EntropyPub Date : 2025-09-18DOI: 10.3390/e27090973
Sarra Manseri, Patrick Solé, Adel Alahmadi, Widyan Basaffar
{"title":"Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine.","authors":"Sarra Manseri, Patrick Solé, Adel Alahmadi, Widyan Basaffar","doi":"10.3390/e27090973","DOIUrl":"10.3390/e27090973","url":null,"abstract":"<p><p>We introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic-self-orthogonal and LCD ternary codes. We characterize right-symplectic ACD codes.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468440/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-18DOI: 10.3390/e27090970
Christopher G Davey, Paul B Badcock
{"title":"Disorder at the Synapse: How the Active Inference Framework Unifies Competing Perspectives on Depression.","authors":"Christopher G Davey, Paul B Badcock","doi":"10.3390/e27090970","DOIUrl":"10.3390/e27090970","url":null,"abstract":"<p><p>Depression is one of the most disabling of all disorders across the community, yet many aspects of the disorder remain contentious. Psychosocial and biological perspectives are often placed in opposition to one another, which in part reflects a failure of our explanatory frameworks. The active inference account of brain function breaks down this dualism, demonstrating that bodily processes are deeply integrated with the social world. It shows us that there is no contradiction in understanding depression as a product of the social environment at the same time as having a brain basis and manifesting in biological symptoms. From an active inference perspective, depression can be thought of as a synaptopathy: a disorder that arises from alterations to the excitatory-inhibitory balance enacted at the synapse, reflecting the interoceptive precision-weightings that have changed in the context of psychosocial instability. Therapies that alleviate depressive symptoms act at different levels of the active inference framework to re-weight precision estimates and the confidence we have in our predictions: this is true for psychotherapies, lifestyle interventions and antidepressant medications. Their effectiveness is often only partial, and while different treatment modalities can complement one another, there is a need for continued development of new and better treatment options.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469171/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-18DOI: 10.3390/e27090974
Ariel Elperin, Aryeh Kontorovich
{"title":"Bounded Variation Separates Weak and Strong Average Lipschitz.","authors":"Ariel Elperin, Aryeh Kontorovich","doi":"10.3390/e27090974","DOIUrl":"10.3390/e27090974","url":null,"abstract":"<p><p>We closely examine a recently introduced notion of average smoothness. The latter defined a <i>weak</i> and <i>strong</i> average-Lipschitz seminorm for real-valued functions on general metric spaces. Specializing to the standard metric on the real line, we compare these notions to bounded variation (BV) and discover that the weak notion is strictly weaker than BV while the strong notion is strictly stronger. Along the way, we discover that the weak average smooth class is also considerably larger in a certain combinatorial sense, which is made precise by the fat-shattering dimension.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468939/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multi-UAV-Assisted ISAC System: Joint User Association, Trajectory Design, and Resource Allocation.","authors":"Jinwei Wang, Renhui Xu, Laixian Peng, Xianglin Wei","doi":"10.3390/e27090967","DOIUrl":"10.3390/e27090967","url":null,"abstract":"<p><p>Unmanned aerial vehicle (UAV)-assisted integrated sensing and communication (ISAC) systems have developed rapidly in the sixth generation (6G) era. However, factors such as the mobility of ground users and malicious jamming pose significant challenges to systems' performance and reliability. Against this backdrop, this paper designs a multi-UAV-assisted ISAC system model under malicious jamming environments. Under the constraint of sensing accuracy, the total communication rate of the system is maximized through joint optimization of user association, UAV trajectory, and transmit power. The problem is then decomposed into three subproblems, which are solved using the improved auction algorithm (IAA), dream optimization algorithm (DOA), and rapidly-exploring random trees-based optimizer algorithm (RRTOA). The global optimal solution is approached through the alternating optimization-based predictive scheduling algorithm (AOPSA). Meanwhile, this paper also introduces a long short-term memory (LSTM) network to predict users' dynamic positions, addressing the impact of user mobility and enhancing the system's real-time performance. Simulation results show that compared with the baseline scheme, the proposed algorithm achieves a 188% improvement in communication rate, which verifies its effectiveness and superiority.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468963/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-17DOI: 10.3390/e27090966
Xin Tong, Ke Li, Xuesen Li
{"title":"Digital Economy and Green Development: Mechanisms of Action, Spillover Effects and Transmission Mechanisms.","authors":"Xin Tong, Ke Li, Xuesen Li","doi":"10.3390/e27090966","DOIUrl":"10.3390/e27090966","url":null,"abstract":"<p><p>The digital economy plays an important role in promoting green economic growth. This study evaluates the degree of green economic development generated by green innovation and green sharing based on data from 30 provinces in China from 2011 to 2022. An empirical analysis of the digital economy's influence on the growth of the green economy and its transmission mechanisms is performed. The analysis results demonstrate that the digital economy can significantly promote green economic development, encompassing improvements in both green innovation and green sharing, and exhibits a nonlinear \"increasing marginal effect\". The analysis of transmission channels reveals that, on one hand, the digital economy can promote green economic development by optimizing the allocation of data elements, while on the other, its impact is also influenced by the intensity of environmental regulations, exhibiting a threshold effect. Further heterogeneity analysis suggests that the promotional effect of the digital economy on green economic development is more pronounced in regions with high levels of economic development, a robust infrastructure, and strong policy support.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469043/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-17DOI: 10.3390/e27090968
Arno Keppens, Jean-Christopher Lambert
{"title":"Thermodynamics of Observations.","authors":"Arno Keppens, Jean-Christopher Lambert","doi":"10.3390/e27090968","DOIUrl":"10.3390/e27090968","url":null,"abstract":"<p><p>This work demonstrates that the four laws of classical thermodynamics apply to the statistics of symmetric observation distributions, and provides examples of how this can be exploited in uncertainty assessments. First, an expression for the partition function <i>Z</i> is derived. In contrast with general classical thermodynamics, however, this can be performed without the need for variational calculus, while <i>Z</i> also equals the number of observations <i>N</i> directly. Apart from the partition function Z≡N as a scaling factor, three state variables <i>m</i>, <i>n</i>, and ϵ fully statistically characterize the observation distribution, corresponding to its expectation value, degrees of freedom, and random error, respectively. Each term in the first law of thermodynamics is then shown to be a variation on δm2=δ(nϵ)2 for both canonical (constant <i>n</i> and ϵ) and macro-canonical (constant ϵ) observation ensembles, while micro-canonical ensembles correspond to a single observation result bin having δm2=0. This view enables the improved fitting and combining of observation distributions, capturing both measurand variability and measurement precision.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12470234/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Information Dynamics of the Mother-Fetus System Using Kolmogorov-Sinai Entropy Derived from Heart Sounds: A Longitudinal Study from Early Pregnancy to Postpartum.","authors":"Sayuri Ishiyama, Takashi Tahara, Hiroaki Iwanaga, Kazutomo Ohashi","doi":"10.3390/e27090969","DOIUrl":"10.3390/e27090969","url":null,"abstract":"<p><p>Kolmogorov-Sinai (KS) entropy is an indicator of the chaotic behavior of entire systems from an information-theoretic viewpoint. Here, we used KS entropy values derived from the heart sounds of four fetus-mother pairs to identify the changes in fetal and maternal informational patterns during the four phases of pregnancy (early, mid, late, and postnatal). Time-series data of the heart sounds were reconstructed in a five-dimensional phase space to obtain the Lyapunov spectrum, and KS entropy was calculated. Statistical analyses were then conducted separately for the fetus and mother for the four phases of pregnancy. The fetal KS entropy significantly increased from early pregnancy to the postnatal period (0.054 ± 0.007 vs. 0.097 ± 0.007; <i>p</i> < 0.001), whereas the maternal KS entropy decreased in late pregnancy and then significantly increased after birth (0.098 ± 0.002 vs. 0.133 ± 0.003; <i>p</i> < 0.001). The increase in KS entropy with the course of fetal gestation reflects an increase in information generation and adaptive capacity during the developmental process. Thus, changes in maternal KS entropy play a dual role, temporarily enhancing physiological stability to support fetal development and helping to rebuild the mother's own adaptive capacity in the postpartum period.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469049/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-16DOI: 10.3390/e27090961
Haihua Lu, Liang Yu, Yantao He, Liwei Tian
{"title":"SE-MSLC: Semantic Entropy-Driven Keyword Analysis and Multi-Stage Logical Combination Recall for Search Engine.","authors":"Haihua Lu, Liang Yu, Yantao He, Liwei Tian","doi":"10.3390/e27090961","DOIUrl":"10.3390/e27090961","url":null,"abstract":"<p><p>Information retrieval serves as a critical methodology for accurately and efficiently obtaining the required information from massive amounts of data. In this paper, we propose an information retrieval framework (SE-MSLC) that utilizes information theory to improve the retrieval effectiveness of inverted index retrieval, thus achieving higher-quality retrieval results in intelligent vertical domain search engines. First, we propose a semantic entropy-driven keyword importance analysis method (SE-KIA) in the query understanding module. This method combines search query logs, the corpus of the search engine, and the theory of semantic entropy, enabling the search engine to dynamically adjust the weights of query keywords, thereby improving its ability to recognize user intent. Then, we propose a hybrid recall strategy that combines a multi-stage strategy and a logical combination strategy (HRS-MSLC) in the recall module. It separately recalls the keywords obtained from the multi-granularity word segmentation of the query in the form of multi-queue recall and simultaneously considers the \"AND\" and \"OR\" logical relationships between the keywords. By systematically managing retrieval uncertainty and giving priority to the keywords with high information content, it achieves the best balance between the quantity of the retrieval results and the relevance of the retrieval results to the query. Finally, we experimentally evaluate our methods using the Hit Rate@K and case analysis. Our results demonstrate that the proposed method improves the Hit Rate@1 by 7.3% and the Hit Rate@3 by 6.6% while effectively solving the bad cases in our vertical domain search engine.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468705/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-16DOI: 10.3390/e27090962
Patrycja Hęćka, Wiktor Ejsmont, Marek Biernacki
{"title":"Healthcare Expenditure and COVID-19 in Europe: Correlation, Entropy, and Functional Data Analysis-Based Prediction of Hospitalizations and ICU Admissions.","authors":"Patrycja Hęćka, Wiktor Ejsmont, Marek Biernacki","doi":"10.3390/e27090962","DOIUrl":"10.3390/e27090962","url":null,"abstract":"<p><p>This article aims to analyze the correlation between healthcare expenditure per capita in 2021 and the sum of the number of hospitalized patients, ICU admissions, confirmed COVID-19 cases, and deaths in a selected period of time. The analysis covers 2017 (before the pandemic), 2021 (during the pandemic), and 2022/2023 (the initial post-pandemic recovery period). To assess the variability and stability of pandemic dynamics across countries, we compute Shannon entropy for hospitalization and ICU admission data. Additionally, we examine functional data on hospitalizations, ICU patients, confirmed cases, and deaths during a selected period of the COVID-19 pandemic in several European countries. To achieve this, we transform the data into smooth functions and apply principal component analysis along with a multiple function-on-function linear regression model to predict the number of hospitalizations and ICU patients.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469899/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2025-09-16DOI: 10.3390/e27090963
Debadrita Saha, Gregory D Scholes
{"title":"Multi-Dimensional Quantum-like Resources from Complex Synchronized Networks.","authors":"Debadrita Saha, Gregory D Scholes","doi":"10.3390/e27090963","DOIUrl":"10.3390/e27090963","url":null,"abstract":"<p><p>Recent publications have introduced the concept of quantum-like (QL) bits, along with their associated QL states and QL gate operations, which emerge from the dynamics of complex, synchronized networks. The present work extends these ideas to multi-level QL resources, referred to as QL dits, as higher-dimensional analogs of QL bits. We employ systems of <i>k</i>-regular graphs to construct QL-dits for arbitrary dimensions, where the emergent eigenspectrum of their adjacency matrices defines the QL-state space. The tensor product structure of multi-QL dit systems is realized through the Cartesian product of graphs. Furthermore, we examine the potential computational advantages of employing <i>d</i>-nary QL systems over two-level QL bit systems, particularly in terms of classical resource efficiency. Overall, this study generalizes the paradigm of using synchronized network dynamics for QL information processing to include higher-dimensional QL resources.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468949/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}