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We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size $L$. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles, respectively. We derive analytic results for the fluctuations in the number of particles exiting the boundaries of the finite confining box. The statistical properties of this quantity crucially depend on how the system is prepared initially. Two common types of averages employed to understand the impact of initial conditions in stochastic systems are annealed and quenched averages. It is well known that for an infinitely extended system, these different initial conditions produce quantitatively different fluctuations, even in the infinite time limit. We demonstrate explicitly that in finite systems, annealed and quenched fluctuations become equal beyond a system-size dependent timescale, $t \sim L^2$. For diffusing particles, the fluctuations exhibit a $\sqrt{t}$ growth at short times and decay as $1/\sqrt{t}$ for time scales, $t \gg L^2/D$, where $D$ is the diffusion constant. Meanwhile, for run-and-tumble particles, the fluctuations grow linearly at short times and then decay as $1/\sqrt{t}$ for time scales, $t \gg L^2/D_{\text{eff}}$, where $D_{\text{eff}}$ represents the effective diffusive constant for run-and-tumble particles. To study the effect of confinement in detail, we also analyze two different setups (i) with one reflecting boundary and (ii) with both boundaries open., Comment: 15 pages, 8 figures

In this paper, over a field of positive characteristic we exhibit an infinite family of counter examples to the Zariski Cancellation Problem in higher dimensions ($\geqslant 3$) which are pairwise non-isomorphic and also non-isomorphic to the existing family of counter examples, demonstrated by Gupta in \cite{adv}.

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv., Comment: On International Conference on Machine Learning (ICML) 2024

Understanding the atmospheric parameters of stars on the top of the RGB is essential to reveal the chemical composition of the Milky Way, as they can be used to probe the farthest parts of our Galaxy. Our goal is to determine the chemical composition of 21 RGB stars with $T_{\mathrm{eff}}<4200$K selected from the APOGEE-2 DR17 database using new observations carried out with the spectrograph mounted on the 1-m telescope of the Hungarian Piszk\'estet\H{o} Observatory and the SONG spectrograph (R=77000) on the Hertzsprung SONG telescope in the 4500$-$5800\r{A} wavelength range. This is the first time the spectrograph (R=18000) on the 1-m telescope at Piszk\'estet\H{o} Observatory was used to measure the abundances of stars. We created a new LTE spectral library using MARCS model atmospheres and SYNSPEC by including the line list of 23 molecules to determine atmospheric parameters ($T_{\mathrm{eff}}$, $\log g$, [Fe/H], [$\alpha$/Fe]) and abundances of Si, Ca, Ti, V, Cr, Mn, and Ni with FERRE. The resulting parameters were compared to that of APOGEE. We found a good agreement in general, the average difference is $-$11.2K in $T_{\mathrm{eff}}$, 0.11dex in $\log g$, 0.10dex in [Fe/H], and $-$0.01dex in [$\alpha$/Fe]. Our analysis successfully demonstrates the ability of the spectrograph at Piszk\'estet\H{o} Observatory to reliably measure the abundance of bright stars., Comment: Accepted for publication in PASP, 18 pages, 6 figures

Swarmalators are entities that swarm through space and sync in time and are potentially considered to replicate the complex dynamics of many real-world systems. So far, the internal dynamics of swarmalators have been taken as a phase oscillator inspired by the Kuramoto model. Here, for the first time, we examine the internal dynamics utilizing an amplitude oscillator capable of exhibiting periodic and chaotic behaviors. To incorporate the dual interplay between spatial and internal dynamics, we propose a general model that keeps the properties of swarmalators intact. This adaptation calls for a detailed study which we present in this paper. We establish our study with the Rossler oscillator by taking parameters from both the chaotic and periodic regions. While the periodic oscillator mimics most of the patterns in the previous phase oscillator model, the chaotic oscillator brings some new fascinating states., Comment: 12 pages, 9 figures; Accepted for publication in Physical Review E (2024)

Passive and active targets, implanted with gold nanoprisms, were designed to achieve enhanced and uniform power absorption during two-sided illumination by short laser pulses. The target length was adjusted to match the short laser pulse-length. Capabilities of three different, uniform, single-peaked Gaussian and adjusted, nanoresonator number density distributions were compared. The average local E-field inside the gain medium and on the surface of the nanoprisms were mapped as a function of the pump E-field strength and dye concentration, assuming a uniform nanoresonator distribution. The optimal parameters were adopted to each inspected nanoprism distributions. The time-evolution of the near-field enhancement (NFE), integrated power-loss and deposited energy were determined, additionally, the time-evolution of the standard deviation of these quantities was monitored. A comparative study was performed on passive and active targets, to determine the most advantageous nanoprism number density distribution type and to consider the advantages of dye doping. Based on the results, the adjusted distribution is proposed both in passive and active targets. Doping with the dye is advantageous in every inspected distribution in decreasing the minimal standard deviation of the NFE. It is advantageous in decreasing the delay of the minimal standard deviation in the power-loss and deposited energy, the standard deviation of the NFE as well as in increasing the FOM of the NFE in the uniform and adjusted distributions. In addition, doping allows for decreasing the delay of the minimal standard deviation in the NFE / increasing the mean NFE / decreasing the standard deviation of the power-loss and deposited energy in the uniform / Gaussian / adjusted distribution.

We carry out deep near-ultraviolet (NUV) and far-ultraviolet (FUV) imaging of an interacting galaxy system, comprised of a Seyfert type 1 galaxy NGC 7469 and its companion IC 5283. Our aim is to resolve and map the star-forming regions in the outer arms and look for signs of interaction between the two galaxies. We used AstroSat Ultra Violet Imaging Telescope (UVIT) to obtain NUV and FUV images of NGC 7469 in a range of filters. We have carried out photometry of star-forming regions in the two galaxies and found their spatial distributions. We also obtained the distributions of star formation rates (SFR) in NGC 7469 and IC 5283 using the estimates obtained from the FUV and NUV bands. We also carried out Kolmogorov-Smirnov tests to look for differences in the SFRs in the two galaxies. We derived the spectral energy distribution (SED), leading to the determination of physical parameters, including the overall SFR, stellar mass ($\text{M}_{*}$), dust mass ($\text{M}_\text{Dust}$), and specific star formation rates (sSFRs) in both the galaxies. Our NUV and FUV images show the presence of an outer spiral arm that is better resolved. We have identified 33 new star-forming regions out of 51 total identified in the UVIT composite image. Enhanced star formation activity is observed to coincide with the interaction, and KS tests show that there are no significant differences in the SFR distributions of NGC 7469 and IC 5283, indicating that the interaction between the galaxies has not influenced their star formation processes differently. The SED plots and the photometric results demonstrate that most of the star formation activity is confined inside the central starburst (SB) ring., Comment: 13 pages, 7 figures, 6 tables. Paper accepted for publication in the Astronomy & Astrophysics (A&A)

Amino acids are essential for the synthesis of protein. Amino acids contain both amine (R$-$NH$_{2}$) and carboxylic acid (R$-$COOH) functional groups, which help to understand the possible formation mechanism of life in the universe. Among the 20 types of amino acids, glycine (NH$_{2}$CH$_{2}$COOH) is known as the simplest non-essential amino acid. In the last 40 years, all surveys of NH$_{2}$CH$_{2}$COOH in the interstellar medium, especially in the star-formation regions, have failed at the millimeter and sub-millimeter wavelengths. We aimed to identify the possible precursors of NH$_{2}$CH$_{2}$COOH, because it is highly challenging to identify NH$_{2}$CH$_{2}$COOH in the interstellar medium. Many laboratory experiments have suggested that methylenimine (CH$_{2}$NH) plays a key role as a possible precursor of NH$_{2}$CH$_{2}$COOH in the star-formation regions via the Strecker synthesis reaction. After spectral analysis using the local thermodynamic equilibrium (LTE) model, we successfully identified the rotational emission lines of CH$_{2}$NH towards the hot molecular core G10.47+0.03 using the Atacama Compact Array (ACA). The estimated column density of CH$_{2}$NH towards G10.47+0.03 is (3.40$\pm$0.2)$\times$10$^{15}$ cm$^{-2}$ with a rotational temperature of 218.70$\pm$20 K, which is estimated from the rotational diagram. The fractional abundance of CH$_{2}$NH with respect to H$_{2}$ towards G10.47+0.03 is 2.61$\times$10$^{-8}$. We found that the derived abundance of CH$_{2}$NH agree fairly well with the existing two-phase warm-up chemical modelling abundance value of CH$_{2}$NH. We discuss the possible formation pathways of CH$_{2}$NH within the context of hot molecular cores, and we find that CH$_{2}$NH is likely mainly formed via neutral-neutral gas-phase reactions of CH$_{3}$ and NH radicals towards G10.47+0.03., Comment: Accepted for publication in International Journal of Astrobiology. arXiv admin note: text overlap with arXiv:2402.16798

Performance modeling is a key issue in queuing theory and operation research. It is well-known that the length of a queue that awaits service or the time spent by a job in a queue depends not only on the service rate, but also crucially on the fluctuations in service time. The larger the fluctuations, the longer the delay becomes and hence, this is a major hindrance for the queue to operate efficiently. Various strategies have been adapted to prevent this drawback. In this perspective, we investigate the effects of one such novel strategy namely resetting or restart, an emerging concept in statistical physics and stochastic complex process, that was recently introduced to mitigate fluctuations-induced delays in queues. In particular, we show that a service resetting mechanism accompanied with an overhead time can remarkably shorten the average queue lengths and waiting times. We examine various resetting strategies and further shed light on the intricate role of the overhead times to the queuing performance. Our analysis opens up future avenues in operation research where resetting-based strategies can be universally promising., Comment: Invited Perspective article to Journal of Physics: Complexity

With the STAR experiment at the BNL Relativisic Heavy Ion Collider, we characterize $\sqrt{s_\mathrm{NN}}$ = 200 GeV p+Au collisions by event activity (EA) measured within the pseudorapidity range $eta$ $in$ [-5, -3.4] in the Au-going direction and report correlations between this EA and hard- and soft- scale particle production at midrapidity ($\eta$ $\in$ [-1, 1]). At the soft scale, charged particle production in low-EA p+Au collisions is comparable to that in p+p collisions and increases monotonically with increasing EA. At the hard scale, we report measurements of high transverse momentum (pT) jets in events of different EAs. In contrast with the soft particle production, high-pT particle production and EA are found to be inversely related. To investigate whether this is a signal of jet quenching in high-EA events, we also report ratios of pT imbalance and azimuthal separation of dijets in high- and low-EA events. Within our measurement precision, no significant differences are observed, disfavoring the presence of jet quenching in the highest 30% EA p+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 200 GeV., Comment: 12 page, 9 figures

We investigate the instabilities and associated bifurcation structure near the onset of rotating magnetoconvection of low Prandtl number fluids by performing three dimensional direct numerical simulations. Previous studies considered zero magnetic Prandtl number ($\mathrm{Pm}$) limit for the investigation of bifurcation structure near the onset of convection. Here we numerically investigate the effect of $\mathrm{Pm}$ on the bifurcation structure. The classical Rayleigh-B\'{e}nard convection setup in the presence of horizontal magnetic field and rotation about the vertical axis are considered for the study. The control parameters, including the Taylor number ($\mathrm{Ta}$), Chandrasekhar number ($\mathrm{Q}$), reduced Rayleigh number ($\mathrm{r}$), and magnetic Prandtl number ($\mathrm{Pm}$) are varied in the ranges $0 < \mathrm{Ta}\leq 500$, $0 < \mathrm{Q}\leq 1000$, $0.8\leq \mathrm{r} \leq 2$ and $0 < \mathrm{Pm} < 1$ by considering Prandtl numbers $\mathrm{Pr}= 0.025$ and $0.1$. The investigation reveals the presence of supercritical, subcritical and hybrid transitions to convection. These transitions leads to infinitesimal and finite amplitude fluid patterns at the onset of convection. The finite amplitude solutions can be both stationary and time dependent. The bifurcation structures associated with these flow patterns at the onset are studied in detail. For very small $\mathrm{Pm}$, the bifurcation structure is found to be qualitatively similar to the ones observed in the $\mathrm{Pm}\rightarrow 0$ limit. However, as $\mathrm{Pm}$ is increased, several new solutions appear at the onset and the resulting bifurcation structures are greatly modified., Comment: 32 pages, 22 figures (Submitted to journal)

We report exchange bias (EB) in single-phase CoO nanoparticles, where two magnetic phases naturally emerge as the crystallite size decreases from 34.6 to 10.8 nm. The N\'eel temperature (TN) associated with antiferromagnetic ordering decreases monotonically with the reduction in crystallite size, highlighting the significant influence of size effects. The 34.6 nm nanoparticles exhibit magnetization irreversibility between zero field cooled (ZFC) and field-cooled (FC) states below TN. This irreversibility appears well above TN with further reduction in size, resulting in the absence of true paramagnetic regime which indicates the occurrence of an additional magnetic phase. The frequency-dependent ac-susceptibility in 10.8 nm nanoparticles suggests slow dynamics of disordered surface spins above TN, coinciding with the establishment of long-range order in the core. The thermoremanent magnetization (TRM) and isothermoremanent magnetization (IRM) curves suggest a core-shell structure: the core is antiferromagnetic, and the shell consists of disordered surface spins causing ferromagnetic interaction. Hence, the exchange bias in these CoO nanoparticles results from the exchange coupling between an antiferromagnetic core and a disordered shell that exhibits unconventional surface spin characteristics., Comment: 33 Pages, 9 figures

We do a careful investigation of the prospects of dark energy (DE) interacting with cold dark matter (CDM) in alleviating the $S_8$ clustering tension. To this end, we consider various well-known parametrizations of the DE equation of state (EoS), and consider perturbations in both the dark sectors, along with an interaction term. Moreover, we perform a separate study for the phantom and non-phantom regimes. Using CMB, BAO and SNIa datasets, the constraints on the model parameters for each case have been obtained and a generic reduction in the $H_0-\sigma_{8,0}$ correlation has been observed, both for constant and dynamical DE EoS. This reduction, coupled with a significant negative correlation between the interaction term and $\sigma_{8,0}$, contributes to easing the clustering tension by lowering $\sigma_{8,0}$ to somewhere in between the early CMB and late-time clustering measurements for the phantom regime, for almost all the models under consideration. In addition, this is achieved without exacerbating the Hubble tension. In this regard, the CPL and JBP models perform the best in relaxing the $S_8$ tension to $<1\sigma$. However, for the non-phantom regime the $\sigma_{8,0}$ tension tends to have worsened, which reassures the merits of phantom dark energy from latest data. We further do an investigation of the role of RSD datasets and find an overall reduction in tension, with a value of $\sigma_{8,0}$ relatively closer to the CMB value. We finally check if further extensions of this scenario, like the inclusion of the sound speed of dark energy and warm dark matter interacting with DE, can have some effects., Comment: 23 pages, 12 sets of figures, 7 tables

Nonlinear effects in microresonators are efficient building blocks for all-optical computing and telecom systems. With the latest advances in microfabrication, coupled microresonators are used in a rapidly growing number of applications. In this work, we investigate the coupling between twin-resonators in the presence of Kerr-nonlinearity. We use an experimental setup with controllable coupling between two high-Q resonators and discuss the effects caused by the simultaneous presence of linear and non-linear coupling between the optical fields. Linear-coupling-induced mode splitting is observed at low input powers, with the controllable coupling leading to a tunable mode splitting. At high input powers, the hybridized resonances show spontaneous symmetry breaking (SSB) effects, in which the optical power is unevenly distributed between the resonators. Our experimental results are supported by a detailed theoretical model of nonlinear twin-resonators. With the recent interest in coupled resonator systems for neuromorphic computing, quantum systems, and optical frequency comb generation, our work provides important insights into the behavior of these systems at high circulating powers., Comment: 11 pages, 5 figures

The conventional low-energy theory employed to describe twisted bilayer graphene (TBG) relies on a local interlayer Hamiltonian. According to this theory, TBG has the same linear-in-momentum dispersion and spinor wave function at the Dirac point as single-layer graphene (SLG), albeit with a renormalized velocity that decreases as the rotation angle between the layers decreases, eventually reaching zero at the magic angle. In this work, I expand upon this low-energy theory by including nonlocal terms in the interlayer part of the Hamiltonian, and explore the consequences at the Dirac point. It is found that the nonlocality predominantly influences the wave function rather than the energy spectrum: despite the persistence of the linear-in-momentum dispersion with a renormalized velocity, the wave functions no longer mirror those of SLG. Instead, an additional contribution to the phase difference between the sublattice components of the spinor emerges. This gives rise to interesting effects in scattering which are demonstrated with a simple example.

Navigation of wheeled vehicles on uneven terrain necessitates going beyond the 2D approaches for trajectory planning. Specifically, it is essential to incorporate the full 6dof variation of vehicle pose and its associated stability cost in the planning process. To this end, most recent works aim to learn a neural network model to predict the vehicle evolution. However, such approaches are data-intensive and fraught with generalization issues. In this paper, we present a purely model-based approach that just requires the digital elevation information of the terrain. Specifically, we express the wheel-terrain interaction and 6dof pose prediction as a non-linear least squares (NLS) problem. As a result, trajectory planning can be viewed as a bi-level optimization. The inner optimization layer predicts the pose on the terrain along a given trajectory, while the outer layer deforms the trajectory itself to reduce the stability and kinematic costs of the pose. We improve the state-of-the-art in the following respects. First, we show that our NLS based pose prediction closely matches the output from a high-fidelity physics engine. This result coupled with the fact that we can query gradients of the NLS solver, makes our pose predictor, a differentiable wheel-terrain interaction model. We further leverage this differentiability to efficiently solve the proposed bi-level trajectory optimization problem. Finally, we perform extensive experiments, and comparison with a baseline to showcase the effectiveness of our approach in obtaining smooth, stable trajectories., Comment: 8 pages, 7 figures, submitted to IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2024)

For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other conservative schemes. However, our work reveals a more fundamental culprit: the smooth Heaviside and delta functions inherent to the standard formulation. Even if reinitialization is done exactly, i.e., the zero contour interface remains stationary, the use of smooth functions lead to violation of mass conservation. We propose a novel approach using variational analysis to incorporate a mass conservation constraint. This introduces a Lagrange multiplier that enforces overall mass balance. Notably, as the delta function sharpens, i.e., approaches the Dirac delta limit, the Lagrange multiplier approaches zero. However, the exact Lagrange multiplier method disrupts the signed distance property of the level set function. This motivates us to develop an approximate version of the Lagrange multiplier that preserves both overall mass and signed distance property of the level set function. Our framework even recovers existing mass-conserving level set methods, revealing some inconsistencies in prior analyses. We extend this approach to three-phase flows for fluid-structure interaction (FSI) simulations. We present variational equations in both immersed and non-immersed forms, demonstrating the convergence of the former formulation to the latter when the body delta function sharpens. Rigorous test problems confirm that the FSI dynamics produced by our simple, easy-to-implement immersed formulation with the approximate Lagrange multiplier method are accurate and match state-of-the-art solvers.

The observation of oxygen (O)- and nitrogen (N)-bearing molecules gives an idea about the complex prebiotic chemistry in the interstellar medium (ISM). In this article, we present the identification of the rotational emission lines of N-bearing molecules ethyl cyanide (C$_{2}$H$_{5}$CN), cyanoacetylene (HC$_{3}$N), and O-bearing molecules methyl formate (CH$_{3}$OCHO) towards high-mass protostar IRAS 18089$-$1732 using the Atacama Compact Array (ACA). We also detected the emission lines of both N- and O-bearing molecule formamide (NH$_{2}$CHO) in the envelope of IRAS 18089$-$1732. We have detected the $v$ = 0 and 1 states rotational emission lines of CH$_{3}$OCHO. We also detected the two vibrationally excited states of HC$_{3}$N ($v$7 = 1 and $v$7 = 2). The estimated fractional abundances of C$_{2}$H$_{5}$CN, HC$_{3}$N ($v$7 = 1), HC$_{3}$N ($v$7 = 2), and NH$_{2}$CHO towards the IRAS 18089$-$1732 are (1.40$\pm$0.5)$\times$10$^{-10}$, (7.5$\pm$0.7)$\times$10$^{-11}$, (3.1$\pm$0.4)$\times$10$^{-11}$, and (6.25$\pm$0.82)$\times$10$^{-11}$. Similarly, the estimated fractional abundances of CH$_{3}$OCHO ($v$ = 0) and CH$_{3}$OCHO ($v$ = 1) are (1.90$\pm$0.9)$\times$10$^{-9}$ and (8.90$\pm$0.8)$\times$10$^{-10}$, respectively. We also created the integrated emission maps of the detected molecules, and the observed molecules may have originated from the extended envelope of the protostar. We show that C$_{2}$H$_{5}$CN and HC$_{3}$N are most probably formed via the subsequential hydrogenation of the CH$_{2}$CHCN and the reaction between C$_{2}$H$_{2}$ and CN on the grain surface of IRAS 18089$-$1732. We found that NH$_{2}$CHO is probably produced due to the reaction between NH$_{2}$ and H$_{2}$CO in the gas phase. Similarly, CH$_{3}$OCHO is possibly created via the reaction between radical CH$_{3}$O and radical HCO on the grain surface of IRAS 18089$-$1732., Comment: Published in Research in Astronomy and Astrophysics

Liu, Pach and S\'andor recently characterized all polynomials $p(z)$ such that the equation $x+y=p(z)$ is $2$-Ramsey, that is, any $2$-coloring of $\mathbb{N}$ contains infinitely many monochromatic solutions for $x+y=p(z)$. In this paper, we find asymptotically tight bounds for the following two quantitative questions. $\bullet$ For $n\in \mathbb{N}$, what is the longest interval $[n,f(n)]$ of natural numbers which admits a $2$-coloring with no monochromatic solutions of $x+y=p(z)$? $\bullet$ For $n\in \mathbb{N}$ and a $2$-coloring of the first $n$ integers $[n]$, what is the smallest possible number $g(n)$ of monochromatic solutions of $x+y=p(z)$? Our theorems determine $f(n)$ up to a multiplicative constant $2+o(1)$, and determine the asymptotics for $g(n)$.

Generating VectorArt from text prompts is a challenging vision task, requiring diverse yet realistic depictions of the seen as well as unseen entities. However, existing research has been mostly limited to the generation of single objects, rather than comprehensive scenes comprising multiple elements. In response, this work introduces SVGCraft, a novel end-to-end framework for the creation of vector graphics depicting entire scenes from textual descriptions. Utilizing a pre-trained LLM for layout generation from text prompts, this framework introduces a technique for producing masked latents in specified bounding boxes for accurate object placement. It introduces a fusion mechanism for integrating attention maps and employs a diffusion U-Net for coherent composition, speeding up the drawing process. The resulting SVG is optimized using a pre-trained encoder and LPIPS loss with opacity modulation to maximize similarity. Additionally, this work explores the potential of primitive shapes in facilitating canvas completion in constrained environments. Through both qualitative and quantitative assessments, SVGCraft is demonstrated to surpass prior works in abstraction, recognizability, and detail, as evidenced by its performance metrics (CLIP-T: 0.4563, Cosine Similarity: 0.6342, Confusion: 0.66, Aesthetic: 6.7832). The code will be available at https://github.com/ayanban011/SVGCraft.

Numerous study on natural and man made systems including rotating convection report the phenomena of supercritical and subcritical transitions from one state to another with the variation of relevant control parameters. However, the complexity of the rotating convection system even under the idealized Rayleigh-B\'enard geometry, hindered the simplest possible description of these transitions to convection. Here we present an one dimensional description of the stationary subcritical and supercritical transitions to rotating Rayleigh-B\'enard convection both for rigid and free-slip boundary conditions. The analysis of the one dimensional models and performance of three dimensional direct numerical simulations of the system show qualitatively similar results in a wide region of the parameter space. A brief discussion on time dependent convection of overstable origin is also presented.

Evaluating autonomous vehicle stacks (AVs) in simulation typically involves replaying driving logs from real-world recorded traffic. However, agents replayed from offline data are not reactive and hard to intuitively control. Existing approaches address these challenges by proposing methods that rely on heuristics or generative models of real-world data but these approaches either lack realism or necessitate costly iterative sampling procedures to control the generated behaviours. In this work, we take an alternative approach and propose CtRL-Sim, a method that leverages return-conditioned offline reinforcement learning (RL) to efficiently generate reactive and controllable traffic agents. Specifically, we process real-world driving data through a physics-enhanced Nocturne simulator to generate a diverse offline RL dataset, annotated with various rewards. With this dataset, we train a return-conditioned multi-agent behaviour model that allows for fine-grained manipulation of agent behaviours by modifying the desired returns for the various reward components. This capability enables the generation of a wide range of driving behaviours beyond the scope of the initial dataset, including adversarial behaviours. We show that CtRL-Sim can generate realistic safety-critical scenarios while providing fine-grained control over agent behaviours., Comment: CoRL 2024

Ultra-hot Jupiters (UHJs) orbiting pulsating A/F stars represent an important subset of the exoplanetary demographic, as they are excellent candidates for the study of exoplanetary atmospheres, as well as being astrophysical laboratories for the investigation of planet-to-star interactions. We analyse the \texttt{TESS} (Transiting Exoplanet Survey Satellite) light curve of the WASP-167 system, consisting of an F1V star and a substellar companion on a $\sim 2.02$ day orbit. We model the combination of the ellipsoidal variability and the Doppler beaming to measure the mass of WASP-167b, and the reflection effect to obtain constraints on the geometric albedo, while placing a special emphasis on noise separation. We implement a basic model to determine the dayside ($T_{\rm Day}$), nightside ($T_{\rm Night}$) and intrinsic ($T_{\rm Internal}$) temperatures of WASP-167b and put a constraint on its Bond albedo. We confirm the transit parameters of the planet seen in the literature. We find that a resonant $\sim 2P^{-1}$ stellar signal (which may originate from planet-to-star interactions) interferes with the phase curve analysis. After considerate treatment of this signal, we find $M_p = 0.34 \pm 0.22$~$M_J$. We measure a dayside temperature of $2790 \pm 100$ K, classifying WASP-167b as an UHJ. We find a $2\sigma$ upper limit of $0.51$ on its Bond albedo, and determine the geometric albedo at $0.34 \pm 0.11$ ($1 \sigma$ uncertainty). With an occultation depth of $106.8 \pm 27.3$ ppm in the \texttt{TESS} passband, the UHJ WASP-167b will be an excellent target for atmospheric studies, especially those at thermal wavelength ranges, where the stellar pulsations are expected to be be less influential., Comment: 19 pages, 15 figures, resubmitted to Astronomy and Astrophysics after minor revision

We report the observation of two additional sub-natural line width quantum interference in the $D_2$ manifold of $^{39}K$ vapor, in addition to the usual single Electromagnetically induced transparency peak. The other two features appear exclusively because $^{39}K$ ground hyperfine splitting is smaller than the Doppler broadened absorption profile. This allows probe and control beams to swap their transition pathways. The control beam detuning captures the nature of the coherence, therefore an unusual phenomenon of conversion from perfect transparency to enhanced absorption is observed and explained by utilizing adiabatic elimination of the excited state in the Master equation. Controlling such dark and bright resonances leads to new applications in quantum technologies viz. frequency offset laser stabilization and long-lived quantum memory., Comment: 16 pages, 11 figures

In recent decades, linear affine threefolds have enabled researchers to solve some of the challenging problems on affine spaces. Koras-Russell threefolds, especially the Russell Cubic over $\mathbb{C}$ and Asanuma threefolds over a field of positive characteristic, are striking examples of such linear threefolds.In this paper, we apply tools from $K$-theory and theory of $\mathbb{G}_a$-actions to linear threefolds of the form $G:=a(X)Y-F(X,Z,T)\in k[X,Y,Z,T]$, over an arbitrary field $k$. We give some equivalent conditions for $G$ to be a hyperplane (i.e., $k[X,Y,Z,T]/(G)=k^{[3]}$) in the following cases: (i) $k$ is a field of characteristic zero (ii) $k$ is an arbitrary field and $a(X)$ has only multiple roots. We also establish the Abhyankar-Sathaye Conjecture affirmatively in these cases., Comment: The earlier version is named as : On Abhyankar-Sathaye Conjecture for a family of linear hypersurfaces in $\mathbb{A}_{k}^4$

We present a reciprocity calibration method for dual-antenna repeaters in wireless networks. The method uses bi-directional measurements between two network nodes, A and B, where for each bi-directional measurement, the repeaters are configured in different states. The nodes A and B could be two access points in a distributed MIMO system, or they could be a base station and a mobile user terminal, for example. From the calibration measurements, the differences between the repeaters' forward and reverse gains are estimated. The repeaters are then (re-)configured to compensate for these differences such that the repeaters appear, transparently to the network, as reciprocal components of the propagation environment, enabling reciprocity-based beamforming in the network., Comment: published version, misprint corrected

We study the Mpemba effect on a non-equilibrium Markov chain that mimics the run and tumble motion of an active particle in a discrete energy landscape. The broken detailed balance, rendered by the activity, gives rise to a unique anomalous relaxation in the system which is distinctly different than the typical equilibrium systems. We observe that the activity can both suppress or induce the Mpemba effect. Furthermore, we report an oscillatory Mpemba effect where the relaxation trajectories, emanating from the hot and cold initial conditions, cross each other multiple times and this occurs due to the emergence of complex eigenvalues in the relaxation spectrum due to the activity. Our work reveals a possible pathway for studying the Mpemba effect in active living systems where broken detailed balance is crucial to achieve many biological functions.

Thresholding of networks has long posed a challenge in brain connectivity analysis. Weighted networks are typically binarized using threshold measures to facilitate network analysis. Previous studies on MRI-based brain networks have predominantly utilized density or sparsity-based thresholding techniques, optimized within specific ranges derived from network metrics such as path length, clustering coefficient, and small-world index. Thus, determination of a single threshold value for facilitating comparative analysis of networks remains elusive. To address this, our study introduces Mutual K-Nearest Neighbor (MKNN)-based thresholding for brain network analysis. Here, nearest neighbor selection is based on the highest correlation between features of brain regions. Construction of brain networks was accomplished by computing Pearson correlations between grey matter volume and white matter volume for each pair of brain regions. Structural MRI data from 180 Parkinsons patients and 70 controls from the NIMHANS, India were analyzed. Subtypes within Parkinsons disease were identified based on grey and white matter volume atrophy using source-based morphometric decomposition. The loading coefficients were correlated with clinical features to discern clinical relationship with the deciphered subtypes. Our data-mining approach revealed: Subtype A (N = 51, intermediate type), Subtype B (N = 57, mild-severe type with mild motor symptoms), and Subtype AB (N = 36, most-severe type with predominance in motor impairment). Subtype-specific weighted matrices were binarized using MKNN-based thresholding for brain network analysis. Permutation tests on network metrics of resulting bipartite graphs demonstrated significant group differences in betweenness centrality and participation coefficient. The identified hubs were specific to each subtype, with some hubs conserved across different subtypes., Comment: 31 pages, 10 figures, 3 tables

Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for complex system models remains a challenge. This paper presents NonlinearSolve.jl - a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for GPU-accelerated computation through static array kernels, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as Sundials and MINPACK, NonlinearSolve.jl demonstrates unparalleled robustness and efficiency, achieving significant advancements in solving benchmark problems and challenging real-world applications. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.

In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two., Comment: arXiv admin note: text overlap with arXiv:1608.02125 by other authors

In this work, we study ad conversion measurement, a central functionality in digital advertising, where an advertiser seeks to estimate advertiser website (or mobile app) conversions attributed to ad impressions that users have interacted with on various publisher websites (or mobile apps). Using differential privacy (DP), a notion that has gained in popularity due to its strong mathematical guarantees, we develop a formal framework for private ad conversion measurement. In particular, we define the notion of an operationally valid configuration of the attribution rule, DP adjacency relation, contribution bounding scope and enforcement point. We then provide, for the set of configurations that most commonly arises in practice, a complete characterization, which uncovers a delicate interplay between attribution and privacy., Comment: To appear in PoPETS 2024

This work addresses the buyer's inspection paradox for information markets. The paradox is that buyers need to access information to determine its value, while sellers need to limit access to prevent theft. To study this, we introduce an open-source simulated digital marketplace where intelligent agents, powered by language models, buy and sell information on behalf of external participants. The central mechanism enabling this marketplace is the agents' dual capabilities: they not only have the capacity to assess the quality of privileged information but also come equipped with the ability to forget. This ability to induce amnesia allows vendors to grant temporary access to proprietary information, significantly reducing the risk of unauthorized retention while enabling agents to accurately gauge the information's relevance to specific queries or tasks. To perform well, agents must make rational decisions, strategically explore the marketplace through generated sub-queries, and synthesize answers from purchased information. Concretely, our experiments (a) uncover biases in language models leading to irrational behavior and evaluate techniques to mitigate these biases, (b) investigate how price affects demand in the context of informational goods, and (c) show that inspection and higher budgets both lead to higher quality outcomes.

The main goal of this paper to introduce a new model of evolvement of narratives (common opinions, information bubble) on networks. Our main tools come from invariant mean theory and graph theory. The case, when the root set of the network (influencers, news agencies, etc.) is ergodic is fully discussed. The other possibility, when the root contains more than one component is partially discussed and it could be a motivation for further research.

Uncertainty in medical image segmentation tasks, especially inter-rater variability, arising from differences in interpretations and annotations by various experts, presents a significant challenge in achieving consistent and reliable image segmentation. This variability not only reflects the inherent complexity and subjective nature of medical image interpretation but also directly impacts the development and evaluation of automated segmentation algorithms. Accurately modeling and quantifying this variability is essential for enhancing the robustness and clinical applicability of these algorithms. We report the set-up and summarize the benchmark results of the Quantification of Uncertainties in Biomedical Image Quantification Challenge (QUBIQ), which was organized in conjunction with International Conferences on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2020 and 2021. The challenge focuses on the uncertainty quantification of medical image segmentation which considers the omnipresence of inter-rater variability in imaging datasets. The large collection of images with multi-rater annotations features various modalities such as MRI and CT; various organs such as the brain, prostate, kidney, and pancreas; and different image dimensions 2D-vs-3D. A total of 24 teams submitted different solutions to the problem, combining various baseline models, Bayesian neural networks, and ensemble model techniques. The obtained results indicate the importance of the ensemble models, as well as the need for further research to develop efficient 3D methods for uncertainty quantification methods in 3D segmentation tasks., Comment: initial technical report

This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for KL Divergence has proven elusive. Past approaches relied on computationally demanding Monte Carlo methods, motivating our introduction of a novel variational approach. Our method offers a closed-form solution, significantly enhancing computational efficiency for swift model comparisons and robust estimation evaluations. Validation using real and simulated data showcases its superior efficiency and accuracy over traditional Monte Carlo-based methods, opening new avenues for rapid exploration of diverse DMM models and advancing statistical analyses of compositional data.

We have identified nearly a hundred close triply eclipsing hierarchical triple star systems from data taken with the space telescope TESS. These systems are noteworthy in that we can potentially determine their dynamical and astrophysical parameters with a high precision. In the present paper, we report the comprehensive study of seven new compact triply eclipsing triple star systems taken from this larger sample: TICs 133771812, 176713425, 185615681, 287756035, 321978218, 323486857, and 650024463. Most of the data for this study come from TESS observations, but two of them have Gaia measurements of their outer orbits, and we obtained supplemental radial velocity (RV) measurements for three of the systems. The eclipse timing variation curves extracted from the TESS data, the photometric light curves, the RV points, and the spectral energy distribution (SED) are combined in a complex photodynamical analysis to yield the stellar and orbital parameters of all seven systems. Four of the systems are quite compact with outer periods in the range of 41-56 days. All of the systems are substantially flat, with mutual inclination angles of < ~2 degrees. Including the systems reported in this work, we have now studied in considerable detail some 30 triply eclipsing triples with TESS, and are accumulating a meaningful census of these systems., Comment: 33 pages, 23 figures, and 19 tables; accepted for publication in Astronomy & Astrophysics

Context. Identifying minerals on asteroid surfaces is difficult as space weathering modifies the minerals infrared spectra. This shouldbe better understood for proper interpretation. Aims. We simulated the space weathering effects on a meteorite and recorded the alterations of the crystalline structure, such as the change in peak positions and full width at half maximum values. Methods. We used proton irradiation to simulate the effects of solar wind on a sample of NWA 10580 CO3 chondrite meteorites. After irradiation in three gradually increased steps with 1 keV ion energy, we used infrared microscopic reflectance and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) to identify and understand the consequences of irradiation. Results. We find negative peak shifts after the first and second irradiations at pyroxene and feldspar minerals, similarly to the literature, and this shift was attributed to Mg loss. However, after the third irradiation a positive change in values in wavenumber emerged for silicates, which could come from the distortion of SiO4 tetrahedra, resembling shock deformation. The full width at half maximum values of major bands show a positive (increasing) trend after irradiations in the case of feldspars, using IR reflection measurements. Comparing DRIFTS and reflection infrared data, the peak positions of major mineral bands were at similar wavenumbers, but differences can be observed in minor bands. Conclusions. We measured the spectral changes of meteorite minerals after high doses of proton irradiation for several minerals. We show the first of these measurements for feldspars; previous works only presented pyroxene, olivine, and phyllosilicates.

A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often influenced by the control of the underlying dynamical system. Existing methods often model the transition function as a differential equation or as a recurrent neural network. Despite their effectiveness in predicting future measurements, few results have successfully established a method for sampling and statistical inference of trajectories using neural networks, partially due to constraints in the parameterization. In this work, we introduce a mechanism to learn the distribution of trajectories by parameterizing the transition function $f$ explicitly as an element in a function space. Our framework allows efficient synthesis of novel trajectories, while also directly providing a convenient tool for inference, i.e., uncertainty estimation, likelihood evaluations and out of distribution detection for abnormal trajectories. These capabilities can have implications for various downstream tasks, e.g., simulation and evaluation for reinforcement learning.

Modern machine learning (ML) systems demand substantial training data, often resorting to external sources. Nevertheless, this practice renders them vulnerable to backdoor poisoning attacks. Prior backdoor defense strategies have primarily focused on the identification of backdoored models or poisoned data characteristics, typically operating under the assumption of access to clean data. In this work, we delve into a relatively underexplored challenge: the automatic identification of backdoor data within a poisoned dataset, all under realistic conditions, i.e., without the need for additional clean data or without manually defining a threshold for backdoor detection. We draw an inspiration from the scaled prediction consistency (SPC) technique, which exploits the prediction invariance of poisoned data to an input scaling factor. Based on this, we pose the backdoor data identification problem as a hierarchical data splitting optimization problem, leveraging a novel SPC-based loss function as the primary optimization objective. Our innovation unfolds in several key aspects. First, we revisit the vanilla SPC method, unveiling its limitations in addressing the proposed backdoor identification problem. Subsequently, we develop a bi-level optimization-based approach to precisely identify backdoor data by minimizing the advanced SPC loss. Finally, we demonstrate the efficacy of our proposal against a spectrum of backdoor attacks, encompassing basic label-corrupted attacks as well as more sophisticated clean-label attacks, evaluated across various benchmark datasets. Experiment results show that our approach often surpasses the performance of current baselines in identifying backdoor data points, resulting in about 4%-36% improvement in average AUROC. Codes are available at https://github.com/OPTML-Group/BackdoorMSPC., Comment: The Twelfth International Conference on Learning Representations (ICLR 2024)

Computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition engine are performed to investigate the impact of gasoline-ethanol blending on autoignition, nitrogen oxide (NOx), and soot emissions under low-load conditions. A four-component toluene primary reference fuel (TPRF) + ethanol (ETPRF) surrogate (with 10% ethanol by volume; E10) is employed to represent the test gasoline (RD5-87). A 3D engine CFD model employing finite-rate chemistry with a skeletal kinetic mechanism, adaptive mesh refinement (AMR), and hybrid method of moments (HMOM) is adopted to capture in-cylinder combustion and soot/NOx emissions. The engine CFD model is validated against experimental data for three gasoline-ethanol blends: E10, E30 and E100, with varying ethanol content by volume. Model validation is carried out for multiple start-of-injection (SOI) timings (-21, -27, -36, and -45 crank angle degrees after top-dead-center (aTDC)) with respect to in-cylinder pressure, heat release rate, combustion phasing, NOx and soot emissions. For late injection timings (-21 and -27oaTDC), E30 yields higher soot than E10; while the trend reverses for early injection cases (-36 and -45oaTDC). E100 yields the lowest amount of soot among all fuels irrespective of SOI timing. Further, E10 shows a non-monotonic trend in soot emissions with SOI timing: SOI-36>SOI-45>SOI-21>SOI-27, while soot emissions from E30 exhibit monotonic decrease with advancing SOI timing. NOx emissions from various fuels follow a trend of E10>E30>E100. NOx emissions increase as SOI timing is advanced for all fuels, with an anomaly for E10 and E100 where NOx decreases when SOI is advanced beyond -36oaTDC. Detailed analysis of the numerical results is performed to investigate the emission trends and elucidate the impact of chemical composition and physical properties on autoignition and emissions characteristics.

An experimental investigation of $^{105}$Pd has revealed, for the first time, the existence of two wobbling bands both having one phonon configuration and originating from the coupling of the wobbling phonon to the ground state band and to its signature partner. The doublet one-phonon wobbling bands are, in turn, found to be the signature partner bands. These observations have been drawn from the measured ratios of the inter-band and intra-band gamma transition rates. The model calculations based on the triaxial projected shell model (TPSM) approach have been performed and are found to be in good agreement with the experimental observations. These calculations provide an insight into the nature of the observed structures at a microscopic level.

Context. Gaia18cjb is one of the Gaia-alerted eruptive young star candidates which has been experiencing a slow and strong brightening during the last 13 years, similar to some FU Orionis-type objects. Aims. The aim of this work is to derive the young stellar nature of Gaia18cjb, determine its physical and accretion properties to classify its variability. Methods. We conducted monitoring observations using multi-filter optical and near-infrared photometry, as well as near-infrared spectroscopy. We present the analysis of pre-outburst and outburst optical and infrared light curves, color-magnitude diagrams in different bands, the detection of near-IR spectral lines, and estimates of both stellar and accretion parameters during the burst. Results. The optical light curve shows an unusually long (8 years) brightening event of 5 mag in the last 13 years, before reaching a plateau indicating that the burst is still on-going, suggesting a FUor-like nature. The same outburst is less strong in the infrared light curves. The near-infrared spectra, obtained during the outburst, exhibit emission lines typical of highly accreting low-intermediate mass young stars with typical EXor features. The spectral index of Gaia18cjb SED classifies it as a Class I in the pre-burst stage and a Flat Spectrum young stellar object (YSO) during the burst. Conclusions. Gaia18cjb is an eruptive YSO which shows FUor-like photometric features (in terms of brightening amplitude and length of the burst) and EXor-like spectroscopic features and accretion rate, as V350 Cep and V1647 Ori, classified as objects in between FUors and EXors, Comment: 21 pages, 13 figures

We propose a fresh take on understanding the mechanisms of neural networks by analyzing the rich directional structure of optimization trajectories, represented by their pointwise parameters. Towards this end, we introduce some natural notions of the complexity of optimization trajectories, both qualitative and quantitative, which hallmark the directional nature of optimization in neural networks: when is there redundancy, and when exploration. We use them to reveal the inherent nuance and interplay involved between various optimization choices, such as momentum and weight decay. Further, the trajectory perspective helps us see the effect of scale on regularizing the directional nature of trajectories, and as a by-product, we also observe an intriguing heterogeneity of Q,K,V dynamics in the middle attention layers in LLMs and which is homogenized by scale. Importantly, we put the significant directional redundancy observed to the test by demonstrating that training only scalar batchnorm parameters some while into training matches the performance of training the entire network, which thus exhibits the potential of hybrid optimization schemes that are geared towards efficiency., Comment: Preprint, 57 pages

This Letter reports a search for charge-parity (CP) symmetry violating non-standard interactions (NSI) of neutrinos with matter using the NOvA Experiment, and examines their effects on the determination of the standard oscillation parameters. Data from $\nu_{\mu}(\bar{\nu}_{\mu})\rightarrow\nu_{\mu}(\bar{\nu}_{\mu})$ and $\nu_{\mu}(\bar{\nu}_{\mu})\rightarrow\nu_{e}(\bar{\nu}_{e})$ oscillation channels are used to measure the effect of the NSI parameters $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$. With 90% C.L. the magnitudes of the NSI couplings are constrained to be $|\varepsilon_{e\mu}| \, \lesssim 0.3$ and $|\varepsilon_{e\tau}| \, \lesssim 0.4$. A degeneracy at $|\varepsilon_{e\tau}| \, \approx 1.8$ is reported, and we observe that the presence of NSI limits sensitivity to the standard CP phase $\delta_{\tiny\text{CP}}$.

We present a Wideband Tapered Gridded Estimator (TGE), which incorporates baseline migration and variation of the primary beam pattern for neutral hydrogen (${\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}$) 21-cm intensity mapping (IM) with large frequency bandwidth radio-interferometric observations. Here we have analysed $394-494 \, {\rm MHz}$ $(z = 1.9 - 2.6)$ uGMRT data to estimate the Multi-frequency Angular Power Spectrum (MAPS) $C_\ell(\Delta\nu)$ from which we have removed the foregrounds using the polynomial fitting (PF) and Gaussian Process Regression (GPR) methods developed in our earlier work. Using the residual $C_\ell(\Delta\nu)$ to estimate the mean squared 21-cm brightness temperature fluctuation $\Delta^2(k)$, we find that this is consistent with $0 \pm 2 \sigma$ in several $k$ bins. The resulting $2\sigma$ upper limit $\Delta^2(k) < (4.68)^2 \, \rm{mK^2}$ at $k=0.219\,\rm{Mpc^{-1}}$ is nearly $15$ times tighter than earlier limits obtained from a smaller bandwidth ($24.4 \, {\rm MHz}$) of the same data. The $2\sigma$ upper limit $[\Omega_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}} b_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}}] < 1.01 \times 10^{-2}$ is within an order of magnitude of the value expected from independent estimates of the ${\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}$ mass density $\Omega_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}}$ and the ${\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}$ bias $b_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}}$. The techniques used here can be applied to other telescopes and frequencies, including $\sim 150 \, {\rm MHz}$ Epoch of Reionization observations., Comment: Accepted for publication in MNRAS

This paper addresses the problem of single snapshot Direction-of-Arrival (DOA) estimation, which is of great importance in a wide-range of applications including automotive radar. A popular approach to achieving high angular resolution when only one temporal snapshot is available is via subspace methods using spatial smoothing. This involves leveraging spatial shift-invariance in the antenna array geometry, typically a uniform linear array (ULA), to rearrange the single snapshot measurement vector into a spatially smoothed matrix that reveals the signal subspace of interest. However, conventional approaches using spatially shifted ULA sub-arrays can lead to a prohibitively high computational complexity due to the large dimensions of the resulting spatially smoothed matrix. Hence, we propose to instead employ judiciously designed sparse sub-arrays, such as nested arrays, to reduce the computational complexity of spatial smoothing while retaining the aperture and identifiability of conventional ULA-based approaches. Interestingly, this idea also suggests a novel beamforming method which linearly combines multiple spatially smoothed matrices corresponding to different sets of shifts of the sparse (nested) sub-array. This so-called shift-domain beamforming method is demonstrated to boost the effective SNR, and thereby resolution, in a desired angular region of interest, enabling single snapshot low-complexity DOA estimation with identifiability guarantees., Comment: \copyright 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

The local atomic structure of NaF-ZrF$_4$ (53-47 mol%) molten system and its evolution with temperature are examined with x-ray scattering measurements and compared with $ab-initio$ and Neural Network-based molecular dynamics (NNMD) simulations in the temperature range 515-700 {\deg}C. The machine-learning enhanced NNMD calculations offer improved efficiency while maintaining accuracy at higher distances compared to ab-initio calculations. Looking at the evolution of the Pair Distribution Function with increasing temperature, a fundamental change in the liquid structure within the selected temperature range, accompanied by a slight decrease in overall correlation is revealed. NNMD calculations indicate the co-existence of three different fluorozirconate complexes: [ZrF$_6$]$^{2-}$, [ZrF$_7$]$^{3-}$, and [ZrF$_8$]$^{4-}$, with a temperature-dependent shift in the dominant coordination state towards a 6-coordinated Zr ion at 700{\deg}C. The study also highlights the metastability of different coordination structures, with frequent interconversions between 6 and 7 coordinate states for the fluorozirconate complex from 525 {\deg}C to 700 {\deg}C. Analysis of the Zr-F-Zr angular distribution function reveals the presence of both $"$edge-sharing$"$ and $"$corner-sharing$"$ fluorozirconate complexes with specific bond angles and distances in accord with previous studies, while the next-nearest neighbor cation-cation correlations demonstrate a clear preference for unlike cations as nearest-neighbor pairs, emphasizing non-random arrangement. These findings contribute to a comprehensive understanding of the complex local structure of the molten salt, providing insights into temperature-dependent preferences and correlations within the molten system., Comment: 26 pages, 15 figures, 3 tables

Faults on electrical power lines could severely compromise both the reliability and safety of power systems, leading to unstable power delivery and increased outage risks. They pose significant safety hazards, necessitating swift detection and mitigation to maintain electrical infrastructure integrity and ensure continuous power supply. Hence, accurate detection and categorization of electrical faults are pivotal for optimized power system maintenance and operation. In this work, we propose a novel approach for detecting and categorizing electrical faults using the Hessian locally linear embedding (HLLE) technique and subsequent clustering with t-SNE (t-distributed stochastic neighbor embedding) and Gaussian mixture model (GMM). First, we employ HLLE to transform high-dimensional (HD) electrical data into low-dimensional (LD) embedding coordinates. This technique effectively captures the inherent variations and patterns in the data, enabling robust feature extraction. Next, we perform the Mann-Whitney U test based on the feature space of the embedding coordinates for fault detection. This statistical approach allows us to detect electrical faults providing an efficient means of system monitoring and control. Furthermore, to enhance fault categorization, we employ t-SNE with GMM to cluster the detected faults into various categories. To evaluate the performance of the proposed method, we conduct extensive simulations on an electrical system integrated with solar farm. Our results demonstrate that the proposed approach exhibits effective fault detection and clustering across a range of fault types with different variations of the same fault. Overall, this research presents an effective methodology for robust fault detection and categorization in electrical systems, contributing to the advancement of fault management practices and the prevention of system failures.

Electrical fault classification is vital for ensuring the reliability and safety of power systems. Accurate and efficient fault classification methods are essential for timely and effective maintenance. In this paper, we propose a novel approach for effective fault classification through Grassmann manifolds, which is a non-Euclidean space that captures the intrinsic structure of high-dimensional data and offers a robust framework for feature extraction. We use simulated data for electrical distribution systems with various types of electrical faults. The proposed method involves transforming the measurement fault data into Grassmann manifold space using techniques from differential geometry. This transformation aids in uncovering the underlying fault patterns and reducing the computational complexity of subsequent classification steps. To achieve fault classification, we employ a machine learning technique optimized for the Grassmann manifold. The support vector machine classifier is adapted to operate within the Grassmann manifold space, enabling effective discrimination between different fault classes. The results illustrate the efficacy of the proposed Grassmann manifold-based approach for electrical fault classification which showcases its ability to accurately differentiate between various fault types.

We propose and study a conceptual one-dimensional model to explore how the combined interplay between fixed resources and particle exchanges between different parts of an extended system can affect the stationary densities in a current carrying channel connecting different parts of the system. To this end, we consider a model composed of a totally asymmetric simple exclusion process (TASEP) connecting two particle reservoirs without any internal dynamics but which can directly exchange particles between each other, ensuring nonvanishing currents in the steady states. The total particle number in the system that defines the "resources" available, although is kept constant by the model dynamics, can take any value independent of the model parameters that define the dynamics of the model. We show how the resulting phase diagrams of the model are controlled by the parameters, which define the various dynamical update rules together with the total available resources. These control parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous with localized domain walls, and can also control populations of the two reservoirs. In general, the phase diagrams are quite different from a TASEP with open boundaries. In the limit of large amount of resources, the phase diagrams in the plane of the control parameters become topologically identical to that for an open TASEP together with delocalization of domain walls., Comment: 21 pages, 14 figures