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Let $\alpha$ range over the set of compositions. Dual immaculate quasisymmetric functions $\mathfrak{S}_\alpha^*$, introduced by Berg, Bergeron, Saliola, Serrano, and Zabrocki, provide a quasisymmetric analogue of Schur functions. They also constructed an indecomposable $0$-Hecke module $\mathcal{V}_\alpha$ whose image under the quasisymmetric characteristic is $\mathfrak{S}_\alpha^*$. In this paper, we prove that $\mathcal{V}_\alpha$ admits a distinguished filtration with respect to the basis of Young quasisymmetric Schur functions. This result offers a novel representation-theoretic interpretation of the positive expansion of $\mathfrak{S}_\alpha^*$ in the basis of Young quasisymmetric Schur functions. A key tool in our proof is Mason's analogue of the Robinson-Schensted-Knuth algorithm, for which we establish a version of Green's theorem. As an unexpected byproduct of our investigation, we construct an indecomposable $0$-Hecke module $\mathbf{Y}_\alpha$ whose image under the quasisymmetric characteristic is the Young quasisymmetric Schur function $\hat{\mathscr{S}}_\alpha$. Further properties of this module are also investigated. And, by applying a suitable automorphism twist to this module, we obtain an indecomposable $0$-Hecke module whose image under the quasisymmetric characteristic is the quasisymmetric Schur function $\mathscr{S}_\alpha$., Comment: 50 pages

Chirality, an intrinsic preference for a specific handedness, is a fundamental characteristic observed in nature. In magnetism, magnetic chirality arises from the anti-symmetric Dzyaloshinskii-Moriya interaction in competition with the symmetric Heisenberg exchange interaction. Traditionally, the anti-symmetric interaction has been considered minor relative to the symmetric interaction. In this study, we demonstrate an observation of giant magnetic chirality during the dimensionality crossover of magnetic materials from three-dimensional to two-dimensional. The ratio between the anti-symmetric and symmetric interactions exhibits a reversal in their dominance over this crossover, overturning the traditional consideration. This observation is validated theoretically using a non-local interaction model and tight-binding calculation with distinct pairing schemes for each exchange interaction throughout the crossover. Additional experiments investigating the asphericity of orbital moments corroborate the robustness of our findings. Our findings highlight the critical role of dimensionality in shaping magnetic chirality and offer strategies for engineering chiral magnet states with unprecedented strength, desired for the design of spintronic materials., Comment: 21 pages, 4 figures

We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-$1/2$ Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ans\"atze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_{2}$ states. Motivated by density-matrix renormalization group (DMRG) calculations suggesting that the Shastry-Sutherland model and the square-lattice $J_{1}$-$J_{2}$ Heisenberg antiferromagnet putatively share the same QSL phase, we establish a mapping of our Ans\"atze to those of the square lattice. This enables us to identify the equivalent of the square-lattice QSL (Z2A$zz$13) in the Shastry-Sutherland system. Employing state-of-the-art variational Monte Carlo calculations with Gutzwiller-projected wavefunctions improved upon by Lanczos steps, we demonstrate the excellent agreement of energies and correlators between a gapless (Dirac) $\mathbb{Z}_{2}$ spin liquid -- characterized by only few parameters -- and approaches based on neural quantum states and DMRG. Furthermore, the real-space spin-spin correlations are shown to decay with the same power law as in the $J_{1}$-$J_{2}$ square lattice model, which also hosts a $\mathbb{Z}_{2}$ Dirac spin liquid. Finally, we apply the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group to compute the dynamical spin structure factor; these correlations exhibit the features expected due to Dirac cones in the excitation spectrum, thus providing strong independent evidence for a Dirac QSL ground state. Our finding of a $d$-wave pairing $\mathbb{Z}_{2}$ Dirac QSL is consistent with the recently observed signatures of QSL behavior in Pr$_2$Ga$_2$BeO$_7$ and outlines predictions for future experiments., Comment: 36 pages, 18 figures, 12 tables

An increasing number of web articles engage the reader with the feeling of being immersed in the data space. However, the exact characteristics of spatial immersion in the context of visual storytelling remain vague. For example, what are the common design patterns of data stories with spatial immersion? How do they affect the reader's experience? To gain a deeper understanding of the subject, we collected 23 distinct data stories with spatial immersion, and identified six design patterns, such as cinematic camera shots and transitions, intuitive data representations, realism, naturally moving elements, direct manipulation of camera or visualization, and dynamic dimension. Subsequently, we designed four data stories and conducted a crowdsourced user study comparing three design variations (static, animated, and immersive). Our results suggest that data stories with the design patterns for spatial immersion are more interesting and persuasive than static or animated ones, but no single condition was deemed more understandable or trustworthy.

We propose a generalized Shastry-Sutherland model which bridges the Shastry-Sutherland model and the $J_1$-$J_2$ Heisenberg model. By employing large scale Density Matrix Renormalization Group and Fully Augmented Matrix Product State calculations, combined with careful finite-size scaling, we find the phase transition between the plaquette valence bond state (PVBS) and Neel anti-ferromagnetic (AFM) phase in the pure Shastry-Sutherland model is a weak first one. This result indicates the existence of an exotic tri-critical point in the PVBS to AFM transition line in the phase diagram, as the transition in the $J_1$-$J_2$ Heisenberg model was previously determined to be continuous. We determine the location of the tri-critical point in the phase diagram at which first-order transition turns to continuous. Our generalized Shastry-Sutherland model provides not only a valuable platform to explore exotic phases and phase transitions but also more realistic description of Shastry-Sutherland materials like SrCu$_2$(BO$_3$)$_2$.

In this work, we research user preferences to see a chart, table, or text given a question asked by the user. This enables us to understand when it is best to show a chart, table, or text to the user for the specific question. For this, we conduct a user study where users are shown a question and asked what they would prefer to see and used the data to establish that a user's personal traits does influence the data outputs that they prefer. Understanding how user characteristics impact a user's preferences is critical to creating data tools with a better user experience. Additionally, we investigate to what degree an LLM can be used to replicate a user's preference with and without user preference data. Overall, these findings have significant implications pertaining to the development of data tools and the replication of human preferences using LLMs. Furthermore, this work demonstrates the potential use of LLMs to replicate user preference data which has major implications for future user modeling and personalization research.

Quantum error correction (QEC) codes are fundamentally linked to quantum phases of matter: the degenerate ground state manifold corresponds to the code space, while topological excitations represent error syndromes. Building on this concept, the Sachdev-Ye-Kitaev (SYK) model, characterized by its extensive quasi-ground state degeneracy, serves as a constant rate approximate QEC code. In this work, we study the impacts of decoherence on the information-theoretic capacity of SYK models and their variants. Such a capacity is closely tied to traversable wormholes via its thermofield double state, which theoretically enables the teleportation of information across a black hole. We calculate the coherent information in the maximally entangled quasi-ground state space of the SYK models under the fermion parity breaking and parity conserving noise. Interestingly, we find that under the strong fermion parity symmetric noise, the mixed state undergoes the strong to weak spontaneous symmetry breaking of fermion parity, which also corresponds to the information-theoretic transition. Our results highlight the degradation of wormhole traversability in realistic quantum scenarios, as well as providing critical insights into the behavior of approximate constant-rate QEC codes under decoherence., Comment: 5 + 7 pages, 2 + 4 figures

This paper presents the development of a dashboard designed specifically for teachers in English as a Foreign Language (EFL) writing education. Leveraging LLMs, the dashboard facilitates the analysis of student interactions with an essay writing system, which integrates ChatGPT for real-time feedback. The dashboard aids teachers in monitoring student behavior, identifying noneducational interaction with ChatGPT, and aligning instructional strategies with learning objectives. By combining insights from NLP and Human-Computer Interaction (HCI), this study demonstrates how a human-centered approach can enhance the effectiveness of teacher dashboards, particularly in ChatGPT-integrated learning., Comment: EMNLP 2024 Workshop CustomNLP4U. arXiv admin note: text overlap with arXiv:2405.19691

Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state. Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models. Our result establishes a rigorous connection between the decoding transition of the quantum code and the phase transition in the random classical SM model. It is also directly confirmed for CSS codes that exact error correction is possible if and only if the maximum-likelihood (ML) decoder always succeeds in the asymptotic limit. Thus, the fundamental threshold is saturated by the optimal decoder., Comment: 11+3 pages, 5 figures

While ChatGPT has significantly impacted education by offering personalized resources for students, its integration into educational settings poses unprecedented risks, such as inaccuracies and biases in AI-generated content, plagiarism and over-reliance on AI, and privacy and security issues. To help teachers address such risks, we conducted a two-phase iterative design process that comprises surveys, interviews, and prototype demonstration involving six EFL (English as a Foreign Language) teachers, who integrated ChatGPT into semester-long English essay writing classes. Based on the needs identified during the initial survey and interviews, we developed a prototype of Prompt Analytics Dashboard (PAD) that integrates the essay editing history and chat logs between students and ChatGPT. Teacher's feedback on the prototype informs additional features and unmet needs for designing future PAD, which helps them (1) analyze contextual analysis of student behaviors, (2) design an overall learning loop, and (3) develop their teaching skills.

We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix. In one dimension, we introduce strong injective matrix product density operators (MPDO), which describe a broad class of short-range correlated mixed states, including the locally decohered SPT states. We map strong injective MPDO to a pure state in the doubled Hilbert space and define the SPT phases according to the cohomology class of the symmetry group in the doubled state. Although the doubled state exhibits an enlarged symmetry, the possible SPT phases are also constrained by the Hermiticity and the semi-positivity of the density matrix. We here obtain a complete classification of SPT phases with a direct product of strong $G$ and weak $K$ unitary symmetry given by the cohomology group $H^2(G, \text{U}(1))\oplus H^1(K, H^1(G, \text{U}(1)))$. The SPT phases in our definition are preserved under symmetric local circuits consisting of non-degenerate channels. This motivates an alternative definition of SPT phases according to the equivalence class of mixed states under a ``one-way" connection using symmetric non-degenerate channels. In locally purifiable MPDO with strong symmetry, we prove that this alternative definition reproduces the cohomology classification. We further extend our results to two-dimensional mixed states described by strong semi-injective tensor network density operators and classify the possible SPT phases., Comment: Appendix D is fixed

The integration of generative AI in education is expanding, yet empirical analyses of large-scale and real-world interactions between students and AI systems still remain limited. Addressing this gap, we present RECIPE4U (RECIPE for University), a dataset sourced from a semester-long experiment with 212 college students in English as Foreign Language (EFL) writing courses. During the study, students engaged in dialogues with ChatGPT to revise their essays. RECIPE4U includes comprehensive records of these interactions, including conversation logs, students' intent, students' self-rated satisfaction, and students' essay edit histories. In particular, we annotate the students' utterances in RECIPE4U with 13 intention labels based on our coding schemes. We establish baseline results for two subtasks in task-oriented dialogue systems within educational contexts: intent detection and satisfaction estimation. As a foundational step, we explore student-ChatGPT interaction patterns through RECIPE4U and analyze them by focusing on students' dialogue, essay data statistics, and students' essay edits. We further illustrate potential applications of RECIPE4U dataset for enhancing the incorporation of LLMs in educational frameworks. RECIPE4U is publicly available at https://zeunie.github.io/RECIPE4U/., Comment: arXiv admin note: text overlap with arXiv:2309.13243

Nakagami imaging holds promise for visualizing and quantifying tissue scattering in ultrasound waves, with potential applications in tumor diagnosis and fat fraction estimation which are challenging to discern by conventional ultrasound B-mode images. Existing methods struggle with optimal window size selection and suffer from estimator instability, leading to degraded resolution images. To address this, here we propose a novel method called UNICORN (Ultrasound Nakagami Imaging via Score Matching and Adaptation), that offers an accurate, closed-form estimator for Nakagami parameter estimation in terms of the score function of ultrasonic envelope. Extensive experiments using simulation and real ultrasound RF data demonstrate UNICORN's superiority over conventional approaches in accuracy and resolution quality., Comment: 12 pages, 5 figure

Object slip perception is essential for mobile manipulation robots to perform manipulation tasks reliably in the dynamic real-world. Traditional approaches to robot arms' slip perception use tactile or vision sensors. However, mobile robots still have to deal with noise in their sensor signals caused by the robot's movement in a changing environment. To solve this problem, we present an anomaly detection method that utilizes multisensory data based on a deep autoencoder model. The proposed framework integrates heterogeneous data streams collected from various robot sensors, including RGB and depth cameras, a microphone, and a force-torque sensor. The integrated data is used to train a deep autoencoder to construct latent representations of the multisensory data that indicate the normal status. Anomalies can then be identified by error scores measured by the difference between the trained encoder's latent values and the latent values of reconstructed input data. In order to evaluate the proposed framework, we conducted an experiment that mimics an object slip by a mobile service robot operating in a real-world environment with diverse household objects and different moving patterns. The experimental results verified that the proposed framework reliably detects anomalies in object slip situations despite various object types and robot behaviors, and visual and auditory noise in the environment.

The toric code is a canonical example of a topological error-correcting code. Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error rate remains below a certain threshold. Recent studies have explored such a threshold behavior as an intrinsic information-theoretic transition, independent of the decoding protocol. These studies have shown that information-theoretic metrics, calculated using the Renyi (replica) approximation, demonstrate sharp transitions at a specific error rate. However, an exact analytic expression that avoids using the replica trick has not been shown, and the connection between the transition in information-theoretic capacity and the random bond Ising model (RBIM) has only been indirectly established. In this work, we present the first analytic expression for the coherent information of a decohered toric code, thereby establishing a rigorous connection between the fundamental error threshold and the criticality of the RBIM., Comment: 5 + 2 pages, 3 figures

We present an architecture for encoding two qubits within the optical "clock" transition and nuclear spin-1/2 degree of freedom of neutral ytterbium-171 atoms. Inspired by recent high-fidelity control of all pairs of states within this four-dimensional ququart space, we present a toolbox for intra-ququart (single atom) one- and two-qubit gates, inter-ququart (two atom) Rydberg-based two- and four-qubit gates, and quantum nondemolition (QND) readout. We then use this toolbox to demonstrate the advantages of the ququart encoding for entanglement distillation and quantum error correction which exhibit superior hardware efficiency and better performance in some cases since fewer two-atom (Rydberg-based) operations are required. Finally, leveraging single-state QND readout in our ququart encoding, we present a unique approach to studying interactive circuits as well as to realizing a symmetry protected topological phase of a spin-1 chain with a shallow, constant-depth circuit. These applications are all within reach of recent experiments with neutral ytterbium-171 atom arrays or with several trapped ion species., Comment: 22 pages, 14 figures