Defining science and demarcating it from pseudoscience are longstanding core issues in the philosophy of science.Hilbert’s traditional axiomatic standards(consistency,completeness,independence)struggle with modern co...Defining science and demarcating it from pseudoscience are longstanding core issues in the philosophy of science.Hilbert’s traditional axiomatic standards(consistency,completeness,independence)struggle with modern complex systems,while existing demarcation criteria like replicability and Popper’s falsificationism have practical limitations.Analyzing incompatibilities in complex systems,this paper proposes a revised framework:modified Hilbert axiomatic standards(clearly defined concepts,logical consistency,unrefuted axioms)and dynamic demarcation criteria.Abandoning unattainable traditional requirements of completeness and independence,it emphasizes conceptual clarity,openness,and progressiveness,offering an operational,self-consistent basis for judging scientificity.展开更多
In the light of a question of J. L. Krivine about the consistency of an extensional λ-theory,an extensional combinatory logic ECL+U(G)+RU_∞+ is established, with its consistency model provedtheoretically and it is s...In the light of a question of J. L. Krivine about the consistency of an extensional λ-theory,an extensional combinatory logic ECL+U(G)+RU_∞+ is established, with its consistency model provedtheoretically and it is shown the it is not equivalent to any system of universal axioms. It is expressed bythe theory in first order logic that, for every given group G of order n, there simultaneously exist infinitelymany universal retractions and a surjective n-tuple notion, such that each element of G acts as a permutationof the components of the n-tuple, and as an Ap-automorphism of the model; further each of the universalretractions is invarian under the action of the Ap-automorphisms induced by G The difference between thetheory and that of Krivine is the G need not be a symmetric group.展开更多
As one of essential multimedia in quantum networks, the copyright protection of quantum audio has gradually be- come an important issue in the domain of quantum information hiding in the decades. In this paper, an imp...As one of essential multimedia in quantum networks, the copyright protection of quantum audio has gradually be- come an important issue in the domain of quantum information hiding in the decades. In this paper, an improved quantum watermarking algorithm based on quantum audio by using least significant qubit （LSQb） modification is proposed. Com- pared with the previous achievements, it can effectively improve the robustness and security of watermark for copyright protection of quantum audio. In the new algorithm, the least significant bites and the peripheral least significant bits of the amplitudes are modified in terms of their logical consistency and correlation to enhance watermark robustness of resisting various illegal attacks. Furthermore, the new algorithm can avoid the weak robustness defect of many previous algorithms that directly embedded the watermark into the least significant bits. In order to implement the new algorithm, some spe- cific quantum circuits are designed to obtain better applicability and scalability for embedding and extracting watermark. Finally, the simulation results including the values of audio waveforms and signal to noise ratios （SNR） prove that the new algorithm has good transparency, robustness, and security.展开更多
基金supported by the start-up funding from Westlake University under Grant Number 041030150118 and the scientific research project of Westlake University“Theoretical Research and Demonstration Application of Complex Systems and Deep-Sea Technology(Phase I)”under Grant Number WU2025A006.
文摘Defining science and demarcating it from pseudoscience are longstanding core issues in the philosophy of science.Hilbert’s traditional axiomatic standards(consistency,completeness,independence)struggle with modern complex systems,while existing demarcation criteria like replicability and Popper’s falsificationism have practical limitations.Analyzing incompatibilities in complex systems,this paper proposes a revised framework:modified Hilbert axiomatic standards(clearly defined concepts,logical consistency,unrefuted axioms)and dynamic demarcation criteria.Abandoning unattainable traditional requirements of completeness and independence,it emphasizes conceptual clarity,openness,and progressiveness,offering an operational,self-consistent basis for judging scientificity.
基金a post-doctor grant of the Chinese Academy of Sciences.
文摘In the light of a question of J. L. Krivine about the consistency of an extensional λ-theory,an extensional combinatory logic ECL+U(G)+RU_∞+ is established, with its consistency model provedtheoretically and it is shown the it is not equivalent to any system of universal axioms. It is expressed bythe theory in first order logic that, for every given group G of order n, there simultaneously exist infinitelymany universal retractions and a surjective n-tuple notion, such that each element of G acts as a permutationof the components of the n-tuple, and as an Ap-automorphism of the model; further each of the universalretractions is invarian under the action of the Ap-automorphisms induced by G The difference between thetheory and that of Krivine is the G need not be a symmetric group.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61373131,61303039,61232016,and 61501247)Sichuan Youth Science and Technique Foundation,China(Grant No.2017JQ0048)+1 种基金NUIST Research Foundation for Talented Scholars of China(Grant No.2015r014)PAPD and CICAEET Funds of China
文摘As one of essential multimedia in quantum networks, the copyright protection of quantum audio has gradually be- come an important issue in the domain of quantum information hiding in the decades. In this paper, an improved quantum watermarking algorithm based on quantum audio by using least significant qubit （LSQb） modification is proposed. Com- pared with the previous achievements, it can effectively improve the robustness and security of watermark for copyright protection of quantum audio. In the new algorithm, the least significant bites and the peripheral least significant bits of the amplitudes are modified in terms of their logical consistency and correlation to enhance watermark robustness of resisting various illegal attacks. Furthermore, the new algorithm can avoid the weak robustness defect of many previous algorithms that directly embedded the watermark into the least significant bits. In order to implement the new algorithm, some spe- cific quantum circuits are designed to obtain better applicability and scalability for embedding and extracting watermark. Finally, the simulation results including the values of audio waveforms and signal to noise ratios （SNR） prove that the new algorithm has good transparency, robustness, and security.
