Mathematics curriculums at most universities tend to perpetuate a belief that higher mathematics is historically and culturally European. First Nations and minority students may not see their identities and cultures reflected in the discipline, yet university mathematics educators are keen to diversify and broaden the appeal of their courses. This article presents an investigation on the mathematics of smoke telegraphy, as a contribution to inlaying cross-cultural mathematical heritage in the curriculum. Across Indigenous societies of Australia the technology and practice of smoke telegraphy was developed to a sophisticated level over millennia to fill a need for long-distance communications. Through an original bibliographic and archival analysis, we show that smoke signalling and telegraphy used empirical mathematics of symmetries, frequency coding, and understanding of fluid dynamics. We juxtapose this applied mathematical knowledge, within context, against the timeline of Western understanding and development of these strands of mathematics.
The exact dynamics of a model consisting of two identical qubits interacting non-resonantly with the electromagnetic field mode of an ideal resonator via single-photon transitions is found in the presence of direct Ising interaction of qubits. The exact solution is used to calculate the two-qubit negativity of qubits in the case of a coherent initial state of qubits and a thermal state of the resonator field. It is shown that in the case of resonant interaction of qubits with the field, the initial atomic coherence leads to a significant increase in the maximum degree of entanglement. The inclusion of direct Ising interaction of qubits can significantly enhance the entanglement of qubits in both coherent and non-coherent initial states of qubits. In the case of non-resonant interaction of qubits and the resonator field, the detuning leads to a weakening of the effect of atomic coherence on the dynamics of qubit entanglement.
Abdulrahman M. Abdulghani, Azizol Abdullah, A. R. Rahiman
et al.
Modern Software-Defined Wide Area Networks (SD-WANs) require adaptive controller placement addressing multi-objective optimization where latency minimization, load balancing, and fault tolerance must be simultaneously optimized. Traditional static approaches fail under dynamic network conditions with evolving traffic patterns and topology changes. This paper presents a novel hybrid framework integrating Gaussian Mixture Model (GMM) clustering with Multi-Agent Reinforcement Learning (MARL) for dynamic controller placement. The approach leverages probabilistic clustering for intelligent MARL initialization, reducing exploration requirements. Centralized Training with Decentralized Execution (CTDE) enables distributed optimization through cooperative agents. Experimental evaluation using real-world topologies demonstrates a noticeable reduction in the latency, improvement in network balance, and significant computational efficiency versus existing methods. Dynamic adaptation experiments confirm superior scalability during network changes. The hybrid architecture achieves linear scalability through problem decomposition while maintaining real-time responsiveness, establishing practical viability.
ABSTRACT This paper proposes a controlled signal technique for visible light non‐orthogonal multiple access (VL‐NOMA) communication in an interference‐controlled environment with intelligent reflecting surfaces (IRS) for beyond 5G (B5G) and 6G communication networks. The light‐emitting diode (LED) is used for carrier signal generation to transmit signals to the two users (photodiodes, PDs) due to its advantages, such as its programmable nature and flexibility. The potential challenge is how the signals could be controlled with an IRS approach, which prompted this research. We have used IRS, which is a cutting‐edge enabling technology that modifies the signal's reflection by utilizing numerous inexpensive passive reflecting elements to improve the signal's performance. Furthermore, deep reinforcement learning (DRL) is deployed to control the reflected signals, simulate, make decisions, and link LED‐IRS‐PDs, redirecting the signals. The entire system is successfully synchronized, and then the bit error rate (BER), line of sight (LOS), and non‐line of sight (NLOS) performances are investigated. Furthermore, we place a blocker at the center of the model as a NLOS to check how the transmitted signals will perform. We observed that the propagated signal improved the BER as per LOS, hence, the NLOS blocker reduced the signal's performance. Furthermore, we optimized the signals to investigate BER, LOS, and NLOS signal performance. We observed that LOS signals performed better than NLOS signals.
Background Dehydration secondary to diarrhoea is a major cause of hospitalization and mortality in children aged less than five years. Most diarrhoea cases in childhood are caused by rotavirus, and routine introduction of rotavirus vaccine is expected to reduce the incidence and severity of dehydration secondary to diarrhoea in vaccinated infants. Previously, studies have examined changes in admissions with stools positive for rotavirus but this study reports on all admissions with dehydration secondary to diarrhoea regardless of stool rotavirus results. We aimed to assess the changes in all-cause severe diarrhoea and dehydration (DAD) admissions following the vaccine’s introduction. Methods We examined changes in admissions of all clinical cases of DAD before and after introduction of routine vaccination with rotavirus vaccine in July 2014 in Kenya. We use data from 13 public hospitals currently involved in a clinical network, the Clinical Information Network (CIN). Routinely collected data for children aged 2-36 months were examined. We used a segmented mixed effects model to assess changes in the burden of diarrhoea and dehydration after introduction of rotavirus vaccine. For sensitivity analysis, we examined trends for non-febrile admissions (surgical or burns). Results There were 17,708 patients classified as having both diarrhoea and dehydration. Average monthly admissions due to DAD for each hospital before vaccine introduction (July 2014) was 35 (standard deviation: ±22) and 17 (standard deviation: ±12) after vaccine introduction. Segmented mixed effects regression model showed there was a 33% (95% CI, 30% to 38%) decrease in DAD admissions immediately after the vaccine was introduced to the Kenya immunization program in July 2014. There was no change in admissions due to non-febrile admissions pre-and post-vaccine introduction. Conclusion The rotavirus vaccine, after introduction into the Kenya routine immunization program resulted in reduction of all-cause admissions of diarrhoea and dehydration in children to public hospitals.
This article is the first in an occasional series for the Australian Mathematical Society Gazette on diverse aspects and topics of Indigenous mathematical knowledge. This is an important, but neglected, part of the mathematical heritage of humankind, and as such is the concern of the mathematics community as a whole. It is hoped that this and future articles may help to inspire mathematics researchers, students, and educators at tertiary and school levels who are seeking to widen their mathematical horizons and develop course and research materials of broad cultural relevance. I would like to honour the Mithaka peoples of the Kurrawoolben and Kirrenderri (Diamantina) and Nooroondinna (Georgina) river channel country of south-western Qld, Australia. The material in this article does not involve culturally restricted knowledge or images, and is shared with respect for the Mithaka ancestors and their descendants.
Abstract Background Diabetic nephropathy (DN) is a major microvascular complication of diabetes and has become the leading cause of end-stage renal disease worldwide. A considerable number of DN patients have experienced irreversible end-stage renal disease progression due to the inability to diagnose the disease early. Therefore, reliable biomarkers that are helpful for early diagnosis and treatment are identified. The migration of immune cells to the kidney is considered to be a key step in the progression of DN-related vascular injury. Therefore, finding markers in this process may be more helpful for the early diagnosis and progression prediction of DN. Methods The gene chip data were retrieved from the GEO database using the search term ' diabetic nephropathy ‘. The ' limma ' software package was used to identify differentially expressed genes (DEGs) between DN and control samples. Gene set enrichment analysis (GSEA) was performed on genes obtained from the molecular characteristic database (MSigDB. The R package ‘WGCNA’ was used to identify gene modules associated with tubulointerstitial injury in DN, and it was crossed with immune-related DEGs to identify target genes. Gene ontology (GO) enrichment analysis and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis were performed on differentially expressed genes using the ‘ClusterProfiler’ software package in R. Three methods, least absolute shrinkage and selection operator (LASSO), support vector machine recursive feature elimination (SVM-RFE) and random forest (RF), were used to select immune-related biomarkers for diagnosis. We retrieved the tubulointerstitial dataset from the Nephroseq database to construct an external validation dataset. Unsupervised clustering analysis of the expression levels of immune-related biomarkers was performed using the ‘ConsensusClusterPlus ‘R software package. The urine of patients who visited Dongzhimen Hospital of Beijing University of Chinese Medicine from September 2021 to March 2023 was collected, and Elisa was used to detect the mRNA expression level of immune-related biomarkers in urine. Pearson correlation analysis was used to detect the effect of immune-related biomarker expression on renal function in DN patients. Results Four microarray datasets from the GEO database are included in the analysis : GSE30122, GSE47185, GSE99340 and GSE104954. These datasets included 63 DN patients and 55 healthy controls. A total of 9415 genes were detected in the data set. We found 153 differentially expressed immune-related genes, of which 112 genes were up-regulated, 41 genes were down-regulated, and 119 overlapping genes were identified. GO analysis showed that they were involved in various biological processes including leukocyte-mediated immunity. KEGG analysis showed that these target genes were mainly involved in the formation of phagosomes in Staphylococcus aureus infection. Among these 119 overlapping genes, machine learning results identified AGR2, CCR2, CEBPD, CISH, CX3CR1, DEFB1 and FSTL1 as potential tubulointerstitial immune-related biomarkers. External validation suggested that the above markers showed diagnostic efficacy in distinguishing DN patients from healthy controls. Clinical studies have shown that the expression of AGR2, CX3CR1 and FSTL1 in urine samples of DN patients is negatively correlated with GFR, the expression of CX3CR1 and FSTL1 in urine samples of DN is positively correlated with serum creatinine, while the expression of DEFB1 in urine samples of DN is negatively correlated with serum creatinine. In addition, the expression of CX3CR1 in DN urine samples was positively correlated with proteinuria, while the expression of DEFB1 in DN urine samples was negatively correlated with proteinuria. Finally, according to the level of proteinuria, DN patients were divided into nephrotic proteinuria group (n = 24) and subrenal proteinuria group. There were significant differences in urinary AGR2, CCR2 and DEFB1 between the two groups by unpaired t test (P < 0.05). Conclusions Our study provides new insights into the role of immune-related biomarkers in DN tubulointerstitial injury and provides potential targets for early diagnosis and treatment of DN patients. Seven different genes ( AGR2, CCR2, CEBPD, CISH, CX3CR1, DEFB1, FSTL1 ), as promising sensitive biomarkers, may affect the progression of DN by regulating immune inflammatory response. However, further comprehensive studies are needed to fully understand their exact molecular mechanisms and functional pathways in DN.
Computer applications to medicine. Medical informatics, Analysis
Automated verification has become an essential part in the security evaluation of cryptographic protocols. In this context privacy-type properties are often modelled by indistinguishability statements, expressed as behavioural equivalences in a process calculus. In this paper we contribute both to the theory and practice of this verification problem. We establish new complexity results for static equivalence, trace equivalence and labelled bisimilarity and provide a decision procedure for these equivalences in the case of a bounded number of protocol sessions. Our procedure is the first to decide trace equivalence and labelled bisimilarity exactly for a large variety of cryptographic primitives -- those that can be represented by a subterm convergent destructor rewrite system. We also implemented the procedure in a new tool, DeepSec. We showed through extensive experiments that it is significantly more efficient than other similar tools, while at the same time raises the scope of the protocols that can be analysed.
This paper is concerned with the existence and multiplicity of monotone positive solutions for a class of nonlinear fractional differential equation with a disturbance parameter in the integral boundary conditions on the infinite interval. By using Guo–Krasnosel’skii fixed-point theorem and the analytic technique, we divide the range of parameter for the existence of at least two, one and no positive solutions for the problem. In the end, an example is given to illustrate our main results.
Josenaide Alves da Silva, Geilsa Costa Santos Baptista, Nataélia Alves da Silva
A pesquisa é qualitativa e o objetivo propõe a análise da comunicação dos licenciandos para desenvolvimento de um ensino intercultural em aulas de ciências. Os envolvidos no trabalho foram dois licenciandos do curso de Ciências Agrárias, do Instituto Federal de Educação, Ciências e Tecnologia Baiano, do campus de Senhor do Bonfim-BA. Para coleta de dados, utilizou-se gravações em vídeos, procedendo a Análise de Conteúdo e a Estrutura de análise das classes comunicativas, para analisá-los. Este artigo apresenta resultados sobre as análises das aulas de ciências dos licenciandos, as quais direcionaram para o desenvolvimento da abordagem comunicativa dialógica, incluindo os saberes socioculturais dos estudantes e os saberes científicos, a partir de uma relação entre essas formas de conhecer. Considera-se que a abordagem comunicativa dialógica é um alicerce para os licenciandos ministrarem a prática de ciências contextualizada.
Special aspects of education, Applied mathematics. Quantitative methods
Abstract The aromatic compounds having structural configurations with two or more fused benzene rings are the polycyclic aromatic hydrocarbons (PAHs). Topological indices are valuable tools for studying the structure property relationships of PAHs and also helps in predicting various properties and activities. They find applications widely in computational chemistry, drug design and QSPR studies. This article focuses on analysing the potential predictive index for Sombor index (SO), elliptic Sombor index (ESO), Euler Sombor index (EU), reverse Sombor index (RSO), reverse elliptic Sombor index (RESO) and reverse Euler Sombor index (REU) using regression models for top priority 38 PAHs. From the study it is evident that, SO and RSO have proved to be potential predictive indices among the considered degree-based and reverse degree-based indices. The variation of best predictive index with minimal RMSE are plotted for linear, quadratic and cubic regression models for better understanding.
The ‘black box’ nature of machine learning (ML) approaches makes it challenging to understand how most artificial intelligence (AI) models make decisions. Explainable AI (XAI) aims to provide analytical techniques to understand the behavior of ML models. XAI utilizes counterfactual explanations that indicate how variations in input features lead to different outputs. However, existing methods must also highlight the importance of features to provide more actionable explanations that would aid in the identification of key drivers behind model decisions—and, hence, more reliable interpretations—ensuring better accuracy. The method we propose utilizes feature weights obtained through adaptive feature weight genetic explanation (AFWGE) with the Pearson correlation coefficient (PCC) to determine the most crucial group of features. The proposed method was tested on four real datasets with nine different classifiers for evaluation against a nonweighted counterfactual explanation method (CERTIFAI) and the original feature values’ correlation. The results show significant enhancements in accuracy, precision, recall, and F1 score for most datasets and classifiers; this indicates the superiority of the feature weights selected via AFWGE with the PCC over CERTIFAI and the original data values in determining the most important group of features. Focusing on important feature groups elaborates the behavior of AI models and enhances decision making, resulting in more reliable AI systems.
We extend Stone duality to a fully faithful embedding of condensed sets into fpqc sheaves over an arbitrary field, which preserves colimits and finite limits. We study how familiar notions from condensed mathematics/topology and algebraic geometry correspond to each other under this form of Stone duality.
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We show that Kähler manifolds provide many computable examples and we emphasize those whose Bergman kernel is constant along the diagonal.
This paper presents a mathematical model for determining the movement of the bearing in an internal gear pump. The paper also performs simulation calculations to find the movement trajectory of the shaft with the given input data.
Evgeniy Savelyev, Andrey Akhmatkhanov, Boris Slautin
et al.
The paper presents the results of an experimental study of the local polarization reversal and creation of domains by a biased tip of scanning probe microscope (SPM) in lithium niobate single crystals of congruent composition with a surface layer modified by soft proton exchange (SPE). The depth dependence of H[Formula: see text] ions concentration in the SPE-modified layer measured by confocal Raman microscopy demonstrates a sufficient composition gradient. The creation of isolated domains and stripe domain structures has been done by two switching modes: (1) point switching by field application in separated points and (2) line scanning switching by motion of the biased tip being in contact with the sample surface. For point switching for pulse durations less than 10[Formula: see text]s, the logarithmic dependence of the domain diameter on the pulse duration was observed. The change of the dependence to a linear one for pulse duration above 10[Formula: see text]s has been attributed to the transition from the stochastic step generation at the domain wall to the deterministic one at the domain vertexes. The periodical structure of stripe domains was created in SPE CLN planar waveguides by scanning at elevated temperature. The revealed switching regime suppresses electrostatic interaction of neighboring domains and leads to a significant improvement of the domain structure regularity. The creation of the stable periodical domain structure with submicron periods in SPE CLN planar waveguides was demonstrated.
The aim of this paper is to study new exact solutions Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) equation. We use modified tanh method along associated with new Ricatti equation. The results are demonstrated for specific values of parameters, which show periodic singular as well as nonsingular solitons for specific values of parameters. Some solutions are plotted and presented in 3D and density graphs. The Mathematica are used for computation and simulations of the results, respectively.