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We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in $\mathbb{C}^2$ and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that Toeplitz operators as well as the Hermitian squares of Hankel operators are compact if and only if the Berezin transforms of the operators vanish on the boundary of the domain.

This study examines the potential of integrating Learning-to-Rank (LTR) with Query-focused Summarization (QFS) to enhance the summary relevance via content prioritization. Using a shared secondary decoder with the summarization decoder, we carry out the LTR task at the segment level. Compared to the state-of-the-art, our model outperforms on QMSum benchmark (all metrics) and matches on SQuALITY benchmark (2 metrics) as measured by Rouge and BertScore while offering a lower training overhead. Specifically, on the QMSum benchmark, our proposed system achieves improvements, particularly in Rouge-L (+0.42) and BertScore (+0.34), indicating enhanced understanding and relevance. While facing minor challenges in Rouge-1 and Rouge-2 scores on the SQuALITY benchmark, the model significantly excels in Rouge-L (+1.47), underscoring its capability to generate coherent summaries. Human evaluations emphasize the efficacy of our method in terms of relevance and faithfulness of the generated summaries, without sacrificing fluency. A deeper analysis reveals our model's superiority over the state-of-the-art for broad queries, as opposed to specific ones, from a qualitative standpoint. We further present an error analysis of our model, pinpointing challenges faced and suggesting potential directions for future research in this field., Comment: Long paper accepted at EMNLP 2024 (Main)

Sparse retrieval methods like BM25 are based on lexical overlap, focusing on the surface form of the terms that appear in the query and the document. The use of inverted indices in these methods leads to high retrieval efficiency. On the other hand, dense retrieval methods are based on learned dense vectors and, consequently, are effective but comparatively slow. Since sparse and dense methods approach problems differently and use complementary relevance signals, approximation methods were proposed to balance effectiveness and efficiency. For efficiency, approximation methods like HNSW are frequently used to approximate exhaustive dense retrieval. However, approximation techniques still exhibit considerably higher latency than sparse approaches. We propose LexBoost that first builds a network of dense neighbors (a corpus graph) using a dense retrieval approach while indexing. Then, during retrieval, we consider both a document's lexical relevance scores and its neighbors' scores to rank the documents. In LexBoost this remarkably simple application of the Cluster Hypothesis contributes to stronger ranking effectiveness while contributing little computational overhead (since the corpus graph is constructed offline). The method is robust across the number of neighbors considered, various fusion parameters for determining the scores, and different dataset construction methods. We also show that re-ranking on top of LexBoost outperforms traditional dense re-ranking and leads to results comparable with higher-latency exhaustive dense retrieval., Comment: ACM DocEng 2024

Generative language models hallucinate. That is, at times, they generate factually flawed responses. These inaccuracies are particularly insidious because the responses are fluent and well-articulated. We focus on the task of Grounded Answer Generation (part of Generative IR), which aims to produce direct answers to a user's question based on results retrieved from a search engine. We address hallucination by adapting an existing genetic generation approach with a new 'balanced fitness function' consisting of a cross-encoder model for relevance and an n-gram overlap metric to promote grounding. Our balanced fitness function approach quadruples the grounded answer generation accuracy while maintaining high relevance., Comment: Gen-IR@SIGIR 2024

Central charge is a fundamental quantity in conformal field theories (CFT), and plays a crucial role in determining universality classes of critical points in two-dimensional systems. Despite its significance, the measurement of central charge has remained elusive thus far. In this work, we present the first experimental determination of the central charge using a universal quantum processor. Using a classically optimized variational quantum circuit and employing advanced error mitigation techniques, we successfully prepare ground states of various $1+1D$ quantum spin chain models at their critical point. Leveraging the heavy-hex structure of IBM quantum processors, we are able to implement periodic boundary conditions and mitigate boundary effects. We then extract the central charge from the scaling behavior of the sub-leading term of R{\'{e}}nyi generalizations of classical Shannon entropy, computed for local Pauli measurements in the conformal bases ($\sigma^{z}$ and $\sigma^x$). The experimental results are consistent with the known central charge values for the transverse field Ising (TFI) chain ($c=0.5$) and the XXZ chain ($c=1$), achieving relative errors as low as 5 percent., Comment: 7 + 13 pages, 4 + 11 figures

Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multi-partite entanglement. Experimental feasibility and possible generalizations are discussed., Comment: 5 + 7 pages, 4 + 4 figures

Simulating quantum dynamics of lattice gauge theories (LGTs) is an exciting frontier in quantum science. Programmable quantum simulators based on neutral atom arrays are a promising approach to achieve this goal, since strong Rydberg blockade interactions can be used to naturally create low energy subspaces that can encode local gauge constraints. However, realizing regimes of LGTs where both matter and gauge fields exhibit significant dynamics requires the presence of tunable multi-body interactions such as those associated with ring exchange, which are challenging to realize directly. Here, we develop a method for generating such interactions based on time-periodic driving. Our approach utilizes controlled deviations from time-reversed trajectories, which are accessible in constrained PXP-type models via the application of frequency modulated global pulses. We show that such driving gives rise to a family of effective Hamiltonians with multi-body interactions whose strength is non-perturbative in their respective operator weight. We apply this approach to a two-dimensional U(1) LGT on the Kagome lattice, where we engineer strong six-body magnetic plaquette terms that are tunable relative to the kinetic energy of matter excitations, demonstrating access to previously unexplored dynamical regimes. Potential generalizations and prospects for experimental implementations are discussed., Comment: 12 + 6 pages, 6 + 3 figures

Understanding the collective quantum dynamics of nonequilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter, fundamental high-energy processes, quantum metrology, and quantum algorithms. Here, we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)D Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode. These observations offer a unique viewpoint into emergent collective dynamics in strongly correlated quantum systems and nonequilibrium quantum processes., Comment: 25 pages, 15 figures

Phonon polaritons (PhPs) are hybrid photon-phonon waves which enable strong light-matter interactions and subdiffractional confinement, potentially empowering applications in sensing, nonlinear optics and nanoscale energy manipulation. In this work, we use confocal Raman microscopy to investigate the coupling between bulk phonon modes and localized surface phonon polariton (SPhP) modes in indium phosphide (InP) nanopillars and 4H-silicon carbide (4H-SiC) gratings. The Raman intensity within the nanostructures is described in terms of the SPhP eigenmodes and used to reconstruct the field intensity, providing a method to map SPhP eigenmodes using visible and near-IR light. Our results indicate that, contrary to expectation, all Raman-active bulk phonon modes of InP and 4H-SiC couple to the localized SPhP modes. Further, we confirm that polarizability selection rules form the predominant coupling mechanism between phonons and SPhP modes, with electron-phonon coupling playing a role for certain phonon modes (A1(LO) and E1(TO) in 4H-SiC). These observations provide a method for extending Raman studies of PhP modes to achieve full 3D reconstruction of the PhP eigenmodes and visualize light-matter interactions within nanostructures, thus advancing Raman scattering as a technique for understanding PhP modes.

This paper is about the operators defined between K\"othe spaces whose associated matrix is a Hankel matrix. After demonstrating how these operators are defined, the conditions for continuity and compactness of these operators are constructed. It is shown that the backward and forward shift operators are mean ergodic and Ces\`aro bounded by establishing a relationship between the backward and forward shift operators and Hankel and Toeplitz operators on power series spaces., Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:2312.13609

Synthetic tracking (ST) has emerged as a potent technique for observing fast-moving near-Earth objects (NEOs), offering enhanced detection sensitivity and astrometric accuracy by avoiding trailing loss. This approach also empowers small telescopes to use prolonged integration times to achieve high sensitivity for NEO surveys and follow-up observations. In this study, we present the outcomes of ST observations conducted with Pomona College's 1 m telescope at the Table Mountain Facility and JPL's robotic telescopes at the Sierra Remote Observatory. The results showcase astrometric accuracy statistics comparable to stellar astrometry, irrespective of an object's rate of motion, and the capability to detect faint asteroids beyond 20.5th magnitude using 11-inch telescopes. Furthermore, we detail the technical aspects of data processing, including the correction of differential chromatic refraction in the atmosphere and accurate timing for image stacking, which contribute to achieving precise astrometry. We also provide compelling examples that showcase the robustness of ST even when asteroids closely approach stars or bright satellites cause disturbances. Moreover, we illustrate the proficiency of ST in recovering NEO candidates with highly uncertain ephemerides. As a glimpse of the potential of NEO surveys utilizing small robotic telescopes with ST, we present significant statistics from our NEO survey conducted for testing purposes. These findings underscore the promise and effectiveness of ST as a powerful tool for observing fast-moving NEOs, offering valuable insights into their trajectories and characteristics. Overall, the adoption of ST stands to revolutionize fast-moving NEO observations for planetary defense and studying these celestial bodies., Comment: 50 pages, 19 figures

The aim of this paper is to define Toeplitz operators between K\"othe spaces, especially power series spaces. We determine the conditions for continuity and compactness of these operators. We define the concept of S-tameness of a family of continuous operators. We construct some conditions on S-tameness for the families consisting of Toeplitz operators., Comment: 20 pages, accepted by Filomat

Retrieval approaches that score documents based on learned dense vectors (i.e., dense retrieval) rather than lexical signals (i.e., conventional retrieval) are increasingly popular. Their ability to identify related documents that do not necessarily contain the same terms as those appearing in the user's query (thereby improving recall) is one of their key advantages. However, to actually achieve these gains, dense retrieval approaches typically require an exhaustive search over the document collection, making them considerably more expensive at query-time than conventional lexical approaches. Several techniques aim to reduce this computational overhead by approximating the results of a full dense retriever. Although these approaches reasonably approximate the top results, they suffer in terms of recall -- one of the key advantages of dense retrieval. We introduce 'LADR' (Lexically-Accelerated Dense Retrieval), a simple-yet-effective approach that improves the efficiency of existing dense retrieval models without compromising on retrieval effectiveness. LADR uses lexical retrieval techniques to seed a dense retrieval exploration that uses a document proximity graph. We explore two variants of LADR: a proactive approach that expands the search space to the neighbors of all seed documents, and an adaptive approach that selectively searches the documents with the highest estimated relevance in an iterative fashion. Through extensive experiments across a variety of dense retrieval models, we find that LADR establishes a new dense retrieval effectiveness-efficiency Pareto frontier among approximate k nearest neighbor techniques. Further, we find that when tuned to take around 8ms per query in retrieval latency on our hardware, LADR consistently achieves both precision and recall that are on par with an exhaustive search on standard benchmarks., Comment: SIGIR 2023

The changing level of haze is one of the main factors which affects the success of the proposed dehazing methods. However, there is a lack of controlled multi-level hazy dataset in the literature. Therefore, in this study, a new multi-level hazy color image dataset is presented. Color video data is captured for two real scenes with a controlled level of haze. The distance of the scene objects from the camera, haze level, and ground truth (clear image) are available so that different dehazing methods and models can be benchmarked. In this study, the dehazing performance of five different dehazing methods/models is compared on the dataset based on SSIM, PSNR, VSI and DISTS image quality metrics. Results show that traditional methods can generalize the dehazing problem better than many deep learning based methods. The performance of deep models depends mostly on the scene and is generally poor on cross-dataset dehazing., Comment: 13 pages

Query-focused summarization (QFS) is a challenging task in natural language processing that generates summaries to address specific queries. The broader field of Generative Information Retrieval (Gen-IR) aims to revolutionize information extraction from vast document corpora through generative approaches, encompassing Generative Document Retrieval (GDR) and Grounded Answer Retrieval (GAR). This paper highlights the role of QFS in Grounded Answer Generation (GAR), a key subdomain of Gen-IR that produces human-readable answers in direct correspondence with queries, grounded in relevant documents. In this study, we propose QontSum, a novel approach for QFS that leverages contrastive learning to help the model attend to the most relevant regions of the input document. We evaluate our approach on a couple of benchmark datasets for QFS and demonstrate that it either outperforms existing state-of-the-art or exhibits a comparable performance with considerably reduced computational cost through enhancements in the fine-tuning stage, rather than relying on large-scale pre-training experiments, which is the focus of current SOTA. Moreover, we conducted a human study and identified improvements in the relevance of generated summaries to the posed queries without compromising fluency. We further conduct an error analysis study to understand our model's limitations and propose avenues for future research., Comment: 9 pages, Long paper accepted at Gen-IR@SIGIR23