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The Hayward regular BH solution attempted to resolve the curvature singularity issue by entering the domain of non-singular spacetimes. Recently, Dutta Roy and Kar (Phys. Rev. D 106, 044028) expanded this solution to encompass a broader range of spacetimes. These spacetimes are constructed based on the Damour-Solodukhin prescription, which involves introducing different metric parameters in the $g_{tt}$ and $g_{rr}$ components of the original Hayward line element, and are characterized by two parameters ($\sigma, \kappa$). This generalization gives rise to both known and novel regular/singular BHs as well as various types of wormhole spacetimes. In this work, we explore the spacetimes that emerge for different values of ($\sigma, \kappa$) from the generalized Hayward metric, particularly focusing on their shadows in vacuum and when surrounded by plasma. Intriguingly, we observe the presence of both photon and anti-photon spheres for certain regular spacetimes. Our study highlights the differences in the shadows of different types of regular spacetime compared to those of the singular BH derived from the generalized Hayward metric and also sheds light on the impact of plasma on the shadow radius., Comment: 29 pages, 15 figures and 2 tables

A rotating version of a known static, spherically symmetric, zero Ricci scalar Lorentzian wormhole is constructed. It turns out that for this given non-rotating geometry, the standard Newman-Janis algorithm does not produce a rotating wormhole and, therefore, the method pioneered by Azreg-A\"inou has to be used. The rotating spacetime thus obtained is shown to be regular with wormhole features, though it is no longer a $R=0$ spacetime. The required matter is found to violate the energy conditions, as expected. A few other characteristic properties of this new rotating spacetime are mentioned. Finally, we calculate the shadow for this geometry and discuss its features {\em vis-a-vis} the Kerr geometry and available EHT observations., Comment: 29 pages, 13 figures

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

This paper addresses the problem of visual target tracking in scenarios where a pursuer may experience intermittent loss of visibility of the target. The design of a Switched Visual Tracker (SVT) is presented which aims to meet the competing requirements of maintaining both proximity and visibility. SVT alternates between a visual tracking mode for following the target, and a recovery mode for regaining visual contact when the target falls out of sight. We establish the stability of SVT by extending the average dwell time theorem from switched systems theory, which may be of independent interest. Our implementation of SVT on an Agilicious drone [1] illustrates its effectiveness on tracking various target trajectories: it reduces the average tracking error by up to 45% and significantly improves visibility duration compared to a baseline algorithm. The results show that our approach effectively handles intermittent vision loss, offering enhanced robustness and adaptability for real-world autonomous missions. Additionally, we demonstrate how the stability analysis provides valuable guidance for selecting parameters, such as tracking speed and recovery distance, to optimize the SVT's performance.

Fairness in multi-document summarization of user-generated content remains a critical challenge in natural language processing (NLP). Existing summarization methods often fail to ensure equitable representation across different social groups, leading to biased outputs. In this paper, we introduce two novel methods for fair extractive summarization: FairExtract, a clustering-based approach, and FairGPT, which leverages GPT-3.5-turbo with fairness constraints. We evaluate these methods using Divsumm summarization dataset of White-aligned, Hispanic, and African-American dialect tweets and compare them against relevant baselines. The results obtained using a comprehensive set of summarization quality metrics such as SUPERT, BLANC, SummaQA, BARTScore, and UniEval, as well as a fairness metric F, demonstrate that FairExtract and FairGPT achieve superior fairness while maintaining competitive summarization quality. Additionally, we introduce composite metrics (e.g., SUPERT+F, BLANC+F) that integrate quality and fairness into a single evaluation framework, offering a more nuanced understanding of the trade-offs between these objectives. This work highlights the importance of fairness in summarization and sets a benchmark for future research in fairness-aware NLP models., Comment: Accepted at Algorithmic Fairness through the Lens of Metrics and Evaluation Workshop @ NeurIPS 2024

Visual odometry (VO) is essential for enabling accurate point-goal navigation of embodied agents in indoor environments where GPS and compass sensors are unreliable and inaccurate. However, traditional VO methods face challenges in wide-baseline scenarios, where fast robot motions and low frames per second (FPS) during inference hinder their performance, leading to drift and catastrophic failures in point-goal navigation. Recent deep-learned VO methods show robust performance but suffer from sample inefficiency during training; hence, they require huge datasets and compute resources. So, we propose a robust and sample-efficient VO pipeline based on motion priors available while an agent is navigating an environment. It consists of a training-free action-prior based geometric VO module that estimates a coarse relative pose which is further consumed as a motion prior by a deep-learned VO model, which finally produces a fine relative pose to be used by the navigation policy. This strategy helps our pipeline achieve up to 2x sample efficiency during training and demonstrates superior accuracy and robustness in point-goal navigation tasks compared to state-of-the-art VO method(s). Realistic indoor environments of the Gibson dataset is used in the AI-Habitat simulator to evaluate the proposed approach using navigation metrics (like success/SPL) and pose metrics (like RPE/ATE). We hope this method further opens a direction of work where motion priors from various sources can be utilized to improve VO estimates and achieve better results in embodied navigation tasks., Comment: Accepted in 50SFM Workshop of the 18th European Conference on Computer Vision (ECCV) 2024

In metric $k$-clustering, we are given as input a set of $n$ points in a general metric space, and we have to pick $k$ centers and cluster the input points around these chosen centers, so as to minimize an appropriate objective function. In recent years, significant effort has been devoted to the study of metric $k$-clustering problems in a dynamic setting, where the input keeps changing via updates (point insertions/deletions), and we have to maintain a good clustering throughout these updates. The performance of such a dynamic algorithm is measured in terms of three parameters: (i) Approximation ratio, which signifies the quality of the maintained solution, (ii) Recourse, which signifies how stable the maintained solution is, and (iii) Update time, which signifies the efficiency of the algorithm. We consider the metric $k$-median problem, where the objective is the sum of the distances of the points to their nearest centers. We design the first dynamic algorithm for this problem with near-optimal guarantees across all three performance measures (up to a constant factor in approximation ratio, and polylogarithmic factors in recourse and update time). Specifically, we obtain a $O(1)$-approximation algorithm for dynamic metric $k$-median with $\tilde{O}(1)$ recourse and $\tilde{O}(k)$ update time. Prior to our work, the state-of-the-art here was the recent result of [Bhattacharya et al., FOCS'24], who obtained $O(\epsilon^{-1})$-approximation ratio with $\tilde{O}(k^{\epsilon})$ recourse and $\tilde{O}(k^{1+\epsilon})$ update time. We achieve our results by carefully synthesizing the concept of robust centers introduced in [Fichtenberger et al., SODA'21] along with the randomized local search subroutine from [Bhattacharya et al., FOCS'24], in addition to several key technical insights of our own.

We propose a method to design a magnetic field detector using a noisy two-qubit system. The system evolves under a noisy Heisenberg interaction Hamiltonian, and we investigate its behavior by calculating both the $l_1$-norm of quantum coherence and the return probability in the presence and absence of an external magnetic field. We allow for decoherence modeled by quasi-static charge noise in the exchange coupling of the two-qubit system and find that, while the magnetic field does not significantly influence the decoherence process, it introduces a distinct oscillation in the return probability over time. Importantly, the oscillation frequency is directly proportional to the strength of the applied magnetic field, providing a clear signature that can be used for magnetic field detection. These results point towards the feasibility of realizing a practical quantum-based magnetic field detector, with the ability to operate under noisy conditions while maintaining sensitivity to the field strength.

Graph Neural Networks (GNN) are indispensable in learning from graph-structured data, yet their rising computational costs, especially on massively connected graphs, pose significant challenges in terms of execution performance. To tackle this, distributed-memory solutions such as partitioning the graph to concurrently train multiple replicas of GNNs are in practice. However, approaches requiring a partitioned graph usually suffer from communication overhead and load imbalance, even under optimal partitioning and communication strategies due to irregularities in the neighborhood minibatch sampling. This paper proposes practical trade-offs for improving the sampling and communication overheads for representation learning on distributed graphs (using popular GraphSAGE architecture) by developing a parameterized continuous prefetch and eviction scheme on top of the state-of-the-art Amazon DistDGL distributed GNN framework, demonstrating about 15-40% improvement in end-to-end training performance on the National Energy Research Scientific Computing Center's (NERSC) Perlmutter supercomputer for various OGB datasets., Comment: In Proc. of the IEEE International Conference on Cluster Computing (CLUSTER), 2024

Natural light-harvesting antenna complexes efficiently capture solar energy using chlorophyll, i.e., magnesium porphyrin pigments, embedded in a protein matrix. Inspired by this natural configuration, artificial clay-porphyrin antenna structures have been experimentally synthesized and have demonstrated remarkable excitation energy transfer properties. The study presents the computational design and simulation of a synthetic light-harvesting system that emulates natural mechanisms by arranging cationic free-base porphyrin molecules on an anionic clay surface. We investigated the transfer of excitation energy among the porphyrin dyes using a multiscale quantum mechanics/molecular mechanics (QM/MM) approach based on the semi-empirical density functional-based tight-binding (DFTB) theory for the ground state dynamics. To improve the accuracy of our results, we incorporated an innovative multifidelity machine learning (MFML) approach, which allows the prediction of excitation energies at the numerically demanding time-dependent density functional theory level with the Def2-SVP basis set. This approach was applied to an extensive dataset of 640K geometries for the 90-atom porphyrin structures, facilitating a thorough analysis of the excitation energy diffusion among the porphyrin molecules adsorbed to the clay surface. The insights gained from this study, inspired by natural light-harvesting complexes, demonstrate the potential of porphyrin-clay systems as effective energy transfer systems.

Using the methods from topological dynamics, H. Furstenberg introduced the notion of a central set and proved the famous Central Sets Theorem. Later D. De, Neil Hindman, and D. Strauss [Fund. Math.199 (2008), 155-175.] established a stronger version of the Central Sets Theorem and then introduced the notion of $C$-sets satisfying the Central Sets Theorem and studied the properties of these sets. For any weak mixing system $\left(X, \mathcal{B},\mu, T\right),$ and $A_{0},A_{1}\in\mathcal{B}$, with $\mu\left(A_{0}\right)\mu\left(A_{1}\right)>0$, R. Kung and X.Ye [Disc. Cont. Dyn. sys., 18 (2007) 817-827.] proved that the set $N\left(A,B\right)= \left\{n:\mu\left(A_{0}\cap T^{-n}A_{1}\right)>0\right\}$ intersects all sets of positive upper Banach density. However, later N. Hindman and D. Strauss [New York J. Math. 26 (2020) 230-260.] proved that there exist $C$-sets having zero upper Banach density. Inspired by this result, in this article, we prove that $N\left(A, B \right)$ intersects with all $C$-sets. Then we introduce the notion of a dynamical $C^{\star}$-set and then we study their combinatorial properties., Comment: 8 pages

High-fidelity quantum optomechanical control of a mechanical oscillator requires the ability to perform efficient, low-noise operations on long-lived phononic excitations. Microfabricated high-overtone bulk acoustic wave resonators ($\mathrm{\mu}$HBARs) have been shown to support high-frequency (> 10 GHz) mechanical modes with exceptionally long coherence times (> 1.5 ms), making them a compelling resource for quantum optomechanical experiments. In this paper, we demonstrate a new optomechanical system that permits quantum optomechanical control of individual high-coherence phonon modes supported by such $\mathrm{\mu}$HBARs for the first time. We use this system to perform laser cooling of such ultra-massive (7.5 $\mathrm{\mu}$g) high frequency (12.6 GHz) phonon modes from an occupation of ${\sim}$22 to fewer than 0.4 phonons, corresponding to laser-based ground-state cooling of the most massive mechanical object to date. Through these laser cooling experiments, no absorption-induced heating is observed, demonstrating the resilience of the $\mathrm{\mu}$HBAR against parasitic heating. The unique features of such $\mathrm{\mu}$HBARs make them promising as the basis for a new class of quantum optomechanical systems that offer enhanced robustness to decoherence, necessary for efficient, low-noise photon-phonon conversion.

Raw nanopore signal analysis is a common approach in genomics to provide fast and resource-efficient analysis without translating the signals to bases (i.e., without basecalling). However, existing solutions cannot interpret raw signals directly if a reference genome is unknown due to a lack of accurate mechanisms to handle increased noise in pairwise raw signal comparison. Our goal is to enable the direct analysis of raw signals without a reference genome. To this end, we propose Rawsamble, the first mechanism that can 1) identify regions of similarity between all raw signal pairs, known as all-vs-all overlapping, using a hash-based search mechanism and 2) use these to construct genomes from scratch, called de novo assembly. Our extensive evaluations across multiple genomes of varying sizes show that Rawsamble provides a significant speedup (on average by 16.36x and up to 41.59x) and reduces peak memory usage (on average by 11.73x and up to by 41.99x) compared to a conventional genome assembly pipeline using the state-of-the-art tools for basecalling (Dorado's fastest mode) and overlapping (minimap2) on a CPU. We find that 36.57% of overlapping pairs generated by Rawsamble are identical to those generated by minimap2. Using the overlaps from Rawsamble, we construct the first de novo assemblies directly from raw signals without basecalling. We show that we can construct contiguous assembly segments (unitigs) up to 2.7 million bases in length (half the genome length of E. coli). We identify previously unexplored directions that can be enabled by finding overlaps and constructing de novo assemblies. Rawsamble is available at https://github.com/CMU-SAFARI/RawHash. We also provide the scripts to fully reproduce our results on our GitHub page.

Graph distillation has emerged as a promising avenue to enable scalable training of GNNs by compressing the training dataset while preserving essential graph characteristics. Our study uncovers significant shortcomings in current graph distillation techniques. First, the majority of the algorithms paradoxically require training on the full dataset to perform distillation. Second, due to their gradient-emulating approach, these methods require fresh distillation for any change in hyperparameters or GNN architecture, limiting their flexibility and reusability. Finally, they fail to achieve substantial size reduction due to synthesizing fully-connected, edge-weighted graphs. To address these challenges, we present Bonsai, a novel graph distillation method empowered by the observation that \textit{computation trees} form the fundamental processing units of message-passing GNNs. Bonsai distills datasets by encoding a careful selection of \textit{exemplar} trees that maximize the representation of all computation trees in the training set. This unique approach imparts Bonsai as the first linear-time, model-agnostic graph distillation algorithm for node classification that outperforms existing baselines across $6$ real-world datasets on accuracy, while being $22$ times faster on average. Bonsai is grounded in rigorous mathematical guarantees on the adopted approximation strategies making it robust to GNN architectures, datasets, and parameters.

Automating the theory-experiment cycle requires effective distributed workflows that utilize a computing continuum spanning lab instruments, edge sensors, computing resources at multiple facilities, data sets distributed across multiple information sources, and potentially cloud. Unfortunately, the obvious methods for constructing continuum platforms, orchestrating workflow tasks, and curating datasets over time fail to achieve scientific requirements for performance, energy, security, and reliability. Furthermore, achieving the best use of continuum resources depends upon the efficient composition and execution of workflow tasks, i.e., combinations of numerical solvers, data analytics, and machine learning. Pacific Northwest National Laboratory's LDRD "Cloud, High-Performance Computing (HPC), and Edge for Science and Security" (CHESS) has developed a set of interrelated capabilities for enabling distributed scientific workflows and curating datasets. This report describes the results and successes of CHESS from the perspective of open science.

Vizing's Theorem from 1964 states that any $n$-vertex $m$-edge graph with maximum degree $\Delta$ can be {\em edge colored} using at most $\Delta + 1$ colors. For over 40 years, the state-of-the-art running time for computing such a coloring, obtained independently by Arjomandi [1982] and by Gabow, Nishizeki, Kariv, Leven and Terada~[1985], was $\tilde O(m\sqrt{n})$. Very recently, this time bound was improved in two independent works, by Bhattacharya, Carmon, Costa, Solomon and Zhang to $\tilde O(mn^{1/3})$, and by Assadi to $\tilde O(n^2)$. In this paper we present an algorithm that computes such a coloring in $\tilde O(mn^{1/4})$ time. Our key technical contribution is a subroutine for extending the coloring to one more edge within time $\tilde O(\Delta^2 + \sqrt{\Delta n})$. The best previous time bound of any color extension subroutine is either the trivial $O(n)$, dominated by the length of a Vizing chain, or the bound $\tilde{O}(\Delta^6)$ by Bernshteyn [2022], dominated by the length of {\em multi-step Vizing chains}, which is basically a concatenation of multiple (carefully chosen) Vizing chains. Our color extension subroutine produces significantly shorter multi-step Vizing chains than in previous works, for sufficiently large $\Delta$., Comment: To appear at SODA 2025

Decentralized learning (DL) is an emerging technique that allows nodes on the web to collaboratively train machine learning models without sharing raw data. Dealing with stragglers, i.e., nodes with slower compute or communication than others, is a key challenge in DL. We present DivShare, a novel asynchronous DL algorithm that achieves fast model convergence in the presence of communication stragglers. DivShare achieves this by having nodes fragment their models into parameter subsets and send, in parallel to computation, each subset to a random sample of other nodes instead of sequentially exchanging full models. The transfer of smaller fragments allows more efficient usage of the collective bandwidth and enables nodes with slow network links to quickly contribute with at least some of their model parameters. By theoretically proving the convergence of DivShare, we provide, to the best of our knowledge, the first formal proof of convergence for a DL algorithm that accounts for the effects of asynchronous communication with delays. We experimentally evaluate DivShare against two state-of-the-art DL baselines, AD-PSGD and Swift, and with two standard datasets, CIFAR-10 and MovieLens. We find that DivShare with communication stragglers lowers time-to-accuracy by up to 3.9x compared to AD-PSGD on the CIFAR-10 dataset. Compared to baselines, DivShare also achieves up to 19.4% better accuracy and 9.5% lower test loss on the CIFAR-10 and MovieLens datasets, respectively.

In this paper, we consider the \emph{metric $k$-center} problem in the fully dynamic setting, where we are given a metric space $(V,d)$ evolving via a sequence of point insertions and deletions and our task is to maintain a subset $S \subseteq V$ of at most $k$ points that minimizes the objective $\max_{x \in V} \min_{y \in S}d(x, y)$. We want to design our algorithm so that we minimize its \emph{approximation ratio}, \emph{recourse} (the number of changes it makes to the solution $S$) and \emph{update time} (the time it takes to handle an update). We give a simple algorithm for dynamic $k$-center that maintains a $O(1)$-approximate solution with $O(1)$ amortized recourse and $\tilde O(k)$ amortized update time, \emph{obtaining near-optimal approximation, recourse and update time simultaneously}. We obtain our result by combining a variant of the dynamic $k$-center algorithm of Bateni et al.~[SODA'23] with the dynamic sparsifier of Bhattacharya et al.~[NeurIPS'23].

Pressure-induced emission enhancement and bandgap narrowing in vacancy-ordered halide double perovskite $Cs_2TeBr_6$ are extensively investigated through photoluminescence and absorption experiments. The below bandgap broad emission is attributed to self-trapped excitons recombination. The $Cs_2TeBr_6$ crystal, consisting of undistorted octahedra, exhibits substantial emission enhancement due to the lowering of the energy barrier between $^3P_1$ and self-trapped exciton states, as well as the suppression of nonradiative energy loss with increasing pressure. In the Raman measurements, the observed behavior of full width at half maximum of all Raman modes implies dominant electron-phonon interactions rather than anharmonic interactions between phonons. The pressure-dependent X-ray diffraction measurements reveal an anomalous behaviour in the normalized pressure as a function of the Eulerian strain.

As LLMs are increasingly deployed in global applications, the importance of cultural sensitivity becomes paramount, ensuring that users from diverse backgrounds feel respected and understood. Cultural harm can arise when these models fail to align with specific cultural norms, resulting in misrepresentations or violations of cultural values. This work addresses the challenges of ensuring cultural sensitivity in LLMs, especially in small-parameter models that often lack the extensive training data needed to capture global cultural nuances. We present two key contributions: (1) A cultural harm test dataset, created to assess model outputs across different cultural contexts through scenarios that expose potential cultural insensitivities, and (2) A culturally aligned preference dataset, aimed at restoring cultural sensitivity through fine-tuning based on feedback from diverse annotators. These datasets facilitate the evaluation and enhancement of LLMs, ensuring their ethical and safe deployment across different cultural landscapes. Our results show that integrating culturally aligned feedback leads to a marked improvement in model behavior, significantly reducing the likelihood of generating culturally insensitive or harmful content. Ultimately, this work paves the way for more inclusive and respectful AI systems, fostering a future where LLMs can safely and ethically navigate the complexities of diverse cultural landscapes.

We have designed and commissioned a new readout board to detect photosensor signals from gas-bubbler panels to continuously monitor the gas flow through the resistive plate chambers of the $K_L^0$ and muon detector of Belle II. The gas flow measurements have been integrated into Belle II's alarm system. The bubbler-monitoring system was first employed during the February 2024 to July 2024 Belle II data-taking period., Comment: 4 pages, 5 figures

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

Vizing's theorem states that any $n$-vertex $m$-edge graph of maximum degree $\Delta$ can be edge colored using at most $\Delta + 1$ different colors [Vizing, 1964]. Vizing's original proof is algorithmic and shows that such an edge coloring can be found in $O(mn)$ time. This was subsequently improved to $\tilde O(m\sqrt{n})$ time, independently by [Arjomandi, 1982] and by [Gabow et al., 1985]. Very recently, independently and concurrently, using randomization, this runtime bound was further improved to $\tilde{O}(n^2)$ by [Assadi, 2024] and $\tilde O(mn^{1/3})$ by [Bhattacharya, Carmon, Costa, Solomon and Zhang, 2024] (and subsequently to $\tilde O(mn^{1/4})$ time by [Bhattacharya, Costa, Solomon and Zhang, 2024]). In this paper, we present a randomized algorithm that computes a $(\Delta+1)$-edge coloring in near-linear time -- in fact, only $O(m\log{\Delta})$ time -- with high probability, giving a near-optimal algorithm for this fundamental problem., Comment: Extended our results for simple graphs to Vizing's and Shannon's theorems for multigraphs

Large Language Models (LLMs) have shown remarkable capabilities in natural language processing, mathematical problem solving, and tasks related to program synthesis. However, their effectiveness in long-term planning and higher-order reasoning has been noted to be limited and fragile. This paper explores an approach for enhancing LLM performance in solving a classical robotic planning task by integrating solver-generated feedback. We explore four different strategies for providing feedback, including visual feedback, we utilize fine-tuning, and we evaluate the performance of three different LLMs across a 10 standard and 100 more randomly generated planning problems. Our results suggest that the solver-generated feedback improves the LLM's ability to solve the moderately difficult problems, but the harder problems still remain out of reach. The study provides detailed analysis of the effects of the different hinting strategies and the different planning tendencies of the evaluated LLMs.

Decentralized learning (DL) is an emerging approach that enables nodes to collaboratively train a machine learning model without sharing raw data. In many application domains, such as healthcare, this approach faces challenges due to the high level of heterogeneity in the training data's feature space. Such feature heterogeneity lowers model utility and negatively impacts fairness, particularly for nodes with under-represented training data. In this paper, we introduce \textsc{Facade}, a clustering-based DL algorithm specifically designed for fair model training when the training data exhibits several distinct features. The challenge of \textsc{Facade} is to assign nodes to clusters, one for each feature, based on the similarity in the features of their local data, without requiring individual nodes to know apriori which cluster they belong to. \textsc{Facade} (1) dynamically assigns nodes to their appropriate clusters over time, and (2) enables nodes to collaboratively train a specialized model for each cluster in a fully decentralized manner. We theoretically prove the convergence of \textsc{Facade}, implement our algorithm, and compare it against three state-of-the-art baselines. Our experimental results on three datasets demonstrate the superiority of our approach in terms of model accuracy and fairness compared to all three competitors. Compared to the best-performing baseline, \textsc{Facade} on the CIFAR-10 dataset also reduces communication costs by 32.3\% to reach a target accuracy when cluster sizes are imbalanced.

Controlling the dynamics of quantum many-body systems is crucial for developing quantum technologies. This work demonstrates that counter-diabatic (CD) driving provides a powerful tool for steering collective spin systems along entangled trajectories for a long time. In particular, CD driving leads to approximate stroboscopic freezing and eternal entanglement oscillations for a large class of initial states in the periodically driven Lipkin-Meshkov-Glick model. This is accompanied by a decrease in the average eigenstate entanglement and inverse participation ratio, thereby signalling greater eigenstate localization. Our work opens a new route to evade Floquet heating and control entanglement generation in collective spin systems., Comment: 6+3 pages, 4+1 figures

Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create particles with local gates and simulate their quantum dynamics via a discretized time evolution. As the effective magnetic field is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent particle and string dynamics.

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

We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a Kagome-strip chain (KSC), a one-dimensional analogue of the Kagome lattice, and construct its phase diagram in an extended exchange parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-$3/2$ state as well as spin-$1/2$ states with and without additional degeneracies. We explore the ground state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.

The optical generation of nonequilibrium spin magnetization plays a crucial role in advancing spintronics, providing ultrafast control of magnetization dynamics without the need for magnetic fields. Here, we demonstrate the feasibility of light-induced nonlinear spin magnetization (LNSM), which becomes a dominant effect in centrosymmetric materials. We reveal the quantum geometric origins of various LNSM contributions in both metallic and insulating systems. Through detailed symmetry analysis, we predict significant LNSM in the antiferromagnetic material CuMnAs. Notably, under circularly polarized light, the spin magnetization exhibits helicity-dependent behavior, reversing with opposite light helicity. These findings open up new possibilities for generating LNSM-driven nonlinear spin-orbit torques and developing innovative opto-spintronic devices., Comment: Comments are welcome. 7 pages, 3 figures, 2 tables

Fueled by the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements in fields like distributed cyber-security and social networks have spurred the creation of probabilistic models of evolution, where individuals make decisions based on only partial information about the network's current state. This paper seeks to explore models that incorporate \emph{network delay}, where new participants receive information from a time-lagged snapshot of the system. In the context of mesoscopic network delays, we develop probabilistic tools built on stochastic approximation to understand asymptotics of both local functionals, such as local neighborhoods and degree distributions, as well as global properties, such as the evolution of the degree of the network's initial founder. A companion paper explores the regime of macroscopic delays in the evolution of the network., Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:2409.06048

We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the relative entropy between the joint density of $N$ particle locations and the $N$-fold product target measure, starting from a regular initial distribution, splits into a dominant `negative part' proportional to $N$ times the expected $\mathsf{KSD}^2$ and a smaller `positive part'. This observation leads to $\mathsf{KSD}$ rates of order $1/\sqrt{N}$, in both continuous and discrete time, providing a near optimal (in the sense of matching the corresponding i.i.d. rates) double exponential improvement over the recent result by Shi and Mackey (2024). Under mild assumptions on the kernel and potential, these bounds also grow polynomially in the dimension $d$. By adding a bilinear component to the kernel, the above approach is used to further obtain Wasserstein-2 convergence in continuous time. For the case of `bilinear + Mat\'ern' kernels, we derive Wasserstein-2 rates that exhibit a curse-of-dimensionality similar to the i.i.d. setting. We also obtain marginal convergence and long-time propagation of chaos results for the time-averaged particle laws., Comment: 23 pages. Discrete-time analysis of SVGD added

In this paper, we have proposed a resilient reinforcement learning method for discrete-time linear systems with unknown parameters, under denial-of-service (DoS) attacks. The proposed method is based on policy iteration that learns the optimal controller from input-state data amidst DoS attacks. We achieve an upper bound for the DoS duration to ensure closed-loop stability. The resilience of the closed-loop system, when subjected to DoS attacks with the learned controller and an internal model, has been thoroughly examined. The effectiveness of the proposed methodology is demonstrated on an inverted pendulum on a cart.

Driven by the explosion of data and the impact of real-world networks, a wide array of mathematical models have been proposed to understand the structure and evolution of such systems, especially in the temporal context. Recent advances in areas such as distributed cyber-security and social networks have motivated the development of probabilistic models of evolution where individuals have only partial information on the state of the network when deciding on their actions. This paper aims to understand models incorporating \emph{network delay}, where new individuals have information on a time-delayed snapshot of the system. We consider the setting where one has macroscopic delays, that is, the ``information'' available to new individuals is the structure of the network at a past time, which scales proportionally with the current time and vertices connect using standard preferential attachment type dynamics. We obtain the local weak limit for the network as its size grows and connect it to a novel continuous-time branching process where the associated point process of reproductions \emph{has memory} of the entire past. A more tractable `dual description' of this branching process using an `edge copying mechanism' is used to obtain degree distribution asymptotics as well as necessary and sufficient conditions for condensation, where the mass of the degree distribution ``escapes to infinity''. We conclude by studying the impact of the delay distribution on macroscopic functionals such as the root degree., Comment: 38 pages + 3 page appendix

We prove that if $A=\{a_1,\dots ,a_{|A|}\}\subset \{1,2,\dots ,n\}$ is a Sidon set so that $|A|=n^{1/2}-L^\prime$, then $$a_m = m\cdot n^{1/2} + \mathcal O\left( n^{7/8}\right) + \mathcal O\left(L^{1/2}\cdot n^{3/4}\right)$$ where $L=\max\{0,L^\prime\}$. As an application of this, we give easy proofs of some previously derived results. We proceed on to proving that for any $\varepsilon >0$, we have $$\sum_{a\in S} a = \frac 12 n^{3/2} + \mathcal O \left (n^{11/8} \right )$$ for all $n\le N$ but at most $\mathcal O_{\varepsilon} \left (N^{\frac 35 + \varepsilon} \right )$ exceptions.

Studying the magnetic field properties on the solar surface is crucial for understanding the solar and heliospheric activities, which in turn shape space weather in the solar system. Surface Flux Transport (SFT) modeling helps us to simulate and analyse the transport and evolution of magnetic flux on the solar surface, providing valuable insights into the mechanisms responsible for solar activity. In this work, we demonstrate the use of machine learning techniques in solving magnetic flux transport, making it accurate. We have developed a novel Physics-Informed Neural Networks (PINN)-based model to study the evolution of Bipolar Magnetic Regions (BMRs) using SFT in one-dimensional azimuthally averaged and also in two-dimensions. We demonstrate the efficiency and computational feasibility of our PINN-based model by comparing its performance and accuracy with that of a numerical model implemented using the Runge-Kutta Implicit-Explicit (RK-IMEX) scheme. The mesh-independent PINN method can be used to reproduce the observed polar magnetic field with better flux conservation. This advancement is important for accurately reproducing observed polar magnetic fields, thereby providing insights into the strength of future solar cycles. This work paves the way for more efficient and accurate simulations of solar magnetic flux transport and showcases the applicability of PINN in solving advection-diffusion equations with a particular focus on heliophysics.

Bipartite graphs are a fundamental concept in graph theory and have significant applications in data analysis and modeling complex processes. A graph is bipartite if its vertices can be divided into two sets, with no connections within each set. Detecting bipartite graphs can be done by examining their cycles; a graph is bipartite if and only if there are no odd cycles present. This characteristic is essential in various problem domains, such as clustering and matching. Bipartite graphs can be identified through the spectrum of the Laplacian, a graph is bipartite if and only if the maximum eigenvalue of the normalized Laplacian equals two. However, graphs are limited to representing pairwise interactions, to model higher-order connections in complex systems, hypergraphs and simplicial complexes are required. This raises the question of what is bipartiteness for simplicial complexes of higher dimensions - whether obtaining the maximum eigenvalue of the normalized Laplacian is equivalent to partitioning the simplexes into two, similar to the graph case. We address this problem by fully characterizing those complexes for which the maximum eigenvalue of the Laplacian is obtained, known as disorientable simplicial complexes, based on the parity of the length of cycles in their down dual graph. We show that a N-dimensional simplicial complex is disorientable if and only if its down dual graph has no simple odd cycle of distinct edges and no twisted even cycle of distinct edges. We note that having no odd cycle is the key to answering the bi-partitioning problem of the simplexes., Comment: 11 pages, 4 figures

Catastrophic forgetting makes neural network models unstable when learning visual domains consecutively. The neural network model drifts to catastrophic forgetting-induced low performance of previously learnt domains when training with new domains. We illuminate this current neural network model weakness and develop a forgetting-resistant incremental learning strategy. Here, we propose a new unsupervised incremental open-set domain adaptation (IOSDA) issue for image classification. Open-set domain adaptation adds complexity to the incremental domain adaptation issue since each target domain has more classes than the Source domain. In IOSDA, the model learns training with domain streams phase by phase in incremented time. Inference uses test data from all target domains without revealing their identities. We proposed IOSDA-Net, a two-stage learning pipeline, to solve the problem. The first module replicates prior domains from random noise using a generative framework and creates a pseudo source domain. In the second step, this pseudo source is adapted to the present target domain. We test our model on Office-Home, DomainNet, and UPRN-RSDA, a newly curated optical remote sensing dataset.

The SuperKEKB/Belle II experiment aims to collect high-statistics data of B meson pairs to explore new physics beyond the Standard Model (SM). SuperKEKB, an upgraded version of the KEKB accelerator, has achieved a world-record luminosity of $4.71 \times 10^{34} \, \mathrm{cm^{-2}s^{-1}}$ in 2022 but continues to strive for higher luminosities. One of the major obstacles is Sudden Beam Loss (SBL) events, which cause substantial beam losses and damage to the Belle~II detector. To find a hint for addressing SBL challenges, advanced beam diagnostic systems and enhanced beam abort systems have been developed. The diagnostic system aims to accurately pinpoint the start of beam losses, while the upgraded abort system quickly disposes of anomalous beams to minimize damage. This paper details the development and implementation of these systems, including high-speed loss monitors, time synchronization with the White Rabbit system, and data acquisition systems. Efforts to understand the mechanisms of SBL events, using acoustic sensors to detect discharges, are also discussed. These measures aim to improve the operational stability and luminosity of SuperKEKB, contributing to the experiment's success., Comment: 17 pages, 25 figures

In [Adv. Math., 321 (2017) 269-286], using the theory of ultrafilters, J. H. Johnson Jr., and F. K. Richter proved the nilpotent polynomial Hales-Jewett theorem. Using this result they proved the restricted version of the van der Waerden theorem for nilprogressions of rank $2$ and conjectured that this result must hold for arbitrary rank. In this article, we give an affirmative answer to their conjecture.

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

The advent of social media platforms has revolutionized information consumption patterns, with individuals frequently engaging in these platforms for social interactions. This trend has fostered an environment where people gravitate towards information that aligns with their preconceived notions, leading to the formation of echo chambers and polarization within the society. Recently introduced activity-driven models have been successful in capturing the dynamics of information propagation and polarization. The present study uses this model to explore the impact of social media on a polarized society. By considering the varying influence of media, ranging from exposing individuals to contradictory views to reinforcing existing opinions, a supercritical pitchfork bifurcation is observed, triggering a transition from consensus to polarization. The transition points from polarization to consensus are derived analytically and is validated through numerical simulations. This research sheds light on the complex interplay between social media dynamics and societal polarization.