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A spring in parallel with an effort source (e.g., electric motor or human muscle) can reduce its energy consumption and effort (i.e., torque or force) depending on the spring stiffness, spring preload, and actuation task. However, selecting the spring stiffness and preload that guarantees effort or energy reduction for an arbitrary set of tasks is a design challenge. This work formulates a convex optimization problem to guarantee that a parallel spring reduces the root-mean-square source effort or energy consumption for multiple tasks. Specifically, we guarantee the benefits across multiple tasks by enforcing a set of convex quadratic constraints in our optimization variables -- the parallel spring stiffness and preload. These quadratic constraints are equivalent to ellipses in the stiffness and preload plane, any combination of stiffness and preload inside the ellipse represents a parallel spring that minimizes effort source or energy consumption with respect to an actuator without a spring. This geometric interpretation intuitively guides the stiffness and preload selection process. We analytically and experimentally prove the convex quadratic function of the spring stiffness and preload. As applications, we analyze the stiffness and preload selection of a parallel spring for a knee exoskeleton using human muscle as the effort source and a prosthetic ankle powered by electric motors. To promote adoption, the optimization and geometric methods are available as supplemental open-source software that can be executed in a web browser., Comment: 10 pages

Monogamy of entanglement is the fundamental property of quantum systems. By using two new entanglement measures based on dual entropy, the $S^{t}$-entropy entanglement and $T^{t}_q$-entropy entanglement measures, we present the general monogamy relations in multi-qubit quantum systems. We show that these newly derived monogamy inequalities are tighter than the existing ones. Based on these general monogamy relations, we construct the set of multipartite entanglement indicators for $N$-qubit states, which are shown to work well even for the cases that the usual concurrence-based indicators do not work. Detailed examples are presented to illustrate our results., Comment: 10 pages, 7 figures

The rapid decline in groundwater around the world poses a significant challenge to sustainable agriculture. To address this issue, agricultural managed aquifer recharge (Ag-MAR) is proposed to recharge the aquifer by artificially flooding agricultural lands using surface water. Ag-MAR requires a carefully selected flooding schedule to avoid affecting the oxygen absorption of crop roots. However, current Ag-MAR scheduling does not take into account complex environmental factors such as weather and soil oxygen, resulting in crop damage and insufficient recharging amounts. This paper proposes MARLP, the first end-to-end data-driven control system for Ag-MAR. We first formulate Ag-MAR as an optimization problem. To that end, we analyze four-year in-field datasets, which reveal the multi-periodicity feature of the soil oxygen level trends and the opportunity to use external weather forecasts and flooding proposals as exogenous clues for soil oxygen prediction. Then, we design a two-stage forecasting framework. In the first stage, it extracts both the cross-variate dependency and the periodic patterns from historical data to conduct preliminary forecasting. In the second stage, it uses weather-soil and flooding-soil causality to facilitate an accurate prediction of soil oxygen levels. Finally, we conduct model predictive control (MPC) for Ag-MAR flooding. To address the challenge of large action spaces, we devise a heuristic planning module to reduce the number of flooding proposals to enable the search for optimal solutions. Real-world experiments show that MARLP reduces the oxygen deficit ratio by 86.8% while improving the recharging amount in unit time by 35.8%, compared with the previous four years., Comment: Accepted by KDD 2024

We introduce MindSpore Quantum, a pioneering hybrid quantum-classical framework with a primary focus on the design and implementation of noisy intermediate-scale quantum (NISQ) algorithms. Leveraging the robust support of MindSpore, an advanced open-source deep learning training/inference framework, MindSpore Quantum exhibits exceptional efficiency in the design and training of variational quantum algorithms on both CPU and GPU platforms, delivering remarkable performance. Furthermore, this framework places a strong emphasis on enhancing the operational efficiency of quantum algorithms when executed on real quantum hardware. This encompasses the development of algorithms for quantum circuit compilation and qubit mapping, crucial components for achieving optimal performance on quantum processors. In addition to the core framework, we introduce QuPack, a meticulously crafted quantum computing acceleration engine. QuPack significantly accelerates the simulation speed of MindSpore Quantum, particularly in variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and tensor network simulations, providing astonishing speed. This combination of cutting-edge technologies empowers researchers and practitioners to explore the frontiers of quantum computing with unprecedented efficiency and performance.

We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of WSe$_2$, which can be described in an adiabatic approximation as particles moving in a periodic potential and an emergent periodic magnetic field with nonzero average. We understand the magnetic-field dependent spectra of WSe$_2$ based on the point net zero flux, at which the external field cancels the average emergent field. At this point, the band structure interpolates between the tightly-bound and nearly-free (weak periodic potential) paradigms as the twist angle increases. For small twist angles, the energy levels in a magnetic field mirror the Hofstadter butterfly of the Haldane model. For larger twist angles, the isolated Chern band at zero flux evolves from nearly-free bands at the point of net zero flux. We also apply our framework to a realistic model of twisted bilayer MoTe$_2$, which has recently been suggested to feature higher Landau level analogs. We show that at negative unit flux per unit cell, the bands exhibit remarkable similarity to a backfolded parabolic dispersion, even though the adiabatic approximation is inapplicable. This backfolded parabolic dispersion naturally explains the similarity of the Chern bands at zero applied flux to the two lowest Landau levels, offering a simple picture supporting the emergence of non-Abelian states in twisted bilayer MoTe$_2$. We propose the study of magnetic field dependent band structures as a versatile method to investigate the nature of topological bands and identify Landau level analogs., Comment: Published version

Graph Partitioning is widely used in many real-world applications such as fraud detection and social network analysis, in order to enable the distributed graph computing on large graphs. However, existing works fail to balance the computation cost and communication cost on machines with different power (including computing capability, network bandwidth and memory size), as they only consider replication factor and neglect the difference of machines in realistic data centers. In this paper, we propose a general graph partitioning algorithm WindGP, which can support fast and high-quality edge partitioning on heterogeneous machines. WindGP designs novel preprocessing techniques to simplify the metric and balance the computation cost according to the characteristics of graphs and machines. Also, best-first search is proposed instead of BFS and DFS, in order to generate clusters with high cohesion. Furthermore, WindGP adaptively tunes the partition results by sophisticated local search methods. Extensive experiments show that WindGP outperforms all state-of-the-art partition methods by 1.35 - 27 times on both dense and sparse distributed graph algorithms, and has good scalability with graph size and machine number., Comment: 19 pages, 15 figures, 18 tables

Recent observations of the fractional anomalous quantum Hall effect in moir\'e materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau level-like single-particle states form an "ideal" Chern band and local interactions lead to Laughlin-like FCIs at $1/3$ filling, has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and e.g. at $2/3$ filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favoured. In fact, even the exact Laughlin-like zero modes at $1/3$ filling have a non-uniform density tracking the underlying quantum geometry. Moreover, by switching to a Coulomb interaction, the ideal Chern band features charge density wave states with no lowest Landau level counterpart., Comment: 5 pages + 4 figures, comments are welcome!

Motivated by an experiment on a superconducting quantum processor [Mi et al., Science 378, 785 (2022)], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana zero and $\pi$ modes when writing the spin model in Jordan-Wigner fermions. Both splittings have lognormal distributions with random transverse fields. In contrast, random longitudinal fields affect the zero and $\pi$ splittings in drastically different ways. While zero pairings are rapidly lifted, the $\pi$ pairings are remarkably robust, or even strengthened, up to vastly larger disorder strengths. We explain our results within a self-consistent Floquet perturbation theory and study implications for boundary spin correlations. The robustness of $\pi$ pairings against longitudinal disorder may be useful for quantum information processing., Comment: 5+7 pages, 3 figures

Pre-trained code models have emerged as crucial tools in various code intelligence tasks. However, their effectiveness depends on the quality of the pre-training dataset, particularly the human reference comments, which serve as a bridge between the programming language and natural language. One significant challenge is that such comments can become inconsistent with the corresponding code as the software evolves. This discrepancy can lead to suboptimal training of the models, decreasing their performances. LLMs have demonstrated superior capabilities in generating high-quality code comments. In light of that, we try to tackle the quality issue of the dataset by harnessing the power of LLMs. Specifically, we raise the question: Can we rebuild the pre-training dataset by substituting the original comments with LLM-generated ones for more effective pre-trained code models? To answer the question, we first conduct a comprehensive evaluation to compare ChatGPT-generated comments with human reference comments. As existing reference-based metrics treat the reference comments as gold standards, we introduce two auxiliary tasks as novel reference-free metrics to assess the quality of comments, i.e., code-comment inconsistency detection and code search. Experimental results show that ChatGPT-generated comments demonstrate superior semantic consistency with the code compared to human references, indicating the potential of utilizing ChatGPT to enhance the quality of the pre-training dataset. We rebuilt the widely used dataset, CodeSearchNet, with ChatGPT-generated comments. Subsequent experiments involve re-pre-training the CodeT5 with our refined dataset.Evaluation results on four generation tasks and one understanding code intelligence tasks show that the model pre-trained by ChatGPT-enhanced data outperforms its counterpart on code summarization, code generation, and code translation tasks., Comment: 10 pages, 5 figures

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal line-gap and point-gap classifications of non-Hermitian systems using K-theory have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines do not in general distinguish whether multiple non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. To address this we consider two different notions: non-Hermitian band gaps and separation gaps that crucially encompass a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and comprehensive classification of both gapped and nodal systems in the presence of physically relevant parity-time ($\mathcal{PT}$) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new stable topology stemming from both eigenvalues and wave functions, and remarkably also implies distinct fragile topological phases. In particular, we reveal different Abelian and non-Abelian phases in $\mathcal{PT}$-symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not induce (exceptional) degeneracy, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneous $\mathcal{PT}$ symmetry breaking is captured by Chern-Euler and Chern-Stiefel-Whitney descriptions, a fingerprint of unprecedented non-Hermitian topology previously overlooked. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms., Comment: 44 pages, 12 figures, published version

Deep neural network (DNN) models have become a critical asset of the model owner as training them requires a large amount of resource (i.e. labeled data). Therefore, many fingerprinting schemes have been proposed to safeguard the intellectual property (IP) of the model owner against model extraction and illegal redistribution. However, previous schemes adopt unnatural images as the fingerprint, such as adversarial examples and noisy images, which can be easily perceived and rejected by the adversary. In this paper, we propose NaturalFinger which generates natural fingerprint with generative adversarial networks (GANs). Besides, our proposed NaturalFinger fingerprints the decision difference areas rather than the decision boundary, which is more robust. The application of GAN not only allows us to generate more imperceptible samples, but also enables us to generate unrestricted samples to explore the decision boundary.To demonstrate the effectiveness of our fingerprint approach, we evaluate our approach against four model modification attacks including adversarial training and two model extraction attacks. Experiments show that our approach achieves 0.91 ARUC value on the FingerBench dataset (154 models), exceeding the optimal baseline (MetaV) over 17\%.

This work proposes provably-correct self-organizing strategies for platoons of heterogeneous vehicles. We refer to self-organization as the capability of a platoon to autonomously homogenize to a common group behavior. We show that self-organization promotes resilience to acceleration limits and communication failures, i.e., homogenizing to a common group behavior makes the platoon recover from these causes of impairments. In the presence of acceleration limits, resilience is achieved by self-organizing to a common constrained group behavior that prevents the vehicles from hitting their acceleration limits. In the presence of communication failures, resilience is achieved by self-organizing to a common group observer to estimate the missing information. Stability of the self-organization mechanism is studied analytically, and correctness with respect to traffic actions (e.g. emergency braking, cut-in, merging) is realized through a provably-correct safety layer. Numerical validations via the platooning toolbox OpenCDA in CARLA and via the CommonRoad platform confirm improved performance through self-organization and the provably-correct safety layer.

Text-to-SQL is a task that converts a natural language question into a structured query language (SQL) to retrieve information from a database. Large language models (LLMs) work well in natural language generation tasks, but they are not specifically pre-trained to understand the syntax and semantics of SQL commands. In this paper, we propose an LLM-based framework for Text-to-SQL which retrieves helpful demonstration examples to prompt LLMs. However, questions with different database schemes can vary widely, even if the intentions behind them are similar and the corresponding SQL queries exhibit similarities. Consequently, it becomes crucial to identify the appropriate SQL demonstrations that align with our requirements. We design a de-semanticization mechanism that extracts question skeletons, allowing us to retrieve similar examples based on their structural similarity. We also model the relationships between question tokens and database schema items (i.e., tables and columns) to filter out scheme-related information. Our framework adapts the range of the database schema in prompts to balance length and valuable information. A fallback mechanism allows for a more detailed schema to be provided if the generated SQL query fails. Ours outperforms state-of-the-art models and demonstrates strong generalization ability on three cross-domain Text-to-SQL benchmarks.

Exceptional points (EPs) are degeneracy of non-Hermitian Hamiltonians, at which the eigenvalues, along with their eigenvectors, coalesce. Their orders are given by the Jordan decomposition. Here, we focus on higher-order EPs arising in fermionic systems with a sublattice symmetry, which restricts the eigenvalues of the Hamitlonian to appear in pairs of $\lbrace E, -E\rbrace $. Thus, a naive prediction might lead to only even-order EPs at zero energy. However, we show that odd-order EPs can exist and exhibit enhanced sensitivity in the behaviour of eigenvector-coalescence in their neighbourhood, depending on how we approach the degenerate point. The odd-order EPs can be understood as a mixture of higher- and lower-valued even-order EPs. Such an anomalous behaviour is related to the irregular topology of the EPs as the subspace of the Hamiltonians in question, which is a unique feature of the Jordan blocks. The enhanced eigenvector sensitivity can be described by observing how the quantum distance to the target eigenvector converges to zero. In order to capture the eigenvector-coalescence, we provide an algebraic method to describe the conditions for the existence of these EPs. This complements previous studies based on resultants and discriminants, and unveils heretofore unexplored structures of higher-order exceptional degeneracy., Comment: published version

We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e. the necessity of compensating the topological charge of a stable nodal point by an anti-dote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how noncommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions., Comment: 5+7 pages, 3+3 figures