide (NH$_{2}$CHO) and isocyanic acid (HNCO), which contain peptide-like bonds toward the chemically rich HMC G358.93$-$0.03 MM1, using high-resolution and high-sensitivity Atacama Large Millimeter/submillimeter Array bands 6 and 7. We estimate that the column densities of NH$_{2}$CHO and HNCO toward G358.93$-$0.03 MM1 are (2.80$\pm$0.29)$\times$10$^{15}$ cm$^{-2}$ and (1.80$\pm$0.42)$\times$10$^{16}$ cm$^{-2}$ with excitation temperatures of 165 $\pm$ 21 K and 170 $\pm$ 32 K, respectively. The fractional abundances of NH$_{2}$CHO and HNCO toward G358.93$-$0.03 MM1 are (9.03$\pm$1.44)$\times$10$^{-10}$ and (5.80$\pm$2.09)$\times$10$^{-9}$. We compare the estimated abundances of NH$_{2}$CHO and HNCO with the existing three-phase warm-up chemical model abundance values and notice that the observed and modelled abundances are very close. We conclude that NH$_{2}$CHO is produced by the reaction of NH$_{2}$ and H$_{2}$CO in the gas phase toward G358.93$-$0.03 MM1. Likewise, HNCO is produced on the surface of grains by the reaction of NH and CO toward G358.93$-$0.03 MM1. We also find that NH$_{2}$CHO and HNCO are chemically linked toward G358.93$-$0.03 MM1., Comment: Published in Research in Astronomy and Astrophysics

Let G be a simple connected graph with vertex set V(G) and edge set E(G. Each vertex of V(G) is colored by a color from the set of colors {c_1, c_2,\dots, c_{\alpha}}. We take a subset S of V(G), such that for every vertex v in V(G)\S, at least one vertex of the same color is present in its set of nearest neighbors in S. We refer to such an S as a consistent subset (CS). The Minimum Consistent Subset (MCS) problem is the computation of a consistent subset of the minimum cardinality. It is established that MCS is NP-complete for general graphs, including planar graphs. The strict consistent subset is a variant of consistent subset problems. We take a subset S^{\prime} of V(G), such that for every vertex v in V(G)\S^{\prime}, all the vertices in its set of nearest neighbors in S^{\prime} have the same color as that of v. We refer to such an S^{\prime} as a strict consistent subset (SCS). The Minimum Strict Consistent Subset (MSCS) problem is the computation of a strict consistent subset of the minimum cardinality. We demonstrate that MSCS is NP-hard for general graphs using a reduction from dominating set problems. We construct a 2-approximation algorithm and a polynomial-time algorithm in trees. Lastly, we conclude the faster polynomial-time algorithms in paths, spiders, and combs.

Machine Learning (ML) potentials such as Gaussian Approximation Potential (GAP) have demonstrated impressive capabilities in mapping structure to properties across diverse systems. Here, we introduce a GAP model for low-dimensional Ni nanoclusters and demonstrate its flexibility and effectiveness in capturing the energetics, structural diversity and thermodynamic properties of Ni nanoclusters across a broad size range. Through a systematic approach encompassing model development, validation, and application, we evaluate the model's efficacy in representing energetics and configurational features in low-dimensional regimes, while also examining its extrapolative nature to vastly different spatiotemporal regimes. Our analysis and discussion shed light on the data quality required to effectively train such models. Trajectories from large scale MD simulations using the GAP model analyzed with data-driven models like Graph Neural Networks (GNN) reveal intriguing insights into the size-dependent phase behavior and thermo-mechanical stability characteristics of porous Ni nanoparticles. Overall, our work underscores the potential of ML models which coupled with data-driven approaches serve as versatile tools for studying low-dimensional systems and complex material dynamics.

In a connected simple graph G = (V,E), each vertex of V is colored by a color from the set of colors C={c1, c2,..., c_{\alpha}}$. We take a subset S of V, such that for every vertex v in V\S, at least one vertex of the same color is present in its set of nearest neighbors in S. We refer to such a S as a consistent subset. The Minimum Consistent Subset (MCS) problem is the computation of a consistent subset of the minimum size. It is established that MCS is NP-complete for general graphs, including planar graphs. We expand our study to interval graphs and circle graphs in an attempt to gain a complete understanding of the computational complexity of the \mcs problem across various graph classes. This work introduces an (4\alpha+ 2)- approximation algorithm for MCS in interval graphs where \alpha is the number of colors in the interval graphs. Later, we show that in circle graphs, MCS is APX-hard.