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For a primitive Dirichlet character $\chi\pmod q$ we let \[M(\chi):= \frac{1}{\sqrt{q}}\max_{1\leq t \leq q} \Big|\sum_{n \leq t} \chi(n) \Big|.\] In this paper, we investigate the distribution of $M(\chi)$, as $\chi$ ranges over primitive cubic characters $\chi\pmod q$ with $(q,3)=1$ and $q\leq Q$. Our first result gives an estimate for the proportion of such characters for which $M(\chi)>V$, in a uniform range of $V$, which is best possible under the assumption of the Generalized Riemann Hypothesis. In particular, we show that the distribution of large cubic character sums behaves very differently from those in the family of non-principal characters modulo a large prime, and the family of quadratic characters. We also investigate the location of the number $N_{\chi}$ where the maximum of $|\sum_{n\leq N} \chi(n)|$ is attained, and show the surprising result that for almost all primitive cubic characters $\chi\pmod q$ with $M(\chi)>V$, $N_{\chi}/q$ is very close to a reduced fraction with a large denominator of size $(\log V)^{1/2+o(1)}$. This contradicts the common belief that for an even character $\chi$, $N_{\chi}/q$ is located near a rational of small denominator and gives a striking difference with the case of even characters in the other two families mentioned above, for which $N_{\chi}/q\approx 1/3$ or $2/3$ for almost all even $\chi$. Furthermore, in the case of cubic characters, the works of Granville-Soundararajan, Goldmakher, and Lamzouri-Mangerel show that if $M(\chi)$ is large, then $\chi$ pretends to be $\xi(n)n^{it}$ for some small $t$, where $\xi$ is an odd character of small conductor $m$. We show that for almost all such characters, we have $M(\chi)=m^{-1/2+o(1)}\big|L(1+it, \chi\overline{\xi})\big|.$, Comment: 32 pages

It is well-known that within the standard three flavor neutrino oscillation formalism, the Majorana phases appearing in the neutrino mixing matrix cannot have any effect on neutrino oscillation probabilities thereby evading testability at neutrino oscillation experiments. We consider an effective non-Hermitian Hamiltonian describing three flavor neutrino oscillations with the possibility of neutrino decay and demonstrate that the two Majorana phases can entangle with the off-diagonal decay terms and appear at the level of oscillation probabilities. Using the Cayley-Hamilton theorem, we derive approximate analytical expressions for three flavor neutrino oscillation probabilities in the presence of neutrino decay, taking into account matter effects. In the context of a long baseline neutrino experiment, we then analyse the impact of Majorana phases on the oscillation probabilities for different channels as well as on observables related to CP violation effects in neutrino oscillations. Finally, we discuss the effect of Majorana phases on the parameter degeneracies in the neutrino oscillation framework., Comment: 27 pages, 8 figures. Comments Welcome

Establishing a unified theory of cognition has been a major goal of psychology. While there have been previous attempts to instantiate such theories by building computational models, we currently do not have one model that captures the human mind in its entirety. Here we introduce Centaur, a computational model that can predict and simulate human behavior in any experiment expressible in natural language. We derived Centaur by finetuning a state-of-the-art language model on a novel, large-scale data set called Psych-101. Psych-101 reaches an unprecedented scale, covering trial-by-trial data from over 60,000 participants performing over 10,000,000 choices in 160 experiments. Centaur not only captures the behavior of held-out participants better than existing cognitive models, but also generalizes to new cover stories, structural task modifications, and entirely new domains. Furthermore, we find that the model's internal representations become more aligned with human neural activity after finetuning. Taken together, Centaur is the first real candidate for a unified model of human cognition. We anticipate that it will have a disruptive impact on the cognitive sciences, challenging the existing paradigm for developing computational models.

Question-asking in collaborative dialogue has long been established as key to knowledge construction, both in internal and collaborative problem solving. In this work, we examine probing questions in collaborative dialogues: questions that explicitly elicit responses from the speaker's interlocutors. Specifically, we focus on modeling the causal relations that lead directly from utterances earlier in the dialogue to the emergence of the probing question. We model these relations using a novel graph-based framework of deliberation chains, and reframe the problem of constructing such chains as a coreference-style clustering problem. Our framework jointly models probing and causal utterances and the links between them, and we evaluate on two challenging collaborative task datasets: the Weights Task and DeliData. Our results demonstrate the effectiveness of our theoretically-grounded approach compared to both baselines and stronger coreference approaches, and establish a standard of performance in this novel task., Comment: Accepted at Findings of EMNLP 2024

Modern instances of combinatorial optimization problems often exhibit billion-scale ground sets, which have many uninformative or redundant elements. In this work, we develop light-weight pruning algorithms to quickly discard elements that are unlikely to be part of an optimal solution. Under mild assumptions on the instance, we prove theoretical guarantees on the fraction of the optimal value retained and the size of the resulting pruned ground set. Through extensive experiments on real-world datasets for various applications, we demonstrate that our algorithm, QuickPrune, efficiently prunes over 90% of the ground set and outperforms state-of-the-art classical and machine learning heuristics for pruning.

The NOvA collaboration reports cross-section measurements for $\nu_{\mu}$ charged-current interactions with low hadronic energy (maximum kinetic energy of 250 MeV for protons and 175 MeV for pions) in the NOvA Near Detector. The results are presented as a double-differential cross section as a function of the direct observables of the final-state muon kinematics. Results are also presented as a single-differential cross section as a function of the derived square of the four-momentum transfer, $Q^{2}$, and as a function of the derived neutrino energy. The data correspond to an accumulated 8.09$\times10^{20}$ protons-on-target (POT) in the neutrino mode of the NuMI beam, with a narrow band of neutrino energies peaked at 1.8 GeV. The analysis provides a sample of neutrino-nucleus interactions with an enhanced fraction of quasi-elastic and two-particle-two-hole (2p2h) interactions. This enhancement allows quantitative comparisons with various nuclear models. We find strong disagreement between data and theory-based models in various regions of the muon kinematic phase space, especially in the forward muon direction., Comment: 20 pages, 12 figures

Reward modeling of human preferences is one of the cornerstones of building usable generative large language models (LLMs). While traditional RLHF-based alignment methods explicitly maximize the expected rewards from a separate reward model, more recent supervised alignment methods like Direct Preference Optimization (DPO) circumvent this phase to avoid problems including model drift and reward overfitting. Although popular due to its simplicity, DPO and similar direct alignment methods can still lead to degenerate policies, and rely heavily on the Bradley-Terry-based preference formulation to model reward differences between pairs of candidate outputs. This formulation is challenged by non-deterministic or noisy preference labels, for example human scoring of two candidate outputs is of low confidence. In this paper, we introduce DRDO (Direct Reward Distillation and policy-Optimization), a supervised knowledge distillation-based preference alignment method that simultaneously models rewards and preferences to avoid such degeneracy. DRDO directly mimics rewards assigned by an oracle while learning human preferences from a novel preference likelihood formulation. Our experimental results on the Ultrafeedback and TL;DR datasets demonstrate that policies trained using DRDO surpass previous methods such as DPO and e-DPO in terms of expected rewards and are more robust, on average, to noisy preference signals as well as out-of-distribution (OOD) settings.

We revisit the problem of spontaneous symmetry breaking (SSB), its restoration and phase transition for a self interacting quantum scalar field in a general curved background, at zero and finite temperature. To the best of our knowledge, most of the earlier computations in this context have been done in the linear order in curvature, which may not be very suitable for the Ricci flat spacetimes. One of our objectives is to see whether the higher order terms can bring in qualitatively new physical effects, and thereby attempting to fill in this gap in the literature. We use the Bunch-Parker local momentum space representation of the Feynman propagator. We compute the renormalised, background spacetime curvature (up to quadratic order) and temperature dependent one loop effective potential for $\phi^4$ plus $\phi^3$ self interaction. In particular for the de Sitter spacetime, we have shown for $\phi^4$-theory that we can have SSB for a scalar even with a positive rest mass squared and non-minimal coupling, at zero temperature. This cannot be achieved by the linear curvature term alone and the result remains valid for a very large range of renormalisation scale. For a phase transition, we have computed the leading curvature correction to the critical temperature. At finite temperature, symmetry restoration is also demonstrated. We also extend some of the above results to two loop level. The symmetry breaking in de Sitter at two loop remains present. We have further motivated the necessity of treating this problem non-perturbatively in some instances., Comment: v1; 32pp, 15 figs

The shallow water equations are numerically solved to simulate free surface flows. The convective flux terms in the shallow water equations need to be discretized using a Riemann solver to capture shocks and discontinuity for certain flow situations such as hydraulic jump, dam-break wave propagation or bore wave propagation, levee-breaching flows, etc. The approximate Riemann solver can capture shocks and is popular for studying open-channel flow dynamics with traditional mesh-based numerical methods. Though meshless methods can work on highly irregular geometry without involving the complex mesh generation procedure, the shock-capturing capability has not been implemented, especially for solving open-channel flows. Therefore, we have proposed a numerical method, namely, a shock-capturing meshless geometric conservation weighted least square (GC-WLS) method for solving the shallow water equations. The HLL (Harten-Lax-Van Leer) Riemann solver is implemented within the framework of the proposed meshless method. The spatial derivatives in the shallow water equations and the reconstruction of conservative variables for high-order accuracy are computed using the GC-WLS method. The proposed meshless method is tested for various numerically challenging open-channel flow problems, including analytical, laboratory experiments, and a large-scale physical model study on dam-break event.

Double- and single-differential cross sections for inclusive charged-current neutrino-nucleus scattering are reported for the kinematic domain 0 to 2 GeV/c in three-momentum transfer and 0 to 2 GeV in available energy, at a mean muon-neutrino energy of 1.86 GeV. The measurements are based on an estimated 995,760 muon-neutrino CC interactions in the scintillator medium of the NOvA Near Detector. The subdomain populated by 2-particle-2-hole reactions is identified by the cross-section excess relative to predictions for neutrino-nucleus scattering that are constrained by a data control sample. Models for 2-particle-2- hole processes are rated by chi-square comparisons of the predicted-versus-measured muon-neutrino CC inclusive cross section over the full phase space and in the restricted subdomain. Shortfalls are observed in neutrino generator predictions obtained using the theory-based Val`encia and SuSAv2 2p2h models., Comment: 20 pages, 14 figures

In this article, we are going to study the quantum mechanical properties of primordial perturbations generated during inflation. Instead of choosing Bunch-Davies vacuum, we are going to prescribe the Coherent state as a non-trivial choice for the initial state of cosmological perturbations. Then we are trying to investigate its implications on the CMB map through the determination of its Correlation function, Covariance matrix and Power spectrum. Also we discuss something regarding the homogeneous and isotropic distribution of the Mukhanov-Sasaki variable over cosmological background. After that we will study the behaviour of Entanglement entropy and Bell inequality violation in the context of Squeezed coherent state, a cosmological time-evolved version of Coherent state. From this investigation, we will show that it is possible to distinguish the initial state of cosmological perturbations through the determination of Bell inequality. Apart from this, we also investigate whether it is possible to find any kind of squeezing for our non-trivial choice of Coherent state. Lastly we conclude this article by discussing some of the implications that arise solely due to our initially prescribed Coherent state., Comment: 32 pages, 9 figures

Mamba is emerging as a novel approach to overcome the challenges faced by Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) in computer vision. While CNNs excel at extracting local features, they often struggle to capture long-range dependencies without complex architectural modifications. In contrast, ViTs effectively model global relationships but suffer from high computational costs due to the quadratic complexity of their self-attention mechanisms. Mamba addresses these limitations by leveraging Selective Structured State Space Models to effectively capture long-range dependencies with linear computational complexity. This survey analyzes the unique contributions, computational benefits, and applications of Mamba models while also identifying challenges and potential future research directions. We provide a foundational resource for advancing the understanding and growth of Mamba models in computer vision. An overview of this work is available at https://github.com/maklachur/Mamba-in-Computer-Vision., Comment: Under Review

Semiconductor quantum dot arrays are a promising platform to perform spin-based error-corrected quantum computation with large numbers of qubits. However, due to the diverging number of possible charge configurations combined with the limited sensitivity of large-footprint charge sensors, achieving single-spin occupancy in each dot in a growing quantum dot array is exceedingly complex. Therefore, to scale-up a spin-based architecture we must change how individual charges are readout and controlled. Here, we demonstrate single-spin occupancy of each dot in a foundry-fabricated array by combining two methods. 1/ Loading a finite number of electrons into the quantum dot array; simplifying electrostatic tuning by isolating the array from the reservoirs. 2/ Deploying multiplex gate-based reflectometry to dispersively probe charge tunneling and spin states without charge sensors or reservoirs. Our isolated arrays probed by embedded multiplex readout can be readily electrostatically tuned. They are thus a viable, scalable approach for spin-based quantum architectures., Comment: 15 pages 5 figures

We survey the combinatorics of the Adinkra, a graphical device for solving differential equations in supersymmetry. These graphs represent an exceptional class of 1-factorizations with further augmentations. As a new feature, we characterize Adinkras using Latin rectangles., Comment: 19 pages, 11 figures

Attitude estimation is crucial in aerospace engineering, robotics, and virtual reality applications, but faces difficulties due to nonlinear system dynamics and sensor limitations. This paper addresses the challenge of attitude estimation using quaternion-based adaptive right invariant extended Kalman filtering (RI-EKF) that integrates data from inertial and magnetometer sensors. Our approach applies the expectation-maximization (EM) algorithm to estimate noise covariance, exploiting RI-EKF symmetry properties. We analyze the adaptive RI-EKF's stability, convergence, and accuracy, validating its performance through simulations and comparison with the left invariant EKF. Monte Carlo simulations validate the effectiveness of our noise covariance estimation technique across various window lengths., Comment: This work has been submitted to the IEEE for possible publication

We developed a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions from RHIC to LHC energies. The success of our model is mainly the estimation of $v_2$ from final state particle kinematic information and learning the centrality and the transverse momentum ($p_{\rm T}$) dependence of $v_2$ in wide $p_{\rm T}$ regime. The deep learning model is trained with AMPT-generated Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events. We present $v_2$ estimates for $\pi^{\pm}$, $\rm K^{\pm}$, and $\rm p+\bar{p}$ in heavy-ion collisions at various LHC energies. These results are compared with the available experimental data wherever possible., Comment: 4 pages, 2 figures

The Superficial Alignment Hypothesis posits that almost all of a language model's abilities and knowledge are learned during pre-training, while post-training is about giving a model the right style and format. We re-examine these claims by empirically studying the scaling behavior of post-training with increasing finetuning examples and evaluating them using objective task-specific standardized benchmarks. Through experiments with the Llama-3, Mistral, and Llama-2 model families of multiple sizes, we observe that, similar to the pre-training scaling laws, post-training task performance scales as a power law against the number of finetuning examples. This power law relationship holds across a broad array of capabilities, including mathematical reasoning, coding, instruction following, and multihop-reasoning. In addition, for tasks like math and multihop reasoning, we observe that a handful of examples merely align the model stylistically but do not saturate performance on the benchmarks. Model performance is instead correlated with its reasoning ability and it improves significantly with more examples, illustrating the need for holistic evaluation programs leveraging objective benchmarks in addition to measurement of alignment to human preferences. We also observe that language models are not necessarily limited to using knowledge learned during pre-training. With appropriate post-training, a model's ability to integrate new knowledge greatly improves on downstream tasks like multihop question-answering. Taken together, these results shed new light on the Superficial Alignment Hypothesis, suggesting that it is, at best, an over-simplification.

Interaction between galaxies play a pivotal role in their evolution. Ongoing star formation in spiral galaxies can be affected by these processes. We select a sample of interacting galaxies in field environments at various interaction stages and are nearly face-on and chose galaxy pairs NGC 2207/IC 2163, NGC 4017/4016 (ARP 305) and NGC 7753/7752 (ARP 86). We use the UltraViolet Imaging Telescope (UVIT) onboard AstroSat to characterize the star-forming regions in the galaxy with a superior resolution of ~1.4". We identified and characterized star-forming regions in the UVIT images of the sample and correlated them with the neutral hydrogen (HI) distribution. We detected localized regions of enhancement in star formation surface density and distortions in the sample of galaxies. We found this consistent with the distribution of HI in the galaxy. These are possible evidence of past and ongoing interactions affecting the star formation properties in the galaxies. We then conducted a study to understand whether the observed enhancements hold true for a wider sample of interacting galaxies. We observe a moderate enhancement in the star formation rate (SFR) with the interaction class, with the maximum of 1.8 being in the merger class of galaxies. We studied the SFR enhancement for the main galaxies in our sample as a function of pair mass ratio and pair separation. We observe a strong anti-correlation between the SFR enhancement and pair mass ratio and no linear correlation between the enhancement and pair separation. This suggests that the enhancement in interaction-induced star formation may be more strongly influenced by the pair mass ratios, rather than the pair separation. We also infer that the pair separation can possibly act as a limiting parameter for the SFR enhancement., Comment: 11 pages, seven figures. Accepted for publication in MNRAS

The recently discovered bright transient black hole candidate Swift J1727.8-1613 is studied in a broad energy range ($0.5-79$ keV) using combined NICER and NuSTAR data on 29 August 2023. A promonient type-C Quasi-Periodic Oscillation (QPO) at $0.89 \pm 0.01$ Hz with its harmonic was observed in NICER data of $0.5-10$ keV. Interestingly, the harmonic becomes weaker in the lower energy bands ($0.5-1$ & $1-3$ keV). We also report the first detection of a soft time-lag of $0.014 \pm 0.001$ s at the QPO frequency between harder ($3-10$ kev) and softer ($0.5-3$ keV) band photons observed with the NICER/XTI instrument. This indicates that the inclination of the accretion disk in the binary system might be high. From the detailed spectral analysis with the relxill reflection model, we found the disk inclination angle of source to be $\sim 85^\circ$. We discuss how the accretion flow configuration inferred from spectral analysis can help us to understand the origin of QPOs and soft lag in this source., Comment: 10 pages, 4 figures, 1 table (in press ApJ)

Among three leptonic mixing angles, $\theta_{23}$ angle, which characterizes the fractional contribution of two flavor eigenstates $\nu_{\mu}$ and $\nu_{\tau}$ to the third mass eigenstate $\nu_3$, is known to be the largest but the least precisely measured. The work investigates possible reach of $\theta_{23}$ precision with two upcoming gigantic accelerator-based long-baseline neutrino experiments, namely Hyper-Kamiokande and DUNE experiments as well as a possible joint analyses of future neutrino facilities. Our simulation yields that each experiment will definitely establish the octant of $\theta_{23}$ angle for all values within 1$\sigma$ parameter interval, while considering the current limitation. However, if the actual value is $0.48\leq \sin^2\theta_{23}\leq 0.54$, it becomes challenging for these two experiments to reject the maximal ($\theta_{23}=\pi/4$) hypothesis and conclude its octant. This octant-blind region can be further explored with the proposed facilities ESSnuSB and a neutrino factory. Accurate determination of the mixing angle $\theta_{23}$, as well as the accuracy of $\delta_{CP}$, is crucial for examining a certain category of discrete non-Abelian leptonic flavor models. Specifically if CP is conserved in leptonic sector, the combined analysis of Hyper-K and DUNE will rule out the majority of these models. However, if the CP is maximally violated, higher precision of $\delta_{CP}$ is necessary for testing these flavor models., Comment: Update DUNE simulation and adding section and appendix for describing the experimental setup

Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman filter (LI-EKF) for attitude estimation, integrated with an adaptive noise covariance estimation algorithm. By employing an iterative expectation-maximization (EM) approach, the filter can effectively estimate both process and measurement noise covariances. Extensive simulations demonstrate the superiority of the proposed method in terms of attitude estimation accuracy and robustness to initial parameter misspecification. The adaptive LI-EKF's ability to adapt to time-varying noise characteristics makes it a promising solution for various applications requiring reliable attitude estimation, such as aerospace, robotics, and autonomous systems., Comment: This work has been submitted to the IEEE for possible publication

We present a peer-to-peer (P2P) live-streaming architecture designed to address challenges such as free-riding, malicious peers, churn, and network instability through the integration of a reputation system. The proposed algorithm incentivizes active peer participation while discouraging opportunistic behaviors, with a reputation mechanism that rewards altruistic peers and penalizes free riders and malicious actors. To manage peer dynamics, the algorithm continuously updates the strategies and adjusts to changing neighbors. It also implements a request-to-join mechanism for flash crowd scenarios, allowing the source node to delegate requests to child nodes, forming an interconnected tree structure that efficiently handles high demand and maintains system stability. The decentralized reputation mechanism promotes long-term sustainability in the P2P live streaming system., Comment: 6 Pages, 6 Figure

Medical imaging analysis faces challenges such as data scarcity, high annotation costs, and privacy concerns. This paper introduces the Medical AI for Synthetic Imaging (MAISI), an innovative approach using the diffusion model to generate synthetic 3D computed tomography (CT) images to address those challenges. MAISI leverages the foundation volume compression network and the latent diffusion model to produce high-resolution CT images (up to a landmark volume dimension of 512 x 512 x 768 ) with flexible volume dimensions and voxel spacing. By incorporating ControlNet, MAISI can process organ segmentation, including 127 anatomical structures, as additional conditions and enables the generation of accurately annotated synthetic images that can be used for various downstream tasks. Our experiment results show that MAISI's capabilities in generating realistic, anatomically accurate images for diverse regions and conditions reveal its promising potential to mitigate challenges using synthetic data., Comment: WACV25 accepted. https://monai.io/research/maisi

This Letter reports new results from the HAYSTAC experiment's search for dark matter axions in our galactic halo. It represents the widest search to date that utilizes squeezing to realize sub-quantum limited noise. The new results cover 1.71 $\mu$eV of newly scanned parameter space in the mass ranges 17.28--18.44 $\mu$eV and 18.71--19.46 $\mu$eV. No statistically significant evidence of an axion signal was observed, excluding couplings $|g_\gamma|\geq$ 2.75$\times$$|g_{\gamma}^{\text{KSVZ}}|$ and $|g_\gamma|\geq$ 2.96$\times$$|g_{\gamma}^{\text{KSVZ}}|$ at the 90$\%$ confidence level over the respective region. By combining this data with previously published results using HAYSTAC's squeezed state receiver, a total of 2.27 $\mu$eV of parameter space has now been scanned between 16.96--19.46 $\mu$eV, excluding $|g_\gamma|\geq$ 2.86$\times$$|g_{\gamma}^{\text{KSVZ}}|$ at the 90$\%$ confidence level. These results demonstrate the squeezed state receiver's ability to probe axion models over a significant mass range while achieving a scan rate enhancement relative to a quantum-limited experiment., Comment: 6 pages, 3 figures

This study explores the application of diffusion models in the field of typhoons, predicting multiple ERA5 meteorological variables simultaneously from Digital Typhoon satellite images. The focus of this study is taken to be Taiwan, an area very vulnerable to typhoons. By comparing the performance of Conditional Denoising Diffusion Probability Model (CDDPM) with Convolutional Neural Networks (CNN) and Squeeze-and-Excitation Networks (SENet), results suggest that the CDDPM performs best in generating accurate and realistic meteorological data. Specifically, CDDPM achieved a PSNR of 32.807, which is approximately 7.9% higher than CNN and 5.5% higher than SENet. Furthermore, CDDPM recorded an RMSE of 0.032, showing a 11.1% improvement over CNN and 8.6% improvement over SENet. A key application of this research can be for imputation purposes in missing meteorological datasets and generate additional high-quality meteorological data using satellite images. It is hoped that the results of this analysis will enable more robust and detailed forecasting, reducing the impact of severe weather events on vulnerable regions. Code accessible at https://github.com/TammyLing/Typhoon-forecasting., Comment: Accepted for spotlight presentation at the NeurIPS 2024 workshop on Tackling Climate Change with Machine Learning. 8 pages, 5 figures

We report the discovery of the Fe K line emission at $\sim6.62^{+0.06}_{-0.06}$ keV with a width of $\sim0.19^{+0.05}_{-0.05}$ keV using two epochs of {\it Chandra} archival data from the nucleus of the galaxy 4C+37.11, which is known to host a binary supermassive black hole (BSMBH) system where the SMBHs are separated by $\sim7$ mas or $\sim$ 7pc. Our study reports the first detection of the Fe K line from a known binary AGN, and has an F-statistic value of 20.98 and probability $2.47\times 10^{-12}$. Stacking of two spectra reveals another Fe K line component at $\sim7.87^{+0.19}_{-0.09}$ keV. Different model scenarios indicate that the lines originate from the combined effects of accretion disk emission and circumnuclear collisionally ionized medium. The observed low column density favors the gas-poor merger scenario, where the high temperature of the hot ionized medium may be associated with the shocked gas in the binary merger and not with star formation activity. The estimated total BSMBH mass and disk inclination are $\sim1.5\times10^{10}$ M$_\odot$ and $\gtrsim75^\circ$, indicating that the BSMBH is probably a high inclination system. The spin parameter could not be tightly constrained from the present data sets. Our results draw attention to the fact that detecting the Fe K line emissions from BSMBHs is important for estimating the individual SMBH masses, and the spins of the binary SMBHs, as well as exploring their emission regions., Comment: 7 pages, 1 table, 3 figure, Accepted in A&A

A pair $(\alpha, \beta)$ of simple closed curves on a surface $S_{g,n}$ of genus $g$ and with $n$ punctures is called a filling pair if the complement of the union of the curves is a disjoint union of topological disks and once punctured disks. In this article, we study the length of filling pairs on once-punctured hyperbolic surfaces. In particular, we find a lower bound of the length of filling pairs which depends only on the topology of the surface., Comment: 14 pages, 5 figures

Current ton-scale dark matter direct detection experiments have reached an important milestone with the detection of solar neutrinos. In this paper, we show that these data can be used to determine a critical parameter of the Standard Model in particle physics, across an energy regime that has never been probed before. In particular, we show that the value of the weak mixing angle ($\theta_W$) which relates the mass of the $W$ and $Z$ bosons can be derived from 1) the recent measurements of coherent neutrino-nucleus scattering by PandaX-4T and XENONnT in the sub-GeV energy range -- a regime which is usually only probed by low energy neutrino experiments -- and from 2) XENONnT electron recoil data through neutrino-electron scattering at energy scale $\simeq 0.1 ~ \rm{ MeV}$, corresponding to a momentum transfer region over an order of magnitude smaller than that explored by atomic parity violation experiments. Future observation of neutrinos in the next generation of dark matter direct detection experiments have therefore the potential to provide accurate tests of the Standard Model weak interactions in the keV-MeV regime., Comment: 8 pages, 2 figures. Included XENONnT $^8$B data. Improved analysis - the error bars on our results have increased

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PlanSearch, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PlanSearch generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PlanSearch explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PlanSearch on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas. Code can be found at https://github.com/scaleapi/plansearch.

Quantum complexity has emerged as a central concept in diverse areas of physics, ranging from quantum computing to the theory of black holes. We perform a systematic study of complexity in random quantum circuits with and without measurements. We observe that complexity grows linearly before saturating to a constant value. For $N$ qubits without measurements, the saturation value scales as $2^{N-1}$, and the saturation time scales as $2^N$. This behaviour remains identical in the presence of random measurements with different probabilities, indicating that this notion of complexity is insensitive to the rate of measurement. We also study the behaviour of complexity in two variants of the random unitary floquet circuit, where we observe that complexity acts as a novel probe of Anderson localization and many-body localization., Comment: 6 pages, 3 figures

Opinion summarization in e-commerce encapsulates the collective views of numerous users about a product based on their reviews. Typically, a product on an e-commerce platform has thousands of reviews, each review comprising around 10-15 words. While Large Language Models (LLMs) have shown proficiency in summarization tasks, they struggle to handle such a large volume of reviews due to context limitations. To mitigate, we propose a scalable framework called Xl-OpSumm that generates summaries incrementally. However, the existing test set, AMASUM has only 560 reviews per product on average. Due to the lack of a test set with thousands of reviews, we created a new test set called Xl-Flipkart by gathering data from the Flipkart website and generating summaries using GPT-4. Through various automatic evaluations and extensive analysis, we evaluated the framework's efficiency on two datasets, AMASUM and Xl-Flipkart. Experimental results show that our framework, Xl-OpSumm powered by Llama-3-8B-8k, achieves an average ROUGE-1 F1 gain of 4.38% and a ROUGE-L F1 gain of 3.70% over the next best-performing model.

The interplay of magnetic correlations, crystal electric field interactions, and spin-orbit coupling in low-dimensional frustrated magnets fosters novel ground states with unusual excitations. Here, we report the magnetic properties and crystal electric field (CEF) scheme of a rare-earth-based square-lattice antiferromagnet NdKNaNbO$_5$ investigated via magnetization, specific heat, electron spin resonance (ESR), and inelastic neutron scattering (INS) experiments. The low-temperature Curie-Weiss temperature $\theta_{\rm CW} \simeq -0.6$ K implies net antiferromagnetic interactions between the Nd$^{3+}$ ions. Two broad maxima are observed in the low temperature specific heat data in magnetic fields, indicating multilevel Schottky anomalies due to the effect of CEF. No magnetic long-range-order is detected down to 0.4 K. The CEF excitations of Kramers' ion Nd$^{3+}$ ($J=9/2$) probed via INS experiments evince dispersionless excitations characterizing the transitions among the CEF energy levels. The fit of the INS spectra enabled the mapping of the CEF Hamiltonian and the energy eigenvalues of the Kramers' doublets. The simulation using the obtained CEF parameters reproduces the broad maxima in specific heat in zero-field as well as in different applied fields. The significant contribution from $J_z = \pm 1/2$ state to the wave function of the ground state doublet indicates the role of strong quantum fluctuations at low temperatures. The magnetic ground state is found to be a Kramers' doublet with effective spin $J_{\rm eff} = 1/2$ at low temperatures., Comment: 14 pages, 10 figures

This study explores integrating reinforcement learning (RL) with idealised climate models to address key parameterisation challenges in climate science. Current climate models rely on complex mathematical parameterisations to represent sub-grid scale processes, which can introduce substantial uncertainties. RL offers capabilities to enhance these parameterisation schemes, including direct interaction, handling sparse or delayed feedback, continuous online learning, and long-term optimisation. We evaluate the performance of eight RL algorithms on two idealised environments: one for temperature bias correction, another for radiative-convective equilibrium (RCE) imitating real-world computational constraints. Results show different RL approaches excel in different climate scenarios with exploration algorithms performing better in bias correction, while exploitation algorithms proving more effective for RCE. These findings support the potential of RL-based parameterisation schemes to be integrated into global climate models, improving accuracy and efficiency in capturing complex climate dynamics. Overall, this work represents an important first step towards leveraging RL to enhance climate model accuracy, critical for improving climate understanding and predictions. Code accessible at https://github.com/p3jitnath/climate-rl., Comment: Accepted for poster presentation at the NeurIPS 2024 workshop on Tackling Climate Change with Machine Learning. 24 pages, 9 figures

Knowledge Distillation (KD) is a powerful approach for compressing a large model into a smaller, more efficient model, particularly beneficial for latency-sensitive applications like recommender systems. However, current KD research predominantly focuses on Computer Vision (CV) and NLP tasks, overlooking unique data characteristics and challenges inherent to recommender systems. This paper addresses these overlooked challenges, specifically: (1) mitigating data distribution shifts between teacher and student models, (2) efficiently identifying optimal teacher configurations within time and budgetary constraints, and (3) enabling computationally efficient and rapid sharing of teacher labels to support multiple students. We present a robust KD system developed and rigorously evaluated on multiple large-scale personalized video recommendation systems within Google. Our live experiment results demonstrate significant improvements in student model performance while ensuring consistent and reliable generation of high quality teacher labels from a continuous data stream of data.

The recent detection of large column density absorption lines from highly ionized gas in a few directions through the circumgalactic medium (CGM) of the Milky Way (MW) has been puzzling. The inferred temperature from these absorption lines far exceeds the virial temperature of the MW, and the column densities are also too large to be easily explained. In this paper, we propose a novel idea to explain these observations and claim that they may not have originated from the CGM, but from a totally different type of source, namely, stellar ejecta from supernovae (SNe) above the Galactic disk that happen to lie in the line of sight to the background quasars. About $\sim 20\%$ of massive OB stars (progenitors of core-collapse supernovae) are known to be runaway stars that have high ejection velocities near the Galactic plane and can end up exploding as SNe above the Galactic disk. We show that the associated reverse shock in the supernova remnant in the early non-radiative phase can heat the ejecta to temperatures of $\gtrsim 10^7\,{\rm K}$ and can naturally explain the observed high column density of ions in the observed `super-virial' phase along with $\alpha$-enriched super-solar abundance that is typical of core-collapse supernovae. However, SNe from runaway stars has a covering fraction of $\lesssim 0.7 \%$ and thus can only explain the observations along limited sightlines., Comment: 14 pages, accepted for publication in the Astrophysical Journal (ApJ)

The presence of the $\approx 10^6$ K gas in the circumgalactic medium of the Milky Way has been well established. However, the location and the origin of the newly discovered hot gas at `super-virial' temperatures of $\approx 10^7$ K have been puzzling. This hot gas has been detected in both absorption and emission; here we focus on the emitting gas only. We show that both the `virial' and the `super-virial' temperature gas as observed in \emph{emission} occupy disk-like extraplanar regions, in addition to the diffuse virial temperature gas filling the halo of the Milky Way. We perform idealized hydrodynamical simulations to show that the $\approx 10^7$ K emitting gas is likely to be produced by stellar feedback in and around the Galactic disk. We further show that the emitting gas at both super-virial and virial temperatures in the extraplanar regions is metal enriched and is not in hydrostatic equilibrium with the halo but is continuously evolving., Comment: 11 pages, accepted for publication in the Astrophysical Journal (ApJ)

Let $pod_2(n)$ denote the number of $2$-regular partitions of $n$ with distinct odd parts (even parts are unrestricted). In this article, we obtain congruences for $pod_2(n)$ mod $2$ and mod $8$ using some generating function manipulations and the theory of Hecke eigenform., Comment: 8 pages

Since the release of Segment Anything 2 (SAM2), the medical imaging community has been actively evaluating its performance for 3D medical image segmentation. However, different studies have employed varying evaluation pipelines, resulting in conflicting outcomes that obscure a clear understanding of SAM2's capabilities and potential applications. We shortly review existing benchmarks and point out that the SAM2 paper clearly outlines a zero-shot evaluation pipeline, which simulates user clicks iteratively for up to eight iterations. We reproduced this interactive annotation simulation on 3D CT datasets and provided the results and code~\url{https://github.com/Project-MONAI/VISTA}. Our findings reveal that directly applying SAM2 on 3D medical imaging in a zero-shot manner is far from satisfactory. It is prone to generating false positives when foreground objects disappear, and annotating more slices cannot fully offset this tendency. For smaller single-connected objects like kidney and aorta, SAM2 performs reasonably well but for most organs it is still far behind state-of-the-art 3D annotation methods. More research and innovation are needed for 3D medical imaging community to use SAM2 correctly.

Optical networks play a crucial role in todays digital topography, enabling the high-speed and reliable transmission of vast amounts of data over optical fibre for long distances. This paper provides an overview of optical networks, especially emphasising on their evolution with time.

To address the data scarcity associated with 3D assets, 2D-lifting techniques such as Score Distillation Sampling (SDS) have become a widely adopted practice in text-to-3D generation pipelines. However, the diffusion models used in these techniques are prone to viewpoint bias and thus lead to geometric inconsistencies such as the Janus problem. To counter this, we introduce MT3D, a text-to-3D generative model that leverages a high-fidelity 3D object to overcome viewpoint bias and explicitly infuse geometric understanding into the generation pipeline. Firstly, we employ depth maps derived from a high-quality 3D model as control signals to guarantee that the generated 2D images preserve the fundamental shape and structure, thereby reducing the inherent viewpoint bias. Next, we utilize deep geometric moments to ensure geometric consistency in the 3D representation explicitly. By incorporating geometric details from a 3D asset, MT3D enables the creation of diverse and geometrically consistent objects, thereby improving the quality and usability of our 3D representations., Comment: 9 pages, 8 figures

Sequences of the form $(\gcd(u_n,v_n))_{n \in \mathbb N}$, with $(u_n)_n$, $(v_n)_n$ sums of $S$-units, have been considered by several authors. The study of $\gcd(n,u_n)$ corresponds, following Silverman, to divisibility sequences arising from the split algebraic group $\mathbb G_{\mathrm{a}} \times \mathbb G_{\mathrm{m}}$; in this case, Sanna determined all asymptotic moments of the arithmetic function $\log\,\gcd (n,u_n)$ when $(u_n)_n$ is a Lucas sequence. Here, we characterize the asymptotic behavior of the moments themselves $\sum_{n \leq x}\,\gcd(n,u_n)^\lambda$, thus solving the moment problem for $\mathbb G_{\mathrm{a}} \times \mathbb G_{\mathrm{m}}$. We give both unconditional and conditional results, the latter only relying on standard conjectures in analytic number theory., Comment: 15 pages, 1 figure

Let $G$ be a group. Associate a graph $\mathcal{E}_G$ (called the co-Engel graph of $G$) with $G$ whose vertex set is $G$ and two distinct vertices $x$ and $y$ are adjacent if $[x, {}_k y] \neq 1$ and $[y, {}_k x] \neq 1$ for all positive integer $k$. This graph, under the name ``Engel graph'', was introduced by Abdollahi. Let $L(G)$ be the set of all left Engel elements of $G$. In this paper, we realize the induced subgraph of co-Engel graphs of certain finite non-Engel groups $G$ induced by $G \setminus L(G)$. We write $\mathcal{E}^-(G)$ to denote the subgraph of $\mathcal{E}_G$ induced by $G \setminus L(G)$. We also compute genus, various spectra, energies and Zagreb indices of $\mathcal{E}^-(G)$ for those groups. As a consequence, we determine (up to isomorphism) all finite non-Engel group $G$ such that the clique number is at most $4$ and $\mathcal{E}^-$ is toroidal or projective. Further, we show that $\coeng{G}$ is super integral and satisfies the E-LE conjecture and the Hansen--Vuki{\v{c}}evi{\'c} conjecture for the groups considered in this paper.

Let A be a graph type and B an equivalence relation on a group $G$. Let $[g]$ be the equivalence class of $g$ with respect to the equivalence relation B. The B superA graph of $G$ is an undirected graph whose vertex set is $G$ and two distinct vertices $g, h \in G$ are adjacent if $[g] = [h]$ or there exist $x \in [g]$ and $y \in [h]$ such that $x$ and $y$ are adjacent in the A graph of $G$. In this paper, we compute spectrum of equality/conjugacy supercommuting graphs of dihedral/dicyclic groups and show that these graphs are not integral.

Purification maps a mixed state to a pure state and a non-unitary evolution into a unitary one by enlarging the Hilbert space. We link the operator complexity of the density matrix to the state/operator complexity of purified states using three purification schemes: time-independent, time-dependent, and instantaneous purification. We propose inequalities among the operator and state complexities of mixed states and their purifications, demonstrated with a single qubit, two-qubit Werner states, and infinite-dimensional diagonal mixed states. We find that the complexity of a vacuum evolving into a thermal state equals the average number of Rindler particles created between left and right Rindler wedges. Finally, for the thermofield double state evolving from zero to finite temperature, we show that 1) the state complexity follows the Lloyd bound, reminiscent of the quantum speed limit, and 2) the Krylov state/operator complexities are subadditive in contrast to the holographic volume complexity., Comment: 11 pages, 5 figures; Lloyd bound with the energy is added and a slight rearrangement of texts, typos are corrected, references are added

A matrix $A\in \mathbb{R}^{m \times n}$ is strictly sign regular/SSR (or sign regular/SR) if for each $1 \leq k \leq \min \{ m, n \}$, all (non-zero) $k\times k$ minors of $A$ have the same sign. This class of matrices contains the totally positive matrices, and was first studied by Schoenberg (1930) to characterize Variation Diminution (VD), a fundamental property in total positivity theory. In this note, we classify all surjective linear mappings $\mathcal{L}:\mathbb{R}^{m\times n}\to\mathbb{R}^{m\times n}$ that preserve: (i) sign regularity and (ii) sign regularity with a given sign pattern, as well as (iii) strict versions of these., Comment: Expositions significantly tightened. 18 pages, no figures

Motivated by the recent Belle II result indicating a $2.7\,\sigma$ excess of $B^+\to K^+ + E_{\text{miss}}$ events compared to the Standard Model (SM) prediction for $B^+ \to K^+ \nu\bar{\nu}$, we explore an explanation to this anomaly based on a KSVZ-type QCD axion model featuring a Peccei-Quinn (PQ) symmetry breaking at high-scale, that can provide a solution to the strong CP problem with dark matter relic abundance. The model contains a PQ-charged scalar} leptoquark which can interact with the SM quarks only via mass-mixing of the latter with vector-like quarks. The mixing between SM and vector-like quarks is determined by the PQ mass scales and can explain the excess $B^+\to K^+ + E_{\text{miss}}$ events while respecting other flavour constraints. The same PQ-charged scalar leptoquarks and vector-like quarks also mediate the two-loop radiative neutrino masses., Comment: 25 pages, 6 figures

We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for the two-qubit case. Considering the particular case of interacting Rydberg two-level atoms, we show that the Krylov basis obtained using an effective Hamiltonian minimizes the complexity compared to that which is obtained from the original Hamiltonian. We further generalize the latter property to an arbitrary Hamiltonian in which the entire Hilbert space comprises of two subspaces provided a weak coupling between them., Comment: 14 pages, 8 figures

We investigate the ground state phases of an extended Bose-Hubbard ladder of unit filling via the density-matrix-renormalization-group method and, in particular, the effect of rung-hoppings. In contrast to a single-chain, a commensurate supersolid emerges, and based on the Luttinger parameter, we classify them into two types. The latter leads to a reentrant gapless behavior as the onsite interaction is increased while keeping all other parameters intact. A reentrant gapped transition is also found as a function of nearest-neighbor interactions. Further, we show that the string order characterizing the Haldane phase vanishes for a finite inter-chain hopping amplitude, however small it is. Finally, we propose two experimental platforms to observe our findings, using either dipolar atoms or polar molecules and Rydberg admixed atoms., Comment: 7 pages, 9 figures