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Conspiracy beliefs (i.e. beliefs in specific conspiracy theories or the more general conspiracy mentality) are associated with a need for uniqueness and lower adherence to social norms. These findings suggest that conspiracy beliefs might be generally associated with less influence by majority opinions - absolutely and compared to minority opinions. In five experiments involving scenarios unrelated to conspiracy theories (overall N = 1669), participants were informed about the majority/minority opinion on a given issue (e.g. the building of a tunnel), afterward indicating their evaluation or voting intentions regarding the issue. We then tested whether the influence of a majority/minority opinion on evaluation or voting intentions is moderated by conspiracy beliefs. Across studies, we find no significant moderation. A meta-analysis confirms no correlation between conspiracy beliefs and susceptibility to majority influence. Taken together, our studies provide no evidence for the assumption that those holding conspiracy beliefs reject majority opinions per se.

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BACKGROUND AND OBJECTIVES: In this paper, we developed a significant class of control issues regulated by nonlinear fractal order systems with input and output signals, our goal is to design a direct transcription method with impulsive instant order. Recent advances in the artificial pancreas system provide an emerging treatment option for type 1 diabetes. The performance of the blood glucose regulation directly relies on the accuracy of the glucose-insulin modeling. This work leads to the monitoring and assessment of comprehensive type-1 diabetes mellitus for controller design of artificial panaceas for the precision of the glucose-insulin glucagon in finite time with Caputo fractional approach for three primary subsystems. METHODS: For the proposed model, we admire the qualitative analysis with equilibrium points lying in the feasible region. Model satisfied the biological feasibility with the Lipschitz criteria and linear growth is examined, considering positive solutions, boundedness and uniqueness at equilibrium points with Leray-Schauder results under time scale ideas. Within each subsystem, the virtual control input laws are derived by the application of input to state theorems and Ulam Hyers Rassias. RESULTS: Chaotic Relation of Glucose insulin glucagon compartmental in the feasible region and stable in finite time interval monitoring is derived through simulations that are stable and bounded in the feasible regions. Additionally, as blood glucose is the only measurable state variable, the unscented power-law kernel estimator appropriately takes into account the significant problem of estimating inaccessible state variables that are bound to significant values for the glucose-insulin system. The comparative results on the simulated patients suggest that the suggested controller strategy performs remarkably better than the compared methods. CONCLUSION: In the model under investigation, parametric uncertainties are identified since the glucose, insulin, and glucagon system's parameters are accurately measured numerically at different fractional order values. In terms of algorithm resilience and Caputo tracking in the presence of glucagon and insulin intake disturbance to maintain the glucose level. A comprehensive analysis of numerous difficult test issues is conducted in order to offer a thorough justification of the planned strategy to control the type 1 diabetes mellitus with designed the artificial pancreas.

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Stochastic delayed modeling has a significant non-pharmaceutical intervention to control transmission dynamics of infectious diseases and its results are close to the reality of nature. The covid-19 has been controlled globally but there is still a threat and appears in different variants like omicron and SARS-CoV-2 etc. globally. This article, considered pattern a mathematical model based on Susceptible, Infected, and recovered populations with highly nonlinear incidence rates. we studied the dynamics of the coronavirus model; a newly proposed version is a stochastic delayed model that is based on nonlinear stochastic delayed differential equations (SDDEs). Transition probabilities and parametric perturbation methods were used for the construction of the stochastic delayed model. The fundamental properties like positivity, boundedness, existence and uniqueness, and stability results of equilibria of the model with certain conditions of reproduction number are studied regularly. Also, the extinction and persistence of disease are studied with the help of well-known theorems. The numerical methods used to find a visualization of results due to the complexity of stochastic delayed differential equations. Furthermore, for computational analysis, we implemented existing methods in the literature and compared their results with the proposed method like nonstandard finite difference for stochastic delayed model. The proposed method restores all dynamical properties of the model with a free choice of time steps.

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In this study, the dynamic behavior of fractional order co-infection model with human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) is analyzed using operational matrix of Hermite wavelet collocation method. Also, the uniqueness and existence of solutions are calculated based on the fixed point hypothesis. For the fractional order co-infection model, its positivity and boundedness are demonstrated. Furthermore, different types of Ulam-Hyres stability are also discussed. The numerical solution of the model are obtained by using the operational matrix of the Hermite wavelet approach. This scheme is used to solve the system of nonlinear equations that are very fruitful and easy to implement. Additionally, the stability analysis of the numerical scheme is explained. The mathematical model taken in this work incorporates the biological characteristics of both HIV-1 and HTLV-I. After that all the equilibrium points of the fractional order co-infection model are found and their existence conditions are explored with the help of the Caputo derivative. The global stability of all equilibrium points of this model are determined with the help of Lyapunov functions and the LaSalle invariance principle. Convergence analysis is also discussed. Hermite wavelet operational matrix methods are more accurate and convergent than other numerical methods. Lastly, variations in model dynamics are found when examining different fractional order values. These findings will be valuable to biologists in the treatment of HIV-1/HTLV-I.

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For numerous viruses, their capsid assembly is composed of two steps. The first step is that virus structural protein monomers are polymerized to building blocks. Then, these building blocks are cumulative and efficiently assembled to virus capsid shell. These building block polymerization reactions in the first step are fundamental for virus assembly, and some drug targets were found in this step. In this work, we focused on the first step. Often, virus building blocks consisted of less than six monomers. That is, dimer, trimer, tetramer, pentamer, and hexamer. We presented mathematical models for polymerization chemical reactions of these five building blocks, respectively. Then, we proved the existence and uniqueness of the positive equilibrium solution for these mathematical models one by one. Subsequently, we also analyzed the stability of the equilibrium states, respectively. These results may provide further insight into property of virus building block polymerization chemical reactions in vivo.

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Recent studies indicate that differences in cognition among individuals may be partially attributed to unique brain wiring patterns. While functional connectivity (FC)-based fingerprinting has demonstrated high accuracy in identifying adults, early studies on neonates suggest that individualized FC signatures are absent. We posit that individual uniqueness is present in neonatal FC data and that conventional linear models fail to capture the rapid developmental trajectories characteristic of newborn brains. To explore this hypothesis, we employed a deep generative model, known as a variational autoencoder (VAE), leveraging two extensive public datasets: one comprising resting-state functional MRI (rs-fMRI) scans from 100 adults and the other from 464 neonates. VAE models trained on rs-fMRI from both adults and newborns produced superior age prediction performance (with r between predicted- and actual age ∼ 0.7) and individual identification accuracy (∼45 %) compared to models trained solely on adult or neonatal data. The VAE model also showed significantly higher individual identification accuracy than linear models (=10∼30 %). Importantly, the VAE differentiated connections reflecting age-related changes from those indicative of individual uniqueness, a distinction not possible with linear models. Moreover, we derived 20 latent variables, each corresponding to distinct patterns of cortical functional network (CFNs). These CFNs varied in their representation of brain maturation and individual signatures; notably, certain CFNs that failed to capture neurodevelopmental traits, in fact, exhibited individual signatures. CFNs associated with neonatal neurodevelopment predominantly encompassed unimodal regions such as visual and sensorimotor areas, whereas those linked to individual uniqueness spanned multimodal and transmodal brain regions. The VAE's capacity to extract features from rs-fMRI data beyond the capabilities of linear models positions it as a valuable tool for delineating cognitive traits inherent in rs-fMRI and exploring individualized imaging phenotypes.

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We consider the new boundary value problem for the generalized Boussinesq model of heat transfer under the inhomogeneous Dirichlet boundary condition for the velocity and under mixed boundary conditions for the temperature. It is assumed that the viscosity, thermal conductivity and buoyancy force in the model equations, as well as the heat exchange boundary coefficient, depend on the temperature. The mathematical apparatus for studying the inhomogeneous boundary value problem under study based on the variational method is being developed. Using this apparatus, we prove the main theorem on the global existence of a weak solution of the mentioned boundary value problem and establish sufficient conditions for the problem data ensuring the local uniqueness of the weak solution that has the additional property of smoothness with respect to temperature. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

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In this study, we explore a coupled system of fractional integro-differential equations with infinite delay and nonlocal conditions. This system encompasses classical derivatives of different orders and the fractional derivative of Caputo-Fabrizio type, as well as the fractional integral of the q -Riemann-Liouville operator. We introduce a novel definition of the Caputo and Fabrizio differential operators, enhancing the mathematical formulation. Our main focus is to investigate the system's fundamental properties, including existence, uniqueness, and continuous dependence. Through rigorous mathematical analysis, we establish the existence and uniqueness of solutions and examine how small perturbations in initial conditions or parameters impact the solutions. For the numerical aspect, we use the finite-trapezoidal approach, a reliable method for solving fractional integro-differential equations. We provide a concise explanation of the approach and demonstrate its effectiveness through two numerical examples. Overall, this comprehensive study contributes to the understanding of coupled systems with fractional derivatives and infinite delays, with implications for various scientific and engineering fields.

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Knowledge about how ecological networks vary across global scales is currently limited given the complexity of acquiring repeated spatial data for species interactions. Yet, recent developments in metawebs highlight efficient ways to first document possible interactions within regional species pools. Downscaling metawebs towards local network predictions is a promising approach to using the current data to investigate the variation of networks across space. However, issues remain in how to represent the spatial variability and uncertainty of species interactions, especially for large-scale food webs. Here, we present a probabilistic framework to downscale a metaweb based on the Canadian mammal metaweb and species occurrences from global databases. We investigated how our approach can be used to represent the variability of networks and communities between ecoregions in Canada. Species richness and interactions followed a similar latitudinal gradient across ecoregions but simultaneously identified contrasting diversity hotspots. Network motifs revealed additional areas of variation in network structure compared with species richness and number of links. Our method offers the potential to bring global predictions down to a more actionable local scale, and increases the diversity of ecological networks that can be projected in space. This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.

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INTRODUCTION: Semantic fluency is the ability to name items from a given category within a limited time, which relies on semantic knowledge, working memory, and executive function. Similar to patients with Parkinson's disease (PD), patients with progressive supranuclear palsy (PSP) scored lower than healthy adults in the well-established semantic fluency test. However, it is unclear how unique are the produced words. This study examined the relationship between semantic fluency and words' uniqueness in patients with PSP. METHODS: Twenty-seven patients with PSP Richardson's syndrome (PSP-RS), 37 patients with PD, and 41 healthy controls (HC) performed a standard semantic fluency test (animals), and their verbal responses were audio-recorded. We used the uniqueness to reflect the ability to produce both original and effective work, that is, creativity. RESULTS: The PSP-RS group produced fewer correct words and fewer unique words than the PD and HC groups. Moreover, the correlation between fluency and uniqueness was positive in the HC and PD groups but negative in the PSP-RS group. Importantly, the actual levodopa dose was positively correlated with the fluency but negatively correlated with the uniqueness in PSP-RS. The PSP-RS patients who took a greater dose of levodopa tended to produce more correct words but fewer unique words. CONCLUSIONS: These results suggested that levodopa may modulate semantic fluency and uniqueness in the early stages of PSP-RS.

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A comprehensive mathematical model is proposed to study two strains of dengue virus with saturated incidence rates and quarantine measures. Imperfect dengue vaccination is also assumed in the model. Existence, uniqueness and stability of the proposed model are proved using the results from fixed point and degree theory. Additionally, well constructed Lyapunov function candidates are also applied to prove the global stability of infection-free equilibria. It is also demonstrated that the model is generalized Ulam-Hyers stable under some appropriate conditions. The model is fitted to the real data of dengue epidemic taken from the city of Espirito Santo in Brazil. For the approximate solution of the model, a non-standard finite difference(NSFD) approach is applied. Sensitivity analysis is also carried out to show the influence of different parameters involved in the model. The behaviour of the NSFD is also assessed under different denominator functions and it is observed that the choice of the denominator function could influence the solution trajectories. Different scenario analysis are also assessed when the reproduction number is below or above one. Furthermore, simulations are also presented to assess the epidemiological impact of dengue vaccination and quarantine measures for infected individuals.

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To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as " R 0 ", to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.

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As a motivational factor, uniqueness drives individuals to seek and choose unique goods or experiences. The act of wearing masks obscures individuals' facial features and influences their desire for uniqueness. This study aims to explore how wearing masks promotes individual uniqueness- seeking behavior. Three experiments were performed using various product categories (Starbucks coffee cups, sweatshirts, suitcases, and baseball caps) and sample types (college student and adult samples). Experiment results show that wearing masks obscures individuals' facial features and weakens their self- perceived uniqueness, thereby increasing their willingness to actively purchase unique products. This study is the first to examine the effect of wearing masks on individuals' choice of unique products. Practically, the results suggest that customized products can compensate for the lack of self-perceived uniqueness brought about by facial occlusion, thus providing valuable guidance for companies and retailers that offer customized services in formulating and designing marketing strategies.

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In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.

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This work chiefly explores fractional-order octonion-valued neural networks involving delays. We decompose the considered fractional-order delayed octonion-valued neural networks into equivalent real-valued systems via Cayley-Dickson construction. By virtue of Lipschitz condition, we prove that the solution of the considered fractional-order delayed octonion-valued neural networks exists and is unique. By constructing a fairish function, we confirm that the solution of the involved fractional-order delayed octonion-valued neural networks is bounded. Applying the stability theory and basic bifurcation knowledge of fractional order differential equations, we set up a sufficient condition remaining the stability behaviour and the appearance of Hopf bifurcation for the addressed fractional-order delayed octonion-valued neural networks. To illustrate the justifiability of the derived theoretical results clearly, we give the related simulation results to support these facts. Simultaneously, the bifurcation plots are also displayed. The established theoretical results in this work have important guiding significance in devising and improving neural networks.

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Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh-Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if R 0 < 1 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

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Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.

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Cryptosporidium spp. are important diarrhea-associated pathogens in humans and livestock. Among the known species, Cryptosporidium xiaoi, which causes cryptosporidiosis in sheep and goats, was previously recognized as a genotype of the bovine-specific Cryptosporidium bovis based on their high sequence identity in the ssrRNA gene. However, the lack of genomic data has limited characterization of the genetic differences between the two closely related species. In this study, we sequenced the genomes of two C. xiaoi isolates and performed comparative genomic analysis to identify the sequence uniqueness of this ovine-adapted species compared with other Cryptosporidium spp. Our results showed that C. xiaoi is genetically related to C. bovis as shown by their 95.8% genomic identity and similar gene content. Consistent with this, both C. xiaoi and C. bovis appear to have fewer genes encoding mitochondrial metabolic enzymes and invasion-related protein families. However, they appear to possess several species-specific genes. Further analysis indicates that the sequence differences between these two Cryptosporidium spp. are mainly in 24 highly polymorphic genes, half of which are located in the subtelomeric regions. Some of these subtelomeric genes encode secretory proteins that have undergone positive selection. In addition, the genomes of two C. xiaoi isolates, identified as subtypes XXIIIf and XXIIIh, share 99.9% nucleotide sequence identity, with six highly divergent genes encoding putative secretory proteins. Therefore, these species-specific genes and sequence polymorphism in subtelomeric genes probably contribute to the different host preference of C. xiaoi and C. bovis.

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In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal-fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal-fractional alcohol addiction model are shown using the Picard-Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam-Hyers coupled with the Ulam-Hyers-Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community.

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