Search Results (37)

Fractional differential equations offer a natural framework for describing systems in which present states are influenced by the past. This work presents a nonlinear Caputo-type fractional differential equation (FDE) with a nonlocal initial condition and attempts to describe a model of memory-dependent behavioral adaptation. The proposed framework uses a fractional-order derivative $\eta \in (0,1)$ to discuss the long-term memory effects. The existence and uniqueness of solutions are demonstrated by Banach’s and Krasnoselskii’s fixed-point theorems. Stability is analyzed through Ulam–Hyers and Ulam–Hyers–Rassias benchmarks, supported by sensitivity results on the kernel structure and fractional order. The model is further employed for behavioral despair and learned helplessness, capturing the role of delayed stimulus feedback in shaping cognitive adaptation. Numerical simulations based on the convolution-based fractional linear multistep (FVI–CQ) and Adams–Bashforth–Moulton (ABM) schemes confirm convergence and accuracy. The proposed setup provides a compact computational and mathematical paradigm for analyzing systems characterized by nonlocal feedback and persistent memory. Full article

Motion perception is a fundamental function of the tactile system, essential for object exploration and manipulation. While human studies have largely focused on discrete or pulsed stimuli with staggered onsets, many natural tactile signals are continuous and rhythmically patterned. Here, we investigate whether phase differences between “simultaneously” presented, “continuous” amplitude-modulated vibrations can induce the perception of motion across fingertips. Participants reliably perceived motion direction at modulation frequencies up to 1 Hz, with discrimination performance systematically dependent on the phase lag between vibrations. Critically, trial-level confidence reports revealed the lowest certainty for anti-phase (180°) conditions, consistent with stimulus ambiguity as predicted by the mathematical framework. I propose two candidate computational mechanisms for tactile motion processing. The first is a conventional cross-correlation computation over the envelopes; the second is a probabilistic model based on the uncertain detection of temporal reference points (e.g., envelope peaks) within threshold-defined windows. This model, despite having only a single parameter (uncertainty width determined by an amplitude discrimination threshold), accounts for both the non-linear shape and asymmetries of observed psychometric functions. These results demonstrate that the human tactile system can extract directional information from distributed phase-coded signals in the absence of spatial displacement, revealing a motion perception mechanism that parallels arthropod systems but potentially arises from distinct perceptual constraints. The findings underscore the feasibility of sparse, phase-coded stimulation as a lightweight and reproducible method for conveying motion cues in wearable, motion-capable haptic devices. Full article

Knowledge visualization has gained significant research attention for its potential to facilitate knowledge construction through interactive graphics while minimizing cognitive load during information processing. However, limited research has examined the integration of knowledge visualization within highly interactive mixed-reality environments and its effects on user experiences and science, technology, engineering, and mathematics (STEM) sustainability. Drawing on the cognitive-affective model of immersive learning, this study investigates how learners’ user experiences, elicited by mixed-reality features and usability, influence their sustainable engagement with STEM learning through knowledge-visualization tools framed within the stimulus–organism–response model. A novel mixed-reality learning system was developed, with the user interface designed using concept maps to graphically visualize concept nodes and their interconnected relationships. A total of 136 learners from two high schools in China participated in an experiment on frictional physics using this novel system. Using structural equation modeling, the collected data were analyzed with partial least squares. The findings demonstrate that mixed-reality features of knowledge visualization (featured by 3D graphics, interface design, and operational functions), as well as usability (featured by the perceived usefulness of the concept map, perceived ease of use, and perceived usefulness of the system), have positive significant impacts on user experience (represented by satisfaction, perceived enjoyment, and attitude). Subsequently, positive user experiences have positive significant impacts on learners’ sustained intention to engage with STEM education. Further mediating analysis provides empirical evidence that positive user experiences, acting as a psychological enabler, mediate the relationship between system design and behavioral intention. The research model explains 65.2% of the variance for system usability, 53.4% for satisfaction, 51.5% for perceived enjoyment, 54.9% for attitude, and 63.2% for continuance intention. By fostering positive user experiences in STEM learning, this study offers valuable insights for educators and practitioners seeking to implement effective interactive knowledge visualizations to support sustainable STEM education and immersive learning. Full article

This study investigates the dual dynamics of investment shocks and policy responses in stabilizing South Korea’s macroeconomy during the COVID-19 pandemic, utilizing a Bayesian DSGE framework. The model integrates sophisticated mathematical components, including stochastic differential equations, Bayesian inference, and impulse response functions, to analyze the transmission mechanisms of investment shocks and the relative efficacy of fiscal and monetary interventions. The estimation is conducted through Markov Chain Monte Carlo simulations. Using data from the first quarter of 2020 to the first quarter of 2023, the analysis quantifies the pandemic-induced shocks’ impact on critical macroeconomic indicators, including enterprise output, household consumption, employment, and investment. The findings reveal that heightened investment costs significantly constrained economic performance, with fiscal measures, such as increased government spending and targeted stimulus packages, demonstrating superior stabilization effects compared to monetary interventions. These results emphasize the importance of well-coordinated policy responses in mitigating economic disruptions and enhancing resilience during crises. This study not only provides novel insights into the mathematical modeling of economic stabilization strategies but also offers actionable recommendations for policymakers navigating pandemic-induced challenges. Full article

A deficit in short-term memory (STM) functions characterizes many neurodevelopmental disorders, in particular, specific learning disorders. Hence, there is a need to develop a web-based platform capable of testing specific variables and administration conditions in a controlled manner. The platform herein presented allows for the assessment of short-term memory (STM) items and order components in a series of different conditions. Stimulus types, presentation, and response modalities were appropriately selected to assess the impact of those variables on memory performances. The usefulness of such a systematic, fine-grained analysis of STM functions was tested by applying the complete assessment in a group of 100 school-age children (47 Typically Developing children and 53 children with learning disorders) and evaluating the capacity of the software to highlight different specific memory processes activated during reading, writing, and calculation. A cluster analysis was applied to the learning performances of the whole group, and a four-cluster solution representing the best division into subgroups of learning disorders (affecting reading, writing, and mathematical skills, variously combined) also showed clear-cut differences in the children’s STM profiles. This confirms the potential and the usefulness of the tool for the characterization of STM in school-age children. Full article

Large amounts of livestock manure production in Bangladesh have created a challenge to the environment by increasing greenhouse gas (GHG) emissions and eutrophication potential (EP) risk. Though some studies have identified the impact of manure on emissions, the consequences of manure exploitation on water bodies are very rare. This study investigated the effects of livestock manure on both air and water environments in the regional context of Bangladesh. Mathematical equations were used to assess manure generation, GHG emissions, manure leach-out amount, EP, and geographic information system (GIS) spatial analysis tools were applied to visualize the outcomes of the research. Between 1990 and 2020, the GHG emissions increased from 7451.26 to 13,244.45 kilotons CO₂eq, and the amount of manure leach-out to water also increased from 236.49 to 493.75 kilotons over these 30 years of time. In 2023, the study demonstrated that approximately 216.97 million tons of livestock manure were produced in Bangladesh, which accounted for a total GHG emission of 16.61 million tons CO₂eq, and about 62.19 million tons of manure leached out to water, which has a total EP of 295.22 kg N-eq/ha/year. This study offers regional pattern emission intensity and eutrophication-susceptible area maps, which indicate the stimulus of livestock manure across Bangladesh. A long-term impact study, distinctive map formation, and eutrophication susceptibility analysis will be helpful for implementing specific policies and strategies to improve the environment of the livestock sector in Bangladesh. Full article

Magnetic scaffolds (MagSs) are magneto-responsive devices obtained by the combination of traditional biomaterials (e.g., polymers, bioceramics, and bioglasses) and magnetic nanoparticles. This work analyzes the literature about MagSs used as drug delivery systems for tissue repair and cancer treatment. These devices can be used as innovative drugs and/or biomolecules delivery systems. Through the application of a static or dynamic stimulus, MagSs can trigger drug release in a controlled and remote way. However, most of MagSs used as drug delivery systems are not optimized and properly modeled, causing a local inhomogeneous distribution of the drug’s concentration and burst release. Few physical–mathematical models have been presented to study and analyze different MagSs, with the lack of a systematic vision. In this work, we propose a modeling framework. We modeled the experimental data of drug release from different MagSs, under various magnetic field types, taken from the literature. The data were fitted to a modified Gompertz equation and to the Korsmeyer–Peppas model (KPM). The correlation coefficient ($R^2$) and the root mean square error (RMSE) were the figures of merit used to evaluate the fitting quality. It has been found that the Gompertz model can fit most of the drug delivery cases, with an average RMSE below 0.01 and $R^2>0.9$. This quantitative interpretation of existing experimental data can foster the design and use of MagSs for drug delivery applications. Full article

Flash converters are suitable analog-to-digital converter architectures for high-speed applications. However, the benefits in terms of the frequency of smaller technology nodes are hampered by variability, which necessitates the use of large transistors. Comparator redundancy was introduced to overcome this trade-off; the best comparators were selected upfront (either at start-up or in the factory), and the unused comparators could be switched off. This work studies the possibility of performing comparator selection in the background concurrently with normal conversion to increase the converter lifetime. Thus, the system can automatically recover its performance from drifts or failures due to aging, temperature, etc. This paper proposes an embedded solution that includes a calibration stimulus generator (which only requires some external passive elements) and develops system design requirements. In addition, mathematical equations and error sensitivities of the system elements were derived. A 6b flash converter is implemented in UMC180nm technology, and transistor-level simulations of the system are provided to demonstrate the feasibility of the proposed system. Full article

Both reading difficulties (RD) and mathematics difficulties (MD) are common neurodevelopmental disorders. The co-occurrence of RD and MD, known as comorbid RDMD, is estimated to range between 21% and 45% of children with learning disabilities. Deficits in working memory have been reported in both RD and MD groups, as well as among comorbid RDMD. However, previous comorbidity studies have only examined the role of some components of working memory, and they do not strictly match their groups on relevant reading and mathematics tasks. Thus, the purpose of this study is to examine the nature of working memory deficits in comorbid RDMD after matching groups based on reading and mathematics tasks. We assessed four groups of children (RD [n = 21, M_age = 10.96 years], MD [n = 24, M_age = 11.04 years], comorbid RDMD [n = 26, M_age = 10.90 years], and chronological-age controls [n = 27, M_age = 10.96 years]) on measures of the phonological loop (word span and digit span forward tasks), central executive (complex word and digit span), and updating tasks (word and digit 2-back). The results of ANCOVA (covarying for gender and non-verbal IQ) showed first that the RD and RDMD groups performed significantly worse than the MD and control groups in both measures of the phonological loop. For the central executive and updating tasks, we found an effect based on stimulus type. For word-related tasks, the RD and comorbid RDMD groups performed worse than the MD and control groups, and for number-related tasks, the MD and comorbid RDMD groups performed worse than the RD and control groups. Taken together, our findings provide support for the correlated liability model of comorbidity, which indicates that working memory deficits experienced by the RDMD group are an additive combination of deficits observed in the RD and MD groups, suggesting that working memory tasks used to examine underlying deficits in reading and/or mathematics difficulties may dictate whether or not significant group differences are found. Full article

Although repolarization has been suggested to propagate in cardiac tissue both theoretically and experimentally, it has been challenging to estimate how and to what extent the propagation of repolarization contributes to relaxation because repolarization only occurs in the course of membrane excitation in normal hearts. We established a mathematical model of a 1D strand of 600 myocytes stabilized at an equilibrium potential near the plateau potential level by introducing a sustained component of the late sodium current (I_NaL). By applying a hyperpolarizing stimulus to a small part of the strand, we succeeded in inducing repolarization which propagated along the strand at a velocity of 1~2 cm/s. The ionic mechanisms responsible for repolarization at the myocyte level, i.e., the deactivation of both the I_NaL and the L-type calcium current (I_CaL), and the activation of the rapid component of delayed rectifier potassium current (I_Kr) and the inward rectifier potassium channel (I_K1), were found to be important for the propagation of repolarization in the myocyte strand. Using an analogy with progressive activation of the sodium current (I_Na) in the propagation of excitation, regenerative activation of the predominant magnitude of I_K1 makes the myocytes at the wave front start repolarization in succession through the electrical coupling via gap junction channels. Full article

Identification is considered a very important procedure, within the control area, to estimate the best-possible approximate model among different designs. Its significance comes from the fact that more than 75% of the cost associated with an advanced control project is aimed at obtaining a precise mathematical modeling. Therefore, in this work, an exhaustive analysis was carried out to determine the appropriate input stimulus for an unknown real system that must be controlled, with the aim of accurately estimating its transfer function (TF) using the empirical identification method (gray-box). The analysis was performed quantitatively by means of three tests: (i) the PID controller step response was evaluated theoretically; (ii) the controller performance was assessed in a Cartesian robot by tracking a trajectory defined through a Gaussian acceleration profile; (iii) the efficiency of the determined input stimulus with the best performance on inferring the TF for the system to be controlled was verified by assessing its operation in a real system, through repeatability tests, utilizing the integral errors. Full article

This case study intends to comprehend students’ perceptions of social support in cultivating their interests and aspirations for science, mathematics, engineering, and technology (STEM) degrees and careers. Survey-based quantitative research was employed, incorporating data from 1426 high school (grade 11th–12th) students in Qatar. The survey instrument encompassed four dimensions, i.e., (1) participants’ demographics, (2) STEM interests, (3) STEM supports/barriers and (4) STEM career aspirations to understand students’ perceptions. Spearman’s Rho correlation test demonstrated a positive correlation between students’ perceived social support (from family, teachers, and society) and their STEM interests (p < 0.01). Findings from the Mann-Whitney U test illustrated that females perceived enhanced social support (from teachers and society) in Qatar (p < 0.05). Even though teachers and society have been the stimulus to developing students’ STEM interests, there is still room to implement a policy for the consequential influence in constructing students’ STEM career aspirations. Thus, we believe these findings would urge policymakers to design tools that enable teachers and society to nurture, cultivate and sustain interest in STEM among the youth to meet Qatar’s National Vision 2030. Full article

Currently, in rural networks with a large amount of distributed generation, PV installations are often disconnected due to the excessively high voltage in the network, which often exceeds the limit value, in accordance with the PN-EN 50160 standard. Disconnecting such an installation extends the return on investment costs by preventing the generation of electricity for the owner’s needs and results in the consumption of this energy from the grid. In such a case, the recipient has to bear the costs related to the purchase of this energy. In order to solve the problem of excessively high voltage in a low-voltage distribution network with a large amount of distributed generation, the authors of this article proposed a new approach to the use of electricity from these sources. In order to present the benefits of the proposed solution, a computer simulation was used. In order to carry it out, a mathematical model of a low-voltage power grid with distributed generation was developed using the electric multipole method and Newton’s method, which is discussed in the paper. To determine the advantages of the proposed solution, nine variants of the operation of an exemplary low-voltage power grid over one day were analyzed. The main conclusion based on the analysis of the results is that the proposed approach improves the operation of the power system by maintaining the voltage values within the standard range for the entire tested part of the network. In addition, the proposed approach does not increase the power or electricity when generating electricity from a PV installation. The proposed solution can also serve as a very attractive stimulus for the creation of energy cooperatives. Full article

Background: The hyperventilation provocation test (HPTest) is a diagnostic tool for idiopathic hyperventilation syndrome (HVS), encountered in some long-COVID patients. However, interpretation of the HPTest remains unclear regarding the relevant P_ETCO₂ values to focus on and whether subjective symptoms should be considered. This study aimed to re-evaluate objective HPTest results for diagnosing HVS by determining accurate P_ETCO₂ kinetics in two groups of patients previously screened via the Nijmegen questionnaire (NQ). Methods: The kinetics of P_ETCO₂ during the HPTest were mathematically modeled and compared between 37 HVS patients (NQ ≥23/64) and 37 healthy controls (NQ <23/64) matched for gender, age, and body dimensions. AUC values with sensitivity and specificity were calculated, and analysis was monitored in a validation cohort of 152 routine HPTests. Results: A threshold value of a less than 12.8 mmHg increment of P_ETCO₂ at the 5th minute of the recovery phase of the HPTest diagnosed HVS patients with excellent sensitivity (0.92) and specificity (0.84). These results were confirmed in the validation cohort, highlighting the presence of 24% false positives/negatives when diagnosing on the basis of complaints in the NQ. Conclusions: For HVS diagnosis, we suggest considering the HPTest, which can more reliably reflect the mechanisms of CO₂ homeostasis and the response of the respiratory center to a stimulus, regardless of the subjective onset of symptoms. Full article

Chemotaxis, the migration of cells in response to chemical stimulus, is an important concept in the angiogenesis model. In most angiogenesis models, chemotaxis is defined as the migration of a sprout tip in response to the upgradient of the VEGF (vascular endothelial growth factor). However, we found that angiogenesis induced by performing arterial patch grafting on rabbits occurred under the decreasing VEGFA gradient. Data show that the VEGFA concentration peaked at approximately 0.3 to 0.5 cm away from the arterial patch and decreased as the measurement approaches the patch. We also observed that the new blood vessels formed are twisted and congested in some areas, in a distinguishable manner from non-pathological blood vessels. To explain these observations, we developed a mathematical model and compared the results from numerical simulations with the experimental data. We introduced a new chemotactic velocity using the temporal change in the chemoattractant gradient to govern the sprout tip migration. We performed a hybrid simulation to illustrate the growth of new vessels. Results indicated the speed of growth of new vessels oscillated before reaching the periphery of the arterial patch. Crowded and congested blood vessel formation was observed during numerical simulations. Thus, our numerical simulation results agreed with the experimental data. Full article