Mathematical

We consider a single genetic locus with two alleles A1 and A2 in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and have reached stationarity, we describe the asymptotic behaviors of the conditional gene genealogy and the latent mutations of a sample with known allele counts, when the count n1 of allele A1 is fixed, and when either or both the sample size n and the selection strength |α| tend to infinity...

Jumping microrobots and insects power their impressive leaps through systems of springs and latches. Using springs and latches, rather than motors or muscles, as actuators to power jumps imposes new challenges on controlling the performance of the jump. In this paper, we show how tuning the motor and spring relative to one another in a torque reversal latch can lead to an ability to control jump output, producing either tuneable (variable) or stereotyped jumps. We developed and utilized a simple mathematical model to explore the underlying design, dynamics, and control of a torque reversal mechanism, provides the opportunity to achieve different outcomes through the interaction between geometry, spring properties, and motor voltage...

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Shape display devices composed of actuation pixels enable dynamic rendering of surface morphological features, which have important roles in virtual reality and metaverse applications. The traditional pin-array solution produces sidestep-like structures between neighboring pins and normally relies on high-density pins to obtain curved surfaces. It remains a challenge to achieve continuous curved surfaces using a small number of actuated units. To address the challenge, we resort to the concept of surface continuity in computational geometry and develop a C0 -continuity shape display device with trichamber fiber-reinforced soft actuators...

In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity...

Household-based tuberculosis (TB) contact evaluation may be an efficient strategy to reach people who could benefit from oral pre-exposure prophylaxis (PrEP) because of the epidemiological links between HIV and TB. This study estimated the number of HIV serodifferent couples in TB-affected households and potential HIV acquisitions averted through their PrEP use in 4 TB-HIV high-burden countries. We conducted a model-based analysis set in Ethiopia, Kenya, South Africa, and Uganda using parameters from population-based household surveys, systematic literature review and meta-analyses, and estimates from the Global Burden of Diseases, Injuries, and Risk Factors Study 2019...

An in-depth study of the mechanisms governing the generation, evolution, and regulation of differences in tourism economics holds significant value for the rational utilization of tourism resources and the promotion of synergistic tourism economic development. This study utilizes mathematical statistical analysis and GIS spatial analysis to construct a single indicator measure and a comprehensive indicator measure to analyze tourism-related data in the research area from 2004 to 2019. The main factors influencing the spatial and temporal differences in the tourism economy are analyzed using two methods, namely, multiple linear regression and geodetector...

Evolution equations with convolution-type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, including delayed and fractional differential equations. We demonstrate, starting from the logistic model structure, that classical, delayed, and fractional models are special cases of a framework using a gamma Mittag-Leffler memory kernel. We discuss and classify different types of this general kernel, analyze the asymptotic behavior of the general model, and provide numerical simulations...

Recent advances in computational methods provide the promise of dramatically accelerating drug discovery. While mathematical modeling and machine learning have become vital in predicting drug-target interactions and properties, there is untapped potential in computational drug discovery due to the vast and complex chemical space. This paper builds on our recently published computational fragment-based drug discovery (FBDD) method called fragment databases from screened ligand drug discovery (FDSL-DD). FDSL-DD uses in silico screening to identify ligands from a vast library, fragmenting them while attaching specific attributes based on predicted binding affinity and interaction with the target subdomain...

A dynamic reaction-diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyi-lytic virus interactions...

Metal-oxide nanocomposites (MONs) are of pivotal importance as electrode materials, yet lack a guiding principle to tune their phase texture. Here we report that the phase texture of MONs can be tuned at the nanoscale by controlling the nanophase separation of precursor alloys. In situ transmission electron microscopy ( in situ TEM) has demonstrated that a MON material of platinum (Pt) and cerium oxide (CeO2 ) is obtained through promoted nanophase separation of a Pt5 Ce precursor alloy in an atmosphere containing oxygen (O2 ) and carbon monoxide (CO)...

While the classic Posner cuing paradigm has been used to study cuing of a single endogenous shift of attention, we present a new multiple cue paradigm to study the competition between multiple endogenous shifts of attention. The new paradigm enables us to manipulate the number of competing attention shifts and their relative importance. In three experiments, we demonstrate that the process of selecting one among other relevant attention shifts is governed by limited capacity and biased competition. We show that the probability of performing the most optimal attention shift is influenced by the total number of attention shifts competing for execution and that reward is a determining factor for the selection between attention shifts...

Statistical models with random intercepts and slopes (RIAS models) are commonly used to analyze longitudinal data. Fitting such models sometimes results in negative estimates of variance components or estimates on parameter space boundaries. This can be an unlucky chance occurrence, but can also occur because certain marginal distributions are mathematically identical to those from RIAS models with negative intercept and/or slope variance components and/or intercept-slope correlations greater than one in magnitude...

Facing the rapid development of 6G communication, long-wave infrared metasurface and biomimetic microfluidics, the performance requirements for microsystems based on metal tiny structures are gradually increasing. As one of powerful methods for fabrication metal complex microstructures, localized electrochemical deposition microadditive manufacturing technology can fabricate copper metal micro overhanging structures without masks and supporting materials. In this study, the role of the microprobe cantilever (MC) in localized electrodeposition was studied...

Recent trends suggest that Chinese herbal medicine formulas (CHM formulas) are promising treatments for complex diseases. To characterize the precise syndromes, precise diseases and precise targets of the precise targets between complex diseases and CHM formulas, we developed an artificial intelligence-based quantitative predictive algorithm (DeepTCM). DeepTCM has gone through multilevel model calibration and validation against a comprehensive set of herb and disease data so that it accurately captures the complex cellular signaling, molecular and theoretical levels of traditional Chinese medicine (TCM)...

This paper studies a variant of the Pollution Traveling Salesman Problem (PTSP) focused on fuel consumption and pollution emissions (PTSPC). The PTSPC generalizes the well-known Traveling Salesman Problem (TSP), classified as NP-Hard. In the PTSPC, a vehicle must deliver a load to each customer through a Hamiltonian cycle, minimizing an objective function that considers the speed of each edge, the mass of the truck, the mass of the load pending delivery, and the distance traveled. We have proposed a three-phase algorithm for the PTSPC...

An extremely important oil crop in the world, Helianthus annuus L. is one of the world's most significant members of the Asteraceae family. The rate and extent of seed germination and agronomic features are consistently affecting  by temperature (T) and changes in water potential (ψ). A broad hydrothermal time model with T and ψ components could explain sunflower responses over suboptimal T and ψ. A lab experiment was performed using the HTT model to discover both T and ψ and their interactive effects on sunflower germination and also to figure  out the cardinal Ts values...

The COVID-19 pandemic caused by the novel SARS-COV-2 virus poses a great risk to the world. During the COVID-19 pandemic, observing and forecasting several important indicators of the epidemic (like new confirmed cases, new cases in intensive care unit, and new deaths for each day) helped prepare the appropriate response (e.g., creating additional intensive care unit beds, and implementing strict interventions). Various predictive models and predictor variables have been used to forecast these indicators...

Quantitative structure permeation relationship (QSPR) models have gained prominence in recent years owing to their capacity to elucidate the influence of physicochemical properties on the dermal absorption of chemicals. These models facilitate the prediction of permeation coefficient (Kp) values, indicating the skin permeability of a chemical under infinite dose conditions. Conversely, obtaining dermal absorption rates (DAs) under finite dose conditions, which are crucial for skin product safety evaluation, remains a challenge when relying solely on Kp predictions from QSPR models...

CTCE-9908, a CXC chemokine receptor 4 (CXCR4) antagonist, prevents CXCR4 phosphorylation and inhibits the interaction with chemokine ligand 12 (CXCL12) and downstream signalling pathways associated with metastasis. This study evaluated the in vitro effects of CTCE-9908 on B16 F10 melanoma cells with the use of mathematical modelling. Crystal violet staining was used to construct a mathematical model of CTCE-9908 B16 F10 (melanoma) and RAW 264.7 (non-cancerous macrophage) cell lines on cell viability to predict the half-maximal inhibitory concentration (IC50 )...