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Human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdisciplinary field of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a neural-symbolic system, named FGeo-DRL, to automatically perform human-like geometric deductive reasoning. The neural part is an AI agent based on deep 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 geometric problem solving (GPS) as a Markov Decision Process (MDP). In the formal symbolic system, the symmetry of plane geometric transformations ensures the uniqueness of geometric problems when converted into states. Finally, the known conditions and objectives of the problem form the state space, while the set of theorems forms the action space. Leveraging FGeo-DRL, 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%. [ABSTRACT FROM AUTHOR]

The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proofs has always been a grand challenge to the interdisciplinary field of mathematics and artificial intelligence. This is the fourth article in a series of our works, in our previous work, we established a geometric formalized system known as FormalGeo. Moreover, we annotated approximately 7000 geometric problems, forming the FormalGeo7k dataset. Despite the fact that 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 the theorem sequences for solving geometry problems. The encoder and decoder components in the transformer architecture naturally establish a mapping between the sequences and embedding vectors, exhibiting inherent symmetry. We compare the effectiveness of various transformer architectures, such as BART or T5, in theorem prediction, and implement pruning in the search process of FGPS, thereby improving its performance when 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 solution times and search steps across problems of varying difficulty levels. [ABSTRACT FROM AUTHOR]

Regulation of food intake is associated with nutrient-sensing systems and the expression of appetite neuropeptides. Nutrient-sensing systems generate the capacity to sense nutrient availability to maintain energy and metabolism homeostasis. Appetite neuropeptides are prominent factors that are essential for regulating the appetite to adapt energy status. However, the link between the expression of appetite neuropeptides and nutrient-sensing systems remains debatable in carnivorous fish. Here, with intracerebroventricular (ICV) administration of six essential amino acids (lysine, methionine, tryptophan, arginine, phenylalanine, or threonine) performed in mandarin fish (Siniperca chuatsi), we found that lysine and methionine are the feeding-stimulating amino acids other than the reported valine, and found a key appetite neuropeptide, neuropeptide Y (NPY), mainly contributes to the regulatory role of the essential amino acids on food intake. With the brain cells of mandarin fish cultured in essential amino acid deleted medium (lysine, methionine, histidine, valine, or leucine), we showed that only lysine deprivation activated the general control nonderepressible 2 (GCN2) signaling pathway, elevated α subunit of eukaryotic translation initiation factor 2 (eIF2α) phosphorylation, increased activating transcription factor 4 (ATF4) protein expression, and finally induced transcription of npy. Furthermore, pharmacological inhibition of GCN2 and eIF2α phosphorylation signaling by GCN2iB or ISRIB, effectively blocked the transcriptional induction of npy in lysine deprivation. Overall, these findings could provide a better understanding of the GCN2 signaling pathway involved in food intake control by amino acids. [ABSTRACT FROM AUTHOR]

Fast radio bursts (FRBs) have been found in great numbers, but the physical mechanism of these sources is still a mystery. The redshift evolutions of the FRB energy distribution function and the volumetric rate shed light on the origin of FRBs. However, such estimations rely on the dispersion measurement (DM)–redshift (z) relationship. A few FRBs that have been detected recently show large excess DMs beyond the expectation from the cosmological and Milky Way contributions, which indicates large spread of DMs from their host galaxies. In this work, we adopt two lognormal-distributed DM host models and estimate the energy function using the non-repeating FRBs selected from the Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB Catalog 1. By comparing the lognormal-distributed DM host models to a constant DM host model, the FRB energy function results are consistent within the measurement uncertainty. We also estimate the volumetric rate of the non-repeating FRBs in three different redshift bins. The volumetric rate shows that the trend is consistent with the stellar-mass density redshift evolution. Since the lognormal-distributed DM host model increases the measurement errors, the inference of FRBs tracking the stellar-mass density is nonetheless undermined. [ABSTRACT FROM AUTHOR]

Geometric problem solving (GPS) has always been a long-standing challenge in the fields of automated reasoning. Its problem representation and solution process embody rich symmetry. This paper is the second in a series of our works. Based on the Geometry Formalization Theory and the FormalGeo geometric formal system, we have developed the Formal Geometric Problem Solver (FGPS) in Python 3.10, which can serve as an interactive assistant or as an automated problem solver. FGPS is capable of executing geometric predicate logic and performing relational reasoning and algebraic computation, ultimately achieving readable, traceable, and verifiable automated solutions for geometric problems. We observed that symmetry phenomena exist at various levels within FGPS and utilized these symmetries to further refine the system's design. FGPS employs symbols to represent geometric shapes and transforms various geometric patterns into a set of symbolic operation rules. This maintains symmetry in basic transformations, shape constructions, and the application of theorems. Moreover, we also have annotated the formalgeo7k dataset, which contains 6981 geometry problems with detailed formal language descriptions and solutions. Experiments on formalgeo7k validate the correctness and utility of the FGPS. The forward search method with random strategy achieved a 39.71% problem-solving success rate. [ABSTRACT FROM AUTHOR]

A novel rectifier based on a triple line-voltage cascaded VIENNA converter (LVC-VC) was proposed. Compared to the conventional cascaded H-bridge converters, the switch voltage stress is lower, and the numbers of switches and dc capacitors are fewer under similar operating conditions in the proposed new multilevel converter. The modeling and control for the LVC-VC ware presented. Based on the analysis of the operation principle of the new converter, the power factor correction of the proposed converter was realized by employing a traditional one-cycle control strategy. The minimum average value and maximum harmonic components of the dc-link voltages of the three VIENNA rectifier modules ware calculated. Three VIENNA dc-link voltages were unbalanced under the unbalanced load conditions, so the zero sequence current was injected to the three inner currents for balancing three VIENNA dc-link voltages. Simulation and the results of the experiment verified the availability of the new proposed multilevel converter and the effectiveness of the corresponding control strategy applied. [ABSTRACT FROM AUTHOR]

Galfenol (Fe1−xGax, 10 < x < 40) may be the only smart material that can be made by electrochemical deposition which enables thick film and nanowire structures. This article reviews the deposition, characterization, and applications of Galfenol thin films and nanowires. Galfenol films have been made by sputter deposition as well as by electrochemical deposition, which can be difficult due to the insolubility of gallium. However, a stable process has been developed, using citrate complexing, a rotating disk electrode, Cu seed layers, and pulsed deposition. Galfenol thin films and nanowires have been characterized for crystal structures and magnetostriction both by our group and by collaborators. Films and nanowires have been shown to be largely polycrystalline, with magnetostrictions that are on the same order of magnitude as textured bulk Galfenol. Electrodeposited Galfenol films were made with epitaxial texture on GaAs. Galfenol nanowires have been made by electrodeposition into anodic aluminum oxide templates using similar parameters defined for films. Segmented nanowires of Galfenol/Cu have been made to provide engineered magnetic properties. Applications of Galfenol and other magnetic nanowires include microfluidic sensors, magnetic separation, cellular radio-frequency identification (RFID) tags, magnetic resonance imaging (MRI) contrast, and hyperthermia. [ABSTRACT FROM AUTHOR]