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We present FastLexRank\footnote{https://github.com/LiMaoUM/FastLexRank}, an efficient and scalable implementation of the LexRank algorithm for text ranking. Designed to address the computational and memory complexities of the original LexRank method, FastLexRank significantly reduces time and memory requirements from $\mathcal{O}(n^2)$ to $\mathcal{O}(n)$ without compromising the quality or accuracy of the results. By employing an optimized approach to calculating the stationary distribution of sentence graphs, FastLexRank maintains an identical results with the original LexRank scores while enhancing computational efficiency. This paper details the algorithmic improvements that enable the processing of large datasets, such as social media corpora, in real-time. Empirical results demonstrate its effectiveness, and we propose its use in identifying central tweets, which can be further analyzed using advanced NLP techniques. FastLexRank offers a scalable solution for text centrality calculation, addressing the growing need for efficient processing of digital content.

Many socio-economical critical domains (such as sustainability, public health, and disasters) are characterized by highly complex and dynamic systems, requiring data and model-driven simulations to support decision-making. Due to a large number of unknowns, decision-makers usually need to generate ensembles of stochastic scenarios, requiring hundreds or thousands of individual simulation instances, each with different parameter settings corresponding to distinct scenarios, As the number of model parameters increases, the number of potential timelines one can simulate increases exponentially. Consequently, simulation ensembles are inherently sparse, even when they are extremely large. This necessitates a platform for (a) deciding which simulation instances to execute and (b) given a large simulation ensemble, enabling decision-makers to explore the resulting alternative timelines, by extracting and visualizing consistent, yet diverse timelines from continuous-coupled simulation ensembles. In this article, we present DataStorm-EM platform for data- and model-driven simulation ensemble management, optimization, analysis, and exploration, describe underlying challenges and present our solution.

Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in $n$-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios., Comment: 17 pages, 2 figures

In the rapidly evolving landscape of Natural Language Processing (NLP), the use of Large Language Models (LLMs) for automated text annotation in social media posts has garnered significant interest. Despite the impressive innovations in developing LLMs like ChatGPT, their efficacy, and accuracy as annotation tools are not well understood. In this paper, we analyze the performance of eight open-source and proprietary LLMs for annotating the stance expressed in social media posts, benchmarking their performance against human annotators' (i.e., crowd-sourced) judgments. Additionally, we investigate the conditions under which LLMs are likely to disagree with human judgment. A significant finding of our study is that the explicitness of text expressing a stance plays a critical role in how faithfully LLMs' stance judgments match humans'. We argue that LLMs perform well when human annotators do, and when LLMs fail, it often corresponds to situations in which human annotators struggle to reach an agreement. We conclude with recommendations for a comprehensive approach that combines the precision of human expertise with the scalability of LLM predictions. This study highlights the importance of improving the accuracy and comprehensiveness of automated stance detection, aiming to advance these technologies for more efficient and unbiased analysis of social media.

We investigate proton-antiproton ($p\bar{p}$) pair production via photon-photon fusion in the ultra-peripheral collisions at RHIC, employing a joint impact parameter and transverse momentum dependent formalism. We consider proton exchange, $s$-channel resonance and hand-bag mechanisms, predicting differential distributions of $p\bar p$ production. Our theoretical predictions can be tested against future measurements at RHIC, to enhance our understanding of photon-photon interactions in strong electromagnetic fields., Comment: 6 pages, 4 figures

Strong nonlocality, proposed by Halder {\it et al}. [\href{https://doi.org/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett. \textbf{122}, 040403 (2019)}], is a stronger manifestation than quantum nonlocality. Subsequently, Shi {\it et al}. presented the concept of the strongest nonlocality [\href{https://doi.org/10.22331/q-2022-01-05-619}{Quantum \textbf{6}, 619 (2022)}]. Recently, Li and Wang [\href{https://doi.org/10.22331/q-2023-09-07-1101}{Quantum \textbf{7}, 1101 (2023)}] posed the conjecture about a lower bound to the cardinality of the strongest nonlocal set $\mathcal{S}$ in $\otimes _{i=1}^{n}\mathbb{C}^{d_i}$, i.e., $|\mathcal{S}|\leq \max_{i}\{\prod_{j=1}^{n}d_j/d_i+1\}$. In this work, we construct the strongest nonlocal set of size $d^2+1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we obtain the strongest nonlocal set of size $d_{2}d_{3}+1$ in $\mathbb{C}^{d_1}\otimes \mathbb{C}^{d_2}\otimes \mathbb{C}^{d_3}$. Our construction reaches the lower bound, which provides an affirmative solution to Li and Wang's conjecture. In particular, the strongest nonlocal sets we present here contain the least number of orthogonal states among the available results., Comment: 10 pages, 7 figures

The notion of strong nonlocality, which refers to local irreducibility of a set of orthogonal multipartite quantum states across each bipartition of the subsystems, was put forward by Halder et al. in [Phys. Rev. Lett. 122, 040403 (2019)]. Here, we show the existence of three orthogonal quantum states in (C^2)^{\otimes N} that cannot be perfectly distinguished locally across any bipartition of the subsystems. Specifically, all these three states are genuinely entangled, among which two are the N-qubit GHZ pairs. Since any three locally indistinguishable states are always locally irreducible, the three N-partite orthogonal states we present are strongly nonlocal. Thus, the caridnality of strongly nonlocal sets here is dramatically smaller than all known ones.

Fairness-aware classification models have gained increasing attention in recent years as concerns grow on discrimination against some demographic groups. Most existing models require full knowledge of the sensitive features, which can be impractical due to privacy, legal issues, and an individual's fear of discrimination. The key challenge we will address is the group dependency of the unavailability, e.g., people of some age range may be more reluctant to reveal their age. Our solution augments general fairness risks with probabilistic imputations of the sensitive features, while jointly learning the group-conditionally missing probabilities in a variational auto-encoder. Our model is demonstrated effective on both image and tabular datasets, achieving an improved balance between accuracy and fairness.

Quantum coherence is the key resource in quantum technologies including faster computing, secure communication and advanced sensing. Its quantification and detection are, therefore, paramount within the context of quantum information processing. Having certain priori knowledge on the observables may enhance the efficiency of coherence detection. In this work, we posit that the trace of the observables is a known quantity. Our investigation confirms that this assumption indeed extends the scope of coherence detection capabilities. Utilizing this prior knowledge of the trace of the observables, we establish a series of coherence detection criteria. We investigate the detection capabilities of these coherence criteria from diverse perspectives and ultimately ascertain the existence of four distinct and inequivalent criteria. These findings contribute to the deepening of our understanding of coherence detection methodologies, thereby potentially opening new avenues for advancements in quantum technologies., Comment: 9 pages, 3 figures

This study investigates measurement strategies in a scenario where multiple pairs of Alices and Bobs independently and sequentially observe entangled states. The aim is to maximize the number of observer pairs $(A_k,B_l)$ that can witness entanglement. Prior research has demonstrated that arbitrary pairs $(A_k, B_k)$ ($k\leq n$) can observe entanglement in all pure entangled states and a specific class of mixed entangled states [Phys. Rev. A 106 032419 (2022)]. However, it should be noted that other pairs $(A_k, B_l)$ with $(k\neq l \leq n)$ may not observe entanglement using the same strategy. Moreover, a novel strategy is presented, enabling every pair of arbitrarily many Alices and Bobs to witness entanglement regardless of the initial state being a Bell state or a particular class of mixed entangled states. These findings contribute to understanding measurement strategies for maximizing entanglement observation in various contexts., Comment: 11 pages, 2 figures

In recent times, there has been a growing scholarly focus on investigating the intricacies of quantum channel mixing. It has been commonly believed, based on intuition in the literature, that every generalized Pauli channel with dimensionality $d$ could be represented as a convex combination of $(d+1)$ generalized Pauli dephasing channels (see [Phys. Rev. A 103, 022605 (2021)] as a reference). To our surprise, our findings indicate the inaccuracy of this intuitive perspective. This has stimulated our interest in exploring the properties of convex combinations of generalized Pauli channels, beyond the restriction to just $(d+1)$ generalized Pauli dephasing channels. We demonstrate that many previously established properties still hold within this broader context. For instance, any mixture of invertible generalized Pauli channels retains its invertibility. It's worth noting that this property doesn't hold when considering the Weyl channels setting. Additionally, we demonstrate that every Pauli channel (for the case of $d=2$) can be represented as a mixture of $(d+1)$ Pauli dephasing channels, but this generalization doesn't apply to higher dimensions. This highlights a fundamental distinction between qubit and general qudit cases. In contrast to prior understanding, we show that non-invertibility of mixed channels is not a prerequisite for the resulting mapping to constitute a Markovian semigroup., Comment: 9 pages, 2 figures

A set of orthogonal multipartite quantum states are called (distinguishability-based) genuinely nonlocal if they are locally indistinguishable across any bipartition of the subsystems. In this work, we consider the problem of constructing small genuinely nonlocal sets consisting of generalized GHZ states in multipartite systems. For system (C^2)^(\otimes N) where N is large, using the language of group theory, we show that a tiny proportion {\Theta}[1/2^(N/2)] of the states among the N-qubit GHZ basis suffice to exhibit genuine nonlocality. Similar arguments also hold for the canonical generalized GHZ bases in systems (C^d)^(\otimes N), wherever d is even and N is large. What is more, moving to the condition that any fixed N is given, we show that d + 1 genuinely nonlocal generalized GHZ states exist in (C^d)^(\otimes N), provided the local dimension d is sufficiently large. As an additional merit, within and beyond an asymptotic sense, the latter result also indicates some evident limitations of the "trivial othogonality-preserving local measurements" (TOPLM) technique that has been utilized frequently for detecting genuine nonlocality., Comment: accepted by PRA in January 2024

The nonlocal set has received wide attention over recent years. Shortly before, Li and Wang arXiv:2202.09034 proposed the concept of a locally stable set: the only possible orthogonality preserving measurement on each subsystem is trivial. Locally stable sets present stronger nonlocality than those sets that are just locally indistinguishable. In this work, we focus on the constructions of locally stable sets in multipartite quantum systems. First, two lemmas are put forward to prove that an orthogonality-preserving local measurement must be trivial. Then we present the constructions of locally stable sets with minimum cardinality in bipartite quantum systems $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ $(d\geq 3)$ and $\mathbb{C}^{d_{1}}\otimes \mathbb{C}^{d_{2}}$ $(3\leq d_{1}\leq d_{2})$. Moreover, for the multipartite quantum systems $(\mathbb{C}^{d})^{\otimes n}$ $(d\geq 2)$ and $\otimes^{n}_{i=1}\mathbb{C}^{d_{i}}$ $(3\leq d_{1}\leq d_{2}\leq\cdots\leq d_{n})$, we also obtain $d+1$ and $d_{n}+1$ locally stable orthogonal states respectively. Fortunately, our constructions reach the lower bound of the cardinality on the locally stable sets, which provides a positive and complete answer to an open problem raised in arXiv:2202.09034 ., Comment: 10 pages, 3 figures

GRB 221009A is the brightest gamma-ray burst ever detected since the discovery of this kind of energetic explosions. However, an accurate measurement of the prompt emission properties of this burst is very challenging due to its exceptional brightness. With joint observations of \textit{Insight}-HXMT and GECAM-C, we made an unprecedentedly accurate measurement of the emission during the first $\sim$1800 s of GRB 221009A, including its precursor, main emission (ME, which dominates the burst in flux), flaring emission and early afterglow, in the hard X-ray to soft gamma-ray band from $\sim$ 10 keV to $\sim$ 6 MeV. Based on the GECAM-C unsaturated data of the ME, we measure a record-breaking isotropic equivalent energy ($E_{\rm iso}$) of $\bf \sim 1.5 \times 10^{55}$ erg, which is about eight times the total rest-mass energy of the Sun. The early afterglow data require a significant jet break between 650 s and 1100 s, most likely at $\sim950$ s from the afterglow starting time $T_{AG}$, which corresponds to a jet opening angle of $\sim {0.7^\circ} \ (\eta_\gamma n)^{1/8}$, where $n$ is the ambient medium density in units of $\rm cm^{-3}$ and $\eta_\gamma$ is the ratio between $\gamma$-ray energy and afterglow kinetic energy. The beaming-corrected total $\gamma$-ray energy $E_{\gamma}$ is $\sim 1.15 \times10^{51} \ (\eta_\gamma n)^{1/4}$ erg, which is typical for long GRBs. These results suggest that this GRB may have a special central engine, which could launch and collimate a very narrowly beamed jet with an ordinary energy budget, leading to exceptionally luminous gamma-ray radiation per unit solid angle. Alternatively, more GRBs might have such a narrow and bright beam, which are missed by an unfavorable viewing angle or have been detected without distance measurement., Comment: Submitted to National Science Review. This paper is under press embargo, contact the corresponding author for details

As a new member of GECAM mission, GECAM-C (also named High Energy Burst Searcher, HEBS) was launched onboard the SATech-01 satellite on July 27th, 2022, which is capable to monitor gamma-ray transients from $\sim$ 6 keV to 6 MeV. As the main detector, there are 12 gamma-ray detectors (GRDs) equipped for GECAM-C. In order to verify the GECAM-C GRD detector performance and to validate the Monte Carlo simulations of detector response, comprehensive on-ground calibration experiments have been performed using X-ray beam and radioactive sources, including Energy-Channel relation, energy resolution, detection efficiency, SiPM voltage-gain relation and the non-uniformity of positional response. In this paper, the detailed calibration campaigns and data analysis results for GECAM-C GRDs are presented, demonstrating the excellent performance of GECAM-C GRD detectors., Comment: third version

A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular "strong nonlocality" in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states -- the d-dimensional GHZ states, featuring systems with local dimension not limited to 2. In the three-partite case, we find the existence of small genuinely nonlocal sets consisting of these states: we show that the cardinality can at least scale down to linear in the local dimension d, with the linear factor l = 1. Specifically, the method we use is semidefinite program and the GHZ states to construct these sets are special ones which we call "GHZ-lattices". This result might arguably suggest a significant gap between the strength of strong nonlocality and the distinguishability-based genuine nonlocality. Moreover, we put forward the notion of (s,n)-threshold distinguishability and utilizing a similar method, we successfully construct (2,3)-threshold sets consisting of GHZ states in three-partite systems.

It is well known that any $N$ orthogonal pure states can always be perfectly distinguished under local operation and classical communications (LOCC) if $(N-1)$ copies of the state are available [Phys. Rev. Lett. 85, 4972 (2000)]. It is important to reduce the number of quantum state copies that ensures the LOCC distinguishability in terms of resource saving and nonlocality strength characterization. Denote $f_r(N)$ the least number of copies needed to LOCC distinguish any $N$ orthogonal $r$-partite product states. This work will be devoted to the estimation of the upper bound of $f_r(N)$. In fact, we first relate this problem with Ramsey theory, a branch of combinatorics dedicated to studying the conditions under which orders must appear. Subsequently, we prove $f_2(N)\leq \lceil\frac{N}{6}\rceil+2$, which is better than $f_2(N)\leq \lceil\frac{N}{4}\rceil$ obtained in [Eur. Phys. J. Plus 136, 1172 (2021)] when $N>24$. We further exhibit that for arbitrary $\epsilon>0$, $f_r(N)\leq\lceil\epsilon N\rceil$ always holds for sufficiently large $N$., Comment: 13 pages

Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging bound entangled states, quantum nonlocality without entanglement, and Bell inequalities with no quantum violation. A generalized concept called uncompletable product basis also attracts much attention. In this paper, we find some unextendible product bases that are uncompletable product bases in every bipartition, which answers a 19 year-old open question proposed by DiVincenzo et al. [Commun. Math. Phys. 238, 379 (2003)]. As a consequence, we connect such unextendible product bases to local hiding of information and give a sufficient condition for the existence of an unextendible product basis, that is still an unextendible product basis in every bipartition. Our results advance the understanding of the geometry of unextendible product bases.

An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett. \textbf{122}, 040403 (2019)}]. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measurement on each subsystems are trivial measurements. We call the set with this property is locally stable. We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. Then we present a characterization of locally stable sets via the dimensions of some states depended spaces. Moreover, we construct two orthogonal sets in general multipartite quantum systems which are locally stable under every bipartition of the subsystems. As a consequence, we obtain a lower bound and an upper bound on the size of the smallest set which is locally stable for each bipartition of the subsystems. Our results provide a complete answer to an open question (that is, can we show strong quantum nonlocality in $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_1}\otimes \cdots \otimes \mathbb{C}^{d_N} $ for any $d_i \geq 2$ and $1\leq i\leq N$?) raised in a recent paper [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.022209}{Phys. Rev. A \textbf{105}, 022209 (2022)}]. Compared with all previous relevant proofs, our proof here is quite concise., Comment: 11 pages, some other minor correction

Let $G$ be a finite abelian group. For any positive integers $d$ and $m$, let $\varphi_G(d)$ be the number of elements in $G$ of order $d$ and $\mathsf M(G,m)$ be the set of all zero-sum sequences of length $m$. In this paper, for any finite abelian group $H$, we prove that $$|\mathsf M(G,|H|)|=|\mathsf M(H,|G|)|$$ if and only if $\varphi_G(d)=\varphi_H(d)$ for any $d|(|G|,|H|)$. We also consider an extension of this result to non-abelian groups in terms of invariant theory., Comment: 16 pages

A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper, we construct a series of UPBs with different large sizes in $d_A\otimes d_B\otimes d_C$ and $d_A\otimes d_B\otimes d_C\otimes d_D$ for $d_A, d_B, d_C, d_D\geq 3$, and we also show that these UPBs have strong quantum nonlocality, which answers an open question given by Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] and Yuan \emph{et al.} [Phys. Rev. A \textbf{102}, 042228 (2020)] for any possible three and four-partite systems. Furthermore, we propose an entanglement-assisted protocol to locally discriminate the UPB in $3\otimes 3\otimes 4$, and it consumes less entanglement resource than the teleportation-based protocol. Our results build the connection between strong quantum nonlocality and UPBs.

Realtime trigger and localization of bursts are the key functions of GECAM, which is an all-sky gamma-ray monitor launched in Dec 10, 2020. We developed a multifunctional trigger and localization software operating on the CPU of the GECAM electronic box (EBOX). This onboard software has the following features: high trigger efficiency for real celestial bursts with a suppression of false triggers caused by charged particle bursts and background fluctuation, dedicated localization algorithm optimized for short and long bursts respetively, short time latency of the trigger information which is downlinked throught the BeiDou satellite navigation System (BDS). This paper presents the detailed design and deveopment of this trigger and localization software system of GECAM, including the main functions, general design, workflow and algorithms, as well as the verification and demonstration of this software, including the on-ground trigger tests with simulated gamma-ray bursts made by a dedicated X-ray tube and the in-flight performance to real gamma-ray bursts and magnetar bursts., Comment: Draft, comments welcome

We studied the distinguishability of generalized Bell states under local operations and classical communication. We introduced the concept of maximally commutative set (MCS), subset of generalized Pauli matrices whose elements are mutually commutative and there is no other generalized Pauli matrix that is commute with all the elements of this set. We found that MCS can be considered as a detector for local distinguishability of set $\mathcal{S}$ of generalized Bell states. In fact, we got an efficient criterion. That is, if the difference set of $\mathcal{S}$ is disjoint with or completely contain in some MCS, then the set $\mathcal{S}$ is locally distinguishable. Furthermore, we gave a useful characterization of MCS for arbitrary dimension, which provides great convenience for detecting the local discrimination of generalized Bell states. Our method can be generalized to more general settings which contains lattice qudit basis. Results in [Phys. Rev. Lett. \textbf{92}, 177905 (2004)], [Phys. Rev. A \textbf{92}, 042320 (2015)] and a recent work [arXiv: 2109.07390] can be deduced as special cases of our result., Comment: 8 pages, 4 figures, minor modification

Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. As Bandyopadhyay and Halder have been pointed out, sets with genuine hidden nonloclity would lead to some applications on the data hiding., Comment: 13 pages, 6 figures, add one more example

A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition. Most known constructions of strongly nonlocal orthogonal product set (OPS) are limited to tripartite systems, and they are lack of intuitive structures. In this work, based on the decomposition for the outermost layer of an $n$-dimensional hypercube for $n= 3,4,5$, we successfully construct strongly nonlocal OPSs in any possible three, four and five-partite systems, which answers an open question given by Halder et al. [Phys. Rev. Lett.122, 040403 (2019)] and Yuan et al. [Phys. Rev. A102, 042228 (2020)] for any possible three, four and five-partite systems. Our results build the connection between hypercubes and strongly nonlocal OPSs, and exhibit the phenomenon of strong quantum nonlocality without entanglement in multipartite systems., Comment: arXiv admin note: substantial text overlap with arXiv:2101.00735

Let $G$ be a reductive group, and let $X$ be an algebraic curve over an algebraically closed field $k$ with positive characteristic. We prove a version of nonabelian Hodge correspondence for tame $G$-local systems over $X$ and logarithmic $G$-Higgs bundles over the Frobenius twist $X'$. To obtain a full description of the correspondence for the noncompact case, we introduce the language of parahoric group schemes to establish the correspondence., Comment: 25 pages