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Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to understand geometric diagrams, performing no better in geometry problem solving than LLMs that only process text. This limitation is amplified by the lack of effective methods for representing geometric relationships. To address these issues, we introduce the Diagram Formalization Enhanced Geometry Problem Solver (DFE-GPS), a new framework that integrates visual features, geometric formal language, and natural language representations. We propose a novel synthetic data approach and create a large-scale geometric dataset, SynthGeo228K, annotated with both formal and natural language captions, designed to enhance the vision encoder for a better understanding of geometric structures. Our framework improves MLLMs' ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.

The electronic structure of high-quality van der Waals multiferroic CuCrP$_2$S6 crystals was investigated applying photoelectron spectroscopy methods in combination with DFT analysis. Using X-ray photoelectron and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy at the Cu L2,3 and Cr L2,3 absorption edges we determine the charge states of ions in the studied compound. Analyzing the systematic NEXAFS and resonant photoelectron spectroscopy data at the Cu/Cr L2,3 absorption edges allowed us to assign the CuCrP$_2$S6 material to a Mott-Hubbard type insulator and identify different Auger-decay channels (participator vs. spectator) during absorption and autoionization processes. Spectroscopic and theoretical data obtained for CuCrP$_2$S6 are very important for the detailed understanding of the electronic structure and electron-correlations phenomena in different layered materials, that will drive their further applications in different areas, like electronics, spintronics, sensing, and catalysis.

Geometric problem solving has always been a long-standing challenge in the fields of automated reasoning and artificial intelligence. We built a neural-symbolic system to automatically perform human-like geometric deductive reasoning. The symbolic part is a formal system built on FormalGeo, which can automatically perform geomertic relational reasoning and algebraic calculations and organize the solving process into a solution hypertree with conditions as hypernodes and theorems as hyperedges. The neural part, called HyperGNet, is a hypergraph neural network based on the attention mechanism, including a encoder to effectively encode the structural and semantic information of the hypertree, and a solver to provide problem-solving guidance. The neural part predicts theorems according to the hypertree, and the symbolic part applies theorems and updates the hypertree, thus forming a predict-apply cycle to ultimately achieve readable and traceable automatic solving of geometric problems. Experiments demonstrate the correctness and effectiveness of this neural-symbolic architecture. We achieved a step-wised accuracy of 87.65% and an overall accuracy of 85.53% on the formalgeo7k datasets., Comment: 13 pages

The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a neural-symbolic system, called FGeoDRL, to automatically perform human-like geometric deductive reasoning. The neural part is an AI agent based on reinforcement learning, capable of autonomously learning problem-solving methods from the feedback of a formalized environment, without the need for human supervision. It leverages a pre-trained natural language model to establish a policy network for theorem selection and employ Monte Carlo Tree Search for heuristic exploration. The symbolic part is a reinforcement learning environment based on geometry formalization theory and FormalGeo, which models GPS as a Markov Decision Process. In this formal symbolic system, the known conditions and objectives of the problem form the state space, while the set of theorems forms the action space. Leveraging FGeoDRL, we have achieved readable and verifiable automated solutions to geometric problems. Experiments conducted on the formalgeo7k dataset have achieved a problem-solving success rate of 86.40%. The project is available at https://github.com/PersonNoName/FGeoDRL., Comment: 15 pages

The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This is the fourth article in a series of our works, in our previous work, we established of a geometric formalized system known as FormalGeo. Moreover we annotated approximately 7000 geometric problems, forming the FormalGeo7k dataset. Despite the FGPS (Formal Geometry Problem Solver) can achieve interpretable algebraic equation solving and human-like deductive reasoning, it often experiences timeouts due to the complexity of the search strategy. In this paper, we introduced FGeo-TP (Theorem Predictor), which utilizes the language model to predict theorem sequences for solving geometry problems. We compared the effectiveness of various Transformer architectures, such as BART or T5, in theorem prediction, implementing pruning in the search process of FGPS, thereby improving its performance in solving geometry problems. Our results demonstrate a significant increase in the problem-solving rate of the language model-enhanced FGeo-TP on the FormalGeo7k dataset, rising from 39.7% to 80.86%. Furthermore, FGeo-TP exhibits notable reductions in solving time and search steps across problems of varying difficulty levels., Comment: 16 pages

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS., Comment: 44 pages

Single-mode high-index-contrast waveguides have been ubiquitously exploited in optical, microwave, and phononic structures for achieving enhanced wave-matter interactions. Although micro-scale optomechanical and electro-optical devices have been widely studied, optomagnonic devices remain a grand challenge at the microscale. Here, we introduce a planar optomagnonic waveguide platform based on a ferrimagnetic insulator that simultaneously supports single transverse mode of spin waves (magnons) and highly confined optical modes. The co-localization of spin and light waves gives rise to enhanced inverse Faraday effect, and as a result, magnons are excited by an effective magnetic field generated by interacting optical photons. Moreover, the strongly enhanced optomagnonic interaction allows us to observe such effect using low-power (milliwatt level) light signals in the continuous-wave form, as opposed to high-intensity (megawatt peak power) light pulses that are typically required in magnetic bulk materials or thin films. The optically-driven magnons are detected electrically with preserved phase coherence, showing the feasibility for launching spin waves with low-power continuous optical fields.

Cavity optomagnonics has emerged as a promising platform for studying coherent photon-spin interactions as well as tunable microwave-to-optical conversion. However, current implementation of cavity optomagnonics in ferrimagnetic crystals remains orders of magnitude larger in volume than state-of-the-art cavity optomechanical devices, resulting in very limited magneto-optical interaction strength. Here, we demonstrate a cavity optomagnonic device based on integrated waveguides and its application for microwave-to-optical conversion. By designing a ferrimagnetic rib waveguide to support multiple magnon modes with maximal mode overlap to the optical field, we realize a high magneto-optical cooperativity which is three orders of magnitude higher compared to previous records obtained on polished YIG spheres. Furthermore, we achieve tunable conversion of microwave photons at around 8.45 GHz to 1550 nm light with a broad conversion bandwidth as large as 16.1 MHz. The unique features of the system point to novel applications at the crossroad between quantum optics and magnonics.

We present a generic theoretical framework to describe non-reciprocal microwave circulation in a multimode cavity magnonic system and assess the optimal performance of practical circulator devices. We show that high isolation (> 56 dB), extremely low insertion loss (< 0.05 dB), and flexible bandwidth control can be potentially realized in high-quality-factor superconducting cavity based magnonic platforms. These circulation characteristics are analyzed with materials of different spin densities. For high-spin-density materials such as yttrium iron garnet, strong coupling operation regime can be harnessed to obtain a broader circulation bandwidth. We also provide practical design principles for a highly integratible low-spin-density material (vanadium tetracyanoethylene) for narrow-band circulator operation, which could benefit noise-sensitive quantum microwave measurements. This theory can be extended to other coupled systems and provide design guidelines for achieving tunable microwave non-reciprocity for both classical and quantum applications.

Integrating patterned, low-loss magnetic materials into microwave devices and circuits presents many challenges due to the specific conditions that are required to grow ferrite materials, driving the need for flip-chip and other indirect fabrication techniques. The low-loss ($\alpha = 3.98 \pm 0.22 \times 10^{-5}$), room-temperature ferrimagnetic coordination compound vanadium tetracyanoethylene ($\mathrm{V[TCNE]}_x$) is a promising new material for these applications that is potentially compatible with semiconductor processing. Here we present the deposition, patterning, and characterization of $\mathrm{V[TCNE]}_x$ thin films with lateral dimensions ranging from 1 micron to several millimeters. We employ electron-beam lithography and liftoff using an aluminum encapsulated poly(methyl methacrylate), poly(methyl methacrylate-methacrylic acid) copolymer bilayer (PMMA/P(MMA-MAA)) on sapphire and silicon. This process can be trivially extended to other common semiconductor substrates. Films patterned via this method maintain low-loss characteristics down to 25 microns with only a factor of 2 increase down to 5 microns. A rich structure of thickness and radially confined spin-wave modes reveals the quality of the patterned films. Further fitting, simulation, and analytic analysis provides an exchange stiffness, $A_{ex} = 2.2 \pm 0.5 \times 10^{-10}$ erg/cm, as well as insights into the mode character and surface spin pinning. Below a micron, the deposition is non-conformal, which leads to interesting and potentially useful changes in morphology. This work establishes the versatility of $\mathrm{V[TCNE]}_x$ for applications requiring highly coherent magnetic excitations ranging from microwave communication to quantum information., Comment: 18 pages, 7 figures, submitted to APL Materials

Public educational systems operate thousands of buildings with vastly different characteristics in terms of size, age, location, construction, thermal behavior and user communities. Their strategic planning and sustainable operation is an extremely complex and requires quantitative evidence on the performance of buildings such as the interaction of indoor-outdoor environment. Internet of Things (IoT) deployments can provide the necessary data to evaluate, redesign and eventually improve the organizational and managerial measures. In this work a data mining approach is presented to analyze the sensor data collected over a period of 2 years from an IoT infrastructure deployed over 18 school buildings spread in Greece, Italy and Sweden. The real-world evaluation indicates that data mining on sensor data can provide critical insights to building managers and custodial staff about ways to lower a building's energy footprint through effectively managing building operations., Comment: 13 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1805.09561

Vanadium tetracyanoethylene (V[TCNE]$_\text{x}$) is an organic-based ferrimagnet that exhibits robust magnetic ordering (T$_\text{C}$ of over 600 K), high quality-factor (high-Q) microwave resonance (Q up to 3,500), and compatibility with a wide variety of substrates and encapsulation technologies. Here, we substantially expand the potential scope and impact of this emerging material by demonstrating the ability to produce engineered nanostructures with tailored magnetic anisotropy that serve as a platform for the exploration of cavity magnonics, revealing strongly coupled quantum confined standing wave modes that can be tuned into and out of resonance with an applied magnetic field. Specifically, time-domain micromagnetic simulations of these nanostructures faithfully reproduce the experimentally measured spectra, including the quasi-uniform mode and higher-order spin-wave (magnon) modes. Finally, when the two dominant magnon modes present in the spectra are brought into resonance by varying the orientation of the in-plane magnetic field, we observe anti-crossing behavior indicating strong coherent coupling between these two magnon modes at room temperature. These results position V[TCNE]$_\text{x}$ as a leading candidate for the development of coherent magnonics, with potential applications ranging from microwave electronics to quantum information., Comment: 25 pages, 3 figures

We demonstrate patterned growth of epitaxial yttrium iron garnet (YIG) thin films using lithographically defined templates on gadolinium gallium garnet (GGG) substrates. The fabricated YIG nanostructures yield the desired crystallographic orientation, excellent surface morphology, and narrow ferromagnetic resonance (FMR) linewidth (~ 4 Oe). Shape-induced magnetic anisotropy is clearly observed in a patterned array of nanobars engineered to exhibit the larger coercivity (40 Oe) compared with that of continuous films. Both hysteresis loop and angle-dependent FMR spectra measurements indicate that the easy axis aligns along the longitudinal direction of the nanobars, with an effective anisotropy field of 195 Oe. Our work overcomes difficulties in patterning YIG thin films and provides an effective means to control their magnetic properties and magnetic bias conditions.

We experimentally demonstrate high quality factor spin wave resonances in an encapsulated thin film of the organic-based ferrimagnet vanadium tetracyanoethylene (V[TCNE]$_\textit{x~2}$) coated on an a-plane sapphire substrate by low temperature chemical vapor deposition. The thickness standing wave modes are observed in a broad frequency range (1 GHz ~ 5 GHz) with high quality factor exceeding 3,200 in ambient air at room temperature, rivaling those of inorganic magnetic materials. The exchange constant of V[TCNE]$_\textit{x~2}$, a crucial material parameter for future study and device design of the V[TCNE]$_\textit{x~2}$, is extracted from the measurement with a value of $(4.61\pm 0.35)\times 10^{-16} \mathrm{\: m^{2}}$. Our result establishes the feasibility of using organic-based materials for building hybrid magnonic devices and circuits., Comment: 12 pages, 3 figures

Magnons in ferrimagnetic insulators such as yttrium iron garnet (YIG) have recently emerged as promising candidates for coherent information processing in microwave circuits. Here we demonstrate optical whispering gallery modes of a YIG sphere interrogated by a silicon nitride photonic waveguide, with quality factors approaching $10^6$ in the telecom c-band after surface treatments. Moreover, in contrast to conventional Faraday setup, this implementation allows input photon polarized colinearly to the magnetization to be scattered to a sideband mode of orthogonal polarization. This Brillouin scattering process is enhanced through triply resonant magnon, pump and signal photon modes - all of whispering gallery nature - within an "optomagnonic cavity". Our results show the potential use of magnons for mediating microwave-to-optical carrier conversion., Comment: 5 pages, 4 figures

Extensive efforts have been expended in developing hybrid quantum systems to overcome the short coherence time of superconducting circuits by introducing the naturally long-lived spin degree of freedom. Among all the possible materials, single-crystal yttrium iron garnet has shown up very recently as a promising candidate for hybrid systems, and various highly coherent interactions, including strong and even ultra-strong coupling, have been demonstrated. One distinct advantage of these systems is that the spins are in the form of well-defined magnon modes, which allows flexible and precise tuning. Here we demonstrate that by dissipation engineering, a non-Markovian interaction dynamics between the magnon and the microwave cavity photon can be achieved. Such a process enables us to build a magnon gradient memory to store information in the magnon dark modes, which decouple from the microwave cavity and thus preserve a long life-time. Our findings provide a promising approach for developing long-lifetime, multimode quantum memories., Comment: 18 pages, 12 figures