To overcome the bottleneck of classical path planning schemes in solving NP problems and address the predicament faced by current mainstream quantum path planning frameworks in the Noisy Intermediate-Scale Quantum (NISQ) era, this study attempts to construct a quantum path planning solution based on parallel Quantum Approximate Optimization Algorithm (QAOA) architecture. Specifically, the grid path planning problem is mapped to the problem of finding the minimum quantum energy state. Two parallel QAOA circuits are built to simultaneously execute two solution processes, namely connectivity energy calculation and path energy calculation. A classical algorithm is employed to filter out unreasonable solutions of connectivity energy, and finally, the approximate optimal solution to the path planning problem is obtained by merging the calculation results of the two parallel circuits. The research findings indicate that by setting appropriate filter parameters, quantum states corresponding to position points with extremely low occurrence probabilities can be effectively filtered out, thereby increasing the probability of obtaining the target quantum state. Even when the circuit layer number p is only 1, the theoretical solution of the optimal path coding combination can still be found by leveraging the critical role of the filter. Compared with serial circuits, parallel circuits exhibit a significant advantage, as they can find the optimal feasible path coding combination with the highest probability.

It is obvious that Eq. (5) holds for k = 2 . The information of the datasets we used is shown in Table 1. The first four rows in Table 1 are the existing label distribution datasets; the last three rows in Table 1 are the datasets we created. Since some examples in the original label distribution datasets do not satisfy the prerequisites of our paper (i.e., there are some examples

Large language models (LLMs) have exhibited impressive competence in various tasks, but their opaque internal mechanisms hinder their use in mathematical problems. In this paper, we study a fundamental question: whether language models understand numbers, a basic element in math. Based on an assumption that LLMs should be capable of compressing numbers in their hidden states to solve mathematical problems, we construct a synthetic dataset comprising addition problems and utilize linear probes to read out input numbers from the hidden states. Experimental results support the existence of compressed numbers in LLMs. However, it is difficult to precisely reconstruct the original numbers, indicating that the compression process may not be lossless. Further experiments show that LLMs can utilize encoded numbers to perform arithmetic computations, and the computational ability scales up with the model size. Our preliminary research suggests that LLMs exhibit a partial understanding of numbers, offering insights for future investigations about the models' mathematical capability.

Reducing wealth inequality and disparity is a global challenge. The economic system is mainly divided into (1) gift and reciprocity, (2) power and redistribution, (3) market exchange, and (4) mutual aid without reciprocal obligations. The current inequality stems from a capitalist economy consisting of (2) and (3). To sublimate (1), which is the human economy, to (4), the concept of a "mixbiotic society" has been proposed in the philosophical realm. This is a society in which free and diverse individuals, "I," mix with each other, recognize their respective "fundamental incapability" and sublimate them into "WE" solidarity. The economy in this society must have moral responsibility as a coadventurer and consideration for vulnerability to risk. Therefore, I focus on two factors of mind perception: moral responsibility and risk vulnerability, and propose a novel model of wealth distribution following an econophysical approach. Specifically, I developed a joint-venture model, a redistribution model in the joint-venture model, and a "WE economy" model. A simulation comparison of a combination of the joint ventures and redistribution with the WE economies reveals that WE economies are effective in reducing inequality and resilient in normalizing wealth distribution as advantages, and susceptible to free riders as disadvantages. However, this disadvantage can be compensated for by fostering consensus and fellowship, and by complementing it with joint ventures. This study essentially presents the effectiveness of moral responsibility, the complementarity between the WE economy and the joint economy, and the direction of the economy toward reducing inequality. Future challenges are to develop the WE economy model based on real economic analysis and psychology, as well as to promote WE economy fieldwork for worker coops and platform cooperatives to realize a desirable mixbiotic society.

Current scientific fact-checking benchmarks exhibit several shortcomings, such as biases arising from crowd-sourced claims and an over-reliance on text-based evidence. We present SCITAB, a challenging evaluation dataset consisting of 1.2K expert-verified scientific claims that 1) originate from authentic scientific publications and 2) require compositional reasoning for verification. The claims are paired with evidence-containing scientific tables annotated with labels. Through extensive evaluations, we demonstrate that SCITAB poses a significant challenge to state-of-the-art models, including table-based pretraining models and large language models. All models except GPT-4 achieved performance barely above random guessing. Popular prompting techniques, such as Chain-of-Thought, do not achieve much performance gains on SCITAB. Our analysis uncovers several unique challenges posed by SCITAB, including table grounding, claim ambiguity, and compositional reasoning. Our codes and data are publicly available at https://github.com/XinyuanLu00/SciTab.

The Interval-valued intuitionistic fuzzy sets (IVIFSs) based on the intuitionistic fuzzy sets combines the classical decision method is in its research and application is attracting attention. After comparative analysis, there are multiple classical methods with IVIFSs information have been applied into many practical issues. In this paper, we extended the classical EDAS method based on cumulative prospect theory (CPT) considering the decision makers (DMs) psychological factor under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, the original EDAS method based on the CPT under IVIFSs (IVIF-CPT-MABAC) method is built for MAGDM issues. Meanwhile, information entropy method is used to evaluate the attribute weight. Finally, a numerical example for project selection of green technology venture capital has been given and some comparisons is used to illustrate advantages of IVIF-CPT-MABAC method and some comparison analysis and sensitivity analysis are applied to prove this new methods effectiveness and stability.

This paper provides a new tool for multi-attribute multi-objective group decision-making with unknown weights and attributes' weights. An interval-valued generalized orthogonal fuzzy group decision-making method is proposed based on the Yager operator and CRITIC-WASPAS method with unknown weights. The method integrates Yager operator, CRITIC, WASPAS, and interval value generalized orthogonal fuzzy group. Its merits lie in allowing decision-makers greater freedom, avoiding bias due to decision-makers' weight, and yielding accurate evaluation. The research includes: expanding the interval value generalized distance measurement method for comparison and application of similarity measurement and decision-making methods; developing a new scoring function for comparing the size of interval value generalized orthogonal fuzzy numbers,and further existing researches. The proposed interval-valued Yager weighted average operator (IVq-ROFYWA) and Yager weighted geometric average operator (IVq-ROFYWG) are used for information aggregation. The CRITIC-WASPAS combines the advantages of CRITIC and WASPAS, which not only work in the single decision but also serve as the basis of the group decision. The in-depth study of the decision-maker's weight matrix overcomes the shortcomings of taking the decision as a whole, and weighs the decision-maker's information aggregation. Finally, the group decision algorithm is used for hypertension risk management. The results are consistent with decision-makers' opinions. Practice and case analysis have proved the effectiveness of the method proposed in this paper. At the same time, it is compared with other operators and decision-making methods, which proves the method effective and feasible.

How to combine uncertain information from different sources has been a hot topic for years. However, with respect to ordinal quantum evidences contained in information, there is no any referable work which is able to provide a solution to this kind of problem. Besides, the method to dispel uncertainty of quantum information is still an open issue. Therefore, in this paper, a specially designed method is designed to provide an excellent method which improves the combination of ordinal quantum evidences reasonably and reduce the effects brought by uncertainty contained in quantum information simultaneously. Besides, some actual applications are provided to verify the correctness and validity of the proposed method.