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The cyclicity and Koblitz conjectures ask about the distribution of primes of cyclic and prime-order reduction, respectively, for elliptic curves over $\mathbb{Q}$. In 1976, Serre gave a conditional proof of the cyclicity conjecture, but the Koblitz conjecture (refined by Zywina in 2011) remains open. The conjectures are now known unconditionally "on average" due to work of Banks--Shparlinski and Balog--Cojocaru--David. Recently, there has been a growing interest in the cyclicity conjecture for primes in arithmetic progressions (AP), with relevant work by Akbal--G\"ulo\u{g}lu and Wong. In this paper, we adapt Zywina's method to formulate the Koblitz conjecture for primes in AP and refine a theorem of Jones to establish results on the moments of the constants in both the cyclicity and Koblitz conjectures for AP. In doing so, we uncover a somewhat counterintuitive phenomenon: On average, these two constants are oppositely biased over congruence classes. Finally, in an accompanying repository, we give Magma code for computing the constants discussed in this paper.

Quantum private query (QPQ) is the quantum version for symmetrically private retrieval. However, the user privacy in QPQ is generally guarded in the non-realtime and cheat sensitive way. That is, the dishonest database holder's cheating to elicit user privacy can only be discovered after the protocol is finished (when the user finds some errors in the retrieved database item). Such delayed detection may cause very unpleasant results for the user in real-life applications. Current efforts to protect user privacy in realtime in existing QPQ protocols mainly use two techniques, i.e., adding an honesty checking on the database or allowing the user to reorder the qubits. We reexamine these two kinds of QPQ protocols and find neither of them can work well. We give concrete cheating strategies for both participants and show that honesty checking of inner participant should be dealt more carefully in for example the choosing of checking qubits. We hope such discussion can supply new concerns when detection of dishonest participant is considered in quantum multi-party secure computations.

Identifying causal relations is crucial for a variety of downstream tasks. In additional to observational data, background knowledge (BK), which could be attained from human expertise or experiments, is usually introduced for uncovering causal relations. This raises an open problem that in the presence of latent variables, what causal relations are identifiable from observational data and BK. In this paper, we propose two novel rules for incorporating BK, which offer a new perspective to the open problem. In addition, we show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data. Our rule-based approach enhances the state-of-the-art method by circumventing a process of enumerating block sets that would otherwise take exponential complexity.

The uncertainty principle is deemed as one of cornerstones in quantum mechanics, and exploring its lower limit of uncertainty will be helpful to understand the principle's nature. In this study, we propose a generalized entropic uncertainty relation for arbitrary multiple-observable in multipartite system, and further derive a tighter lower bound by considering Holevo quality and mutual information. Importantly, we detailedly discuss the proposed uncertainty relations and quantum coherence in the context of Schwarzschild space-time. It is interesting to find that Hawking radiation will damage the coherence of the physically accessible region and increase the uncertainty. Furthermore, we argue that the properties of the uncertainty in Schwarzschild space-time can be explained from the systems' purity and the information redistribution of the different regions. Therefore, it is believed that our findings provide the generalized entropic uncertainty relations in multipartite systems, which may facilitate us deeper understanding of quantumness and information paradox of the black holes., Comment: 8 pages, 6 figures, comments are welcome

In the NISQ era, achieving large-scale quantum computing demands compact circuits to mitigate decoherence and gate error accumulation. Quantum operations with diverse degrees of freedom hold promise for circuit compression, but conventional approaches encounter challenges in simultaneously adjusting multiple parameters. Here, we propose a transition composite gate (TCG) scheme grounded on state-selective transition path engineering, enabling more expressive conditional operations. We experimentally validate a controlled unitary (CU) gate as an example, with independent and continuous parameters. By adjusting the parameters of $\rm X^{12}$ gate, we obtain the CU family with a fidelity range of 95.2% to 99.0% leveraging quantum process tomography (QPT). To demonstrate the capability of circuit compression, we use TCG scheme to prepare 3-qubit Greenberger-Horne-Zeilinger (GHZ) and W states, with the fidelity of 96.77% and 95.72%. TCG can achieve the reduction in circuit depth of about 40% and 44% compared with the use of CZ gates only. Moreover, we show that short-path TCG (SPTCG) can further reduce the state-preparation circuit time cost. The TCG scheme exhibits advantages in certain quantum circuits and shows significant potential for large-scale quantum algorithms., Comment: 21 pages, 12 figures

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than $0.2\%$, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science., Comment: 31 pages, 10 figures

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existed works build the model in the original geometric space, leading to high computational costs when the number of sample points is large. We present the Latent Neural Operator (LNO) solving PDEs in the latent space. In particular, we first propose Physics-Cross-Attention (PhCA) transforming representation from the geometric space to the latent space, then learn the operator in the latent space, and finally recover the real-world geometric space via the inverse PhCA map. Our model retains flexibility that can decode values in any position not limited to locations defined in training set, and therefore can naturally perform interpolation and extrapolation tasks particularly useful for inverse problems. Moreover, the proposed LNO improves in both prediction accuracy and computational efficiency. Experiments show that LNO reduces the GPU memory by 50%, speeds up training 1.8 times, and reaches state-of-the-art accuracy on four out of six benchmarks for forward problems and a benchmark for inverse problem.

Aiming at privacy preservation, Federated Learning (FL) is an emerging machine learning approach enabling model training on decentralized devices or data sources. The learning mechanism of FL relies on aggregating parameter updates from individual clients. However, this process may pose a potential security risk due to the presence of malicious devices. Existing solutions are either costly due to the use of compute-intensive technology, or restrictive for reasons of strong assumptions such as the prior knowledge of the number of attackers and how they attack. Few methods consider both privacy constraints and uncertain attack scenarios. In this paper, we propose a robust FL approach based on the credibility management scheme, called Fed-Credit. Unlike previous studies, our approach does not require prior knowledge of the nodes and the data distribution. It maintains and employs a credibility set, which weighs the historical clients' contributions based on the similarity between the local models and global model, to adjust the global model update. The subtlety of Fed-Credit is that the time decay and attitudinal value factor are incorporated into the dynamic adjustment of the reputation weights and it boasts a computational complexity of O(n) (n is the number of the clients). We conducted extensive experiments on the MNIST and CIFAR-10 datasets under 5 types of attacks. The results exhibit superior accuracy and resilience against adversarial attacks, all while maintaining comparatively low computational complexity. Among these, on the Non-IID CIFAR-10 dataset, our algorithm exhibited performance enhancements of 19.5% and 14.5%, respectively, in comparison to the state-of-the-art algorithm when dealing with two types of data poisoning attacks.

For $E_1$ and $E_2$ elliptic curves defined over a number field $K$, without complex multiplication, we consider the function ${\mathcal{F}}_{E_1, E_2}(x)$ counting non-zero prime ideals $\mathfrak{p}$ of the ring of integers of $K$, of good reduction for $E_1$ and $E_2$, of norm at most $x$, and for which the Frobenius fields $\mathbb{Q}(\pi_{\mathfrak{p}}(E_1))$ and $\mathbb{Q}(\pi_{\mathfrak{p}}(E_2))$ are equal. Motivated by an isogeny criterion of Kulkarni, Patankar, and Rajan, which states that $E_1$ and $E_2$ are not potentially isogenous if and only if ${\mathcal{F}}_{E_1, E_2}(x) = \operatorname{o} \left(\frac{x}{\log x}\right)$, we investigate the growth in $x$ of ${\mathcal{F}}_{E_1, E_2}(x)$. We prove that if $E_1$ and $E_2$ are not potentially isogenous, then there exist positive constants $\kappa(E_1, E_2, K)$, $\kappa'(E_1, E_2, K)$, and $\kappa''(E_1, E_2, K)$ such that the following bounds hold: (i) ${\mathcal{F}}_{E_1, E_2}(x) < \kappa(E_1, E_2, K) \frac{ x (\log\log x)^{\frac{1}{9}}}{ (\log x)^{\frac{19}{18}}}$; (ii) ${\mathcal{F}}_{E_1, E_2}(x) < \kappa'(E_1, E_2, K) \frac{ x^{\frac{6}{7}}}{ (\log x)^{\frac{5}{7}}}$ under the Generalized Riemann Hypothesis for Dedekind zeta functions (GRH); (iii) ${\mathcal{F}}_{E_1, E_2}(x) < \kappa''(E_1, E_2, K) x^{\frac{2}{3}} (\log x)^{\frac{1}{3}}$ under GRH, Artin's Holomorphy Conjecture for the Artin $L$-functions of number field extensions, and a Pair Correlation Conjecture for the zeros of the Artin $L$-functions of number field extensions.

Large-scale cosmic filaments may have played an important role in shaping the properties of galaxies. Meanwhile, cosmic filaments are believed to harbor a substantial portion of the missing baryons at redshift z < 2. To inspect the role of filaments in these issues, many properties of filaments need to be examined, including their lengths, thicknesses, and density profiles. However, measuring some of these properties poses challenges. This study concentrates on estimating filament width/thickness, investigating potential correlations between the local width of filaments and the properties of dark matter halos within filaments. We find that the local width of filaments generally increases with the mass of dark matter halos embedded in filaments per unit length, roughly following a secondorder polynomial, although with notable scatter. We probe and discuss means that may refine our findings. After further verification and improvements, this relation could be applied to filament samples constructed from the observed galaxy distribution, aiding in understanding the roles of cosmic filaments in galaxy evolution and uncovering the missing baryons., Comment: 11 pages, 7 figures, accepted to ApJ

Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic gradient descent (SGD). In this paper, we propose a simple yet efficient sampling method to significantly accelerate SAM. Concretely, we discover that the gradient of SAM is a combination of the gradient of SGD and the Projection of the Second-order gradient matrix onto the First-order gradient (PSF). PSF exhibits a gradually increasing frequency of change during the training process. To leverage this observation, we propose an adaptive sampling method based on the variation of PSF, and we reuse the sampled PSF for non-sampling iterations. Extensive empirical results illustrate that the proposed method achieved state-of-the-art accuracies comparable to SAM on diverse network architectures.

Let $A/K$ be an absolutely simple abelian surface defined over a number field $K$. We give unconditional upper bounds for the number of prime ideals $\mathfrak{p}$ of $K$ with norm up to $x$ such that $A$ has supersingular reduction at $\mathfrak{p}$ when $A$ has a trivial endomorphism ring, real multiplication, and quaternion multiplication, respectively. Particularly, in the real multiplication case and when $K=\mathbb{Q}$, the bound is related to an upper bound for the distribution of Frobenius traces of $A$. Also in the real multiplication case, we provide unconditional upper bounds for a variant of the problem, which concerns the number of prime ideals for which the reduction of $A$ at the prime has a particular Newton datum and is not simple., Comment: Comments are welcome!

Quantum effects in photosynthetic energy transport in nature, especially for the typical Fenna-Matthews-Olson (FMO) complexes, are extensively studied in quantum biology. Such energy transport processes can be investigated as open quantum systems that blend the quantum coherence and environmental noises, and have been experimentally simulated on a few quantum devices. However, the existing experiments always lack a solid quantum simulation for the FMO energy transport due to their constraints to map a variety of issues in actual FMO complexes that have rich biological meanings. Here we successfully map the full coupling profile of the seven-site FMO structure by comprehensive characterization and precise control of the evanescent coupling of the three-dimensional waveguide array. By applying a stochastic dynamical modulation on each waveguide, we introduce the base site energy and the dephasing term in colored noises to faithfully simulate the power spectral density of the FMO complexes. We show our photonic model well interprets the issues including the reorganization energy, vibrational assistance, exciton transfer and energy localization. We further experimentally demonstrate the existence of an optimal transport efficiency at certain dephasing strength, providing a window to closely investigate environment-assisted quantum transport.

FemTech or Female Technology, is an expanding field dedicated to providing affordable and accessible healthcare solutions for women, prominently through Female Health Applications that monitor health and reproductive data. With the leading app exceeding 1 billion downloads, these applications are gaining widespread popularity. However, amidst contemporary challenges to women's reproductive rights and privacy, there is a noticeable lack of comprehensive studies on the security and privacy aspects of these applications. This exploratory study delves into the privacy risks associated with seven popular applications. Our initial quantitative static analysis reveals varied and potentially risky permissions and numerous third-party trackers. Additionally, a preliminary examination of privacy policies indicates non-compliance with fundamental data privacy principles. These early findings highlight a critical gap in establishing robust privacy and security safeguards for FemTech apps, especially significant in a climate where women's reproductive rights face escalating threats., Comment: 9 pages, 3 tables

The multi-armed bandit (MAB) models have attracted significant research attention due to their applicability and effectiveness in various real-world scenarios such as resource allocation, online advertising, and dynamic pricing. As an important branch, the adversarial MAB problems with delayed feedback have been proposed and studied by many researchers recently where a conceptual adversary strategically selects the reward distributions associated with each arm to challenge the learning algorithm and the agent experiences a delay between taking an action and receiving the corresponding reward feedback. However, the existing models restrict the feedback to be generated from only one user, which makes models inapplicable to the prevailing scenarios of multiple users (e.g. ad recommendation for a group of users). In this paper, we consider that the delayed feedback results are from multiple users and are unrestricted on internal distribution. In contrast, the feedback delay is arbitrary and unknown to the player in advance. Also, for different users in a round, the delays in feedback have no assumption of latent correlation. Thus, we formulate an adversarial MAB problem with multi-user delayed feedback and design a modified EXP3 algorithm MUD-EXP3, which makes a decision at each round by considering the importance-weighted estimator of the received feedback from different users. On the premise of known terminal round index $T$, the number of users $M$, the number of arms $N$, and upper bound of delay $d_{max}$, we prove a regret of $\mathcal{O}(\sqrt{TM^2\ln{N}(N\mathrm{e}+4d_{max})})$. Furthermore, for the more common case of unknown $T$, an adaptive algorithm AMUD-EXP3 is proposed with a sublinear regret with respect to $T$. Finally, extensive experiments are conducted to indicate the correctness and effectiveness of our algorithms., Comment: This is an extended version of "A Modified EXP3 in Adversarial Bandits with Multi-User Delayed Feedback" published in COCOON 2023

Target proteins that lack accessible binding pockets and conformational stability have posed increasing challenges for drug development. Induced proximity strategies, such as PROTACs and molecular glues, have thus gained attention as pharmacological alternatives, but still require small molecule docking at binding pockets for targeted protein degradation. The computational design of protein-based binders presents unique opportunities to access "undruggable" targets, but have often relied on stable 3D structures or structure-influenced latent spaces for effective binder generation. In this work, we introduce PepMLM, a target sequence-conditioned generator of de novo linear peptide binders. By employing a novel span masking strategy that uniquely positions cognate peptide sequences at the C-terminus of target protein sequences, PepMLM fine-tunes the state-of-the-art ESM-2 pLM to fully reconstruct the binder region, achieving low perplexities matching or improving upon validated peptide-protein sequence pairs. After successful in silico benchmarking with AlphaFold-Multimer, outperforming RFDiffusion on structured targets, we experimentally verify PepMLM's efficacy via fusion of model-derived peptides to E3 ubiquitin ligase domains, demonstrating endogenous degradation of emergent viral phosphoproteins and Huntington's disease-driving proteins. In total, PepMLM enables the generative design of candidate binders to any target protein, without the requirement of target structure, empowering downstream therapeutic applications.

In Edge Computing (EC), containers have been increasingly used to deploy applications to provide mobile users services. Each container must run based on a container image file that exists locally. However, it has been conspicuously neglected by existing work that effective task scheduling combined with dynamic container image caching is a promising way to reduce the container image download time with the limited bandwidth resource of edge nodes. To fill in such gaps, in this paper, we propose novel joint Task Scheduling and Image Caching (TSIC) algorithms, specifically: 1) We consider the joint task scheduling and image caching problem and formulate it as a Markov Decision Process (MDP), taking the communication delay, waiting delay, and computation delay into consideration; 2) To solve the MDP problem, a TSIC algorithm based on deep reinforcement learning is proposed with the customized state and action spaces and combined with an adaptive caching update algorithm. 3) A real container system is implemented to validate our algorithms. The experiments show that our strategy outperforms the existing baseline approaches by 23\% and 35\% on average in terms of total delay and waiting delay, respectively.

Space-based gravitational wave detectors such as TianQin, LISA, and TaiJi have the potential to outperform themselves through joint observation. To achieve this, it is desirable to practice joint data analysis in advance on simulated data that encodes the intrinsic correlation among the signals found in different detectors that operate simultaneously. In this paper, we introduce \texttt{GWSpace}, a package that can simulate the joint detection data from TianQin, LISA, and TaiJi. The software is not a groundbreaking work that starts from scratch. Rather, we use as many open-source resources as possible, tailoring them to the needs of simulating the multi-mission science data and putting everything into a ready-to-go and easy-to-use package. We shall describe the main components, the construction, and a few examples of application of the package. A common coordinate system, namely the Solar System Barycenter (SSB) coordinate system, is utilized to calculate spacecraft orbits for all three missions. The paper also provides a brief derivation of the detection process and outlines the general waveform of sources detectable by these detectors., Comment: 24 pages, 13 figures, GWSpace will be uploaded at https://github.com/TianQinSYSU/GWSpace

Terahertz communication networks and intelligent reflecting surfaces exhibit significant potential in advancing wireless networks, particularly within the domain of aerial-based multi-access edge computing systems. These technologies enable efficient offloading of computational tasks from user electronic devices to Unmanned Aerial Vehicles or local execution. For the generation of high-quality task-offloading allocations, conventional numerical optimization methods often struggle to solve challenging combinatorial optimization problems within the limited channel coherence time, thereby failing to respond quickly to dynamic changes in system conditions. To address this challenge, we propose a deep learning-based optimization framework called Iterative Order-Preserving policy Optimization (IOPO), which enables the generation of energy-efficient task-offloading decisions within milliseconds. Unlike exhaustive search methods, IOPO provides continuous updates to the offloading decisions without resorting to exhaustive search, resulting in accelerated convergence and reduced computational complexity, particularly when dealing with complex problems characterized by extensive solution spaces. Experimental results demonstrate that the proposed framework can generate energy-efficient task-offloading decisions within a very short time period, outperforming other benchmark methods., Comment: 16 pages