Mathematic

Existing theories of diffusioosmosis have neglected ion-ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion-ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion-ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis...

Human ageing, along with the ageing of conventional model organisms, is depicted as a continuous and progressive decline of biological capabilities accompanied by an exponentially increasing mortality risk. However, not all organisms experience ageing identically and our understanding of the phenomenon is coloured by human-centric views. Ageing is multifaceted and influences a diverse range of species in varying ways. Some undergo swift declines post-reproduction, while others exhibit insubstantial changes throughout their existence...

SIGNIFICANCE: Compressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs). AIM: Our previous research involved rather general CS measurements, where each ILD can contribute to any measurement...

Unsupervised learning based on restricted Boltzmann machine or autoencoders has become an important research domain in the area of neural networks. In this paper mathematical expressions to adaptive learning step calculation for RBM with ReLU transfer function are proposed. As a result, we can automatically estimate the step size that minimizes the loss function of the neural network and correspondingly update the learning step in every iteration. We give a theoretical justification for the proposed adaptive learning rate approach, which is based on the steepest descent method...

In this study, we examine multiple perspectives on soliton solutions to the (3+1)-dimensional Boussinesq model by applying the unified Riccati equation expansion (UREE) approach. The Boussinesq model examines wave propagation in shallow water, which is derived from the fluid dynamics of a dynamical system. The UREE approach allows us to derive a range of distinct solutions, such as single, periodic, dark, and rational wave solutions. Furthermore, we present the bifurcation, chaotic, and sensitivity analysis of the proposed model...

Reliable detection of substances present at potentially low concentrations is a problem common to many biomedical applications. Complementary to well-established enzyme-, antibody-antigen-, and sequencing-based approaches, so-called microbial whole-cell sensors, i.e., synthetically engineered microbial cells that sense and report substances, have been proposed as alternatives. Typically these cells operate independently: a cell reports an analyte upon local detection.In this work, we analyze a distributed algorithm for microbial whole-cell sensors, where cells communicate to coordinate if an analyte has been detected...

Where there are bacteria, there will be bacteriophages. These viruses are known to be important players in shaping the wider microbial community in which they are embedded, with potential implications for human health. On the other hand, bacteria possess a range of distinct immune mechanisms that provide protection against bacteriophages, including the mutation or complete loss of the phage receptor, and CRISPR-Cas adaptive immunity. While our previous work showed how a microbial community may impact phage resistance evolution, little is known about the inverse, namely how interactions between phages and these different phage resistance mechanisms affect the wider microbial community in which they are embedded...

Almond pruning biomass is an important agricultural residue that has been scarcely studied for the co-production of sugars and solid biofuels. In this work, the production of monosaccharides from almond prunings was optimised by a two-step process scheme: pretreatment with dilute sulphuric acid (0.025 M, at 185.9-214.1 ℃ for 0.8-9.2 min) followed by enzyme saccharification of the pretreated cellulose. The application of a response surface methodology enabled the mathematical modelling of the process, establishing pretreatment conditions to maximise both the amount of sugar in the acid prehydrolysate (23...

Haemorrhoidal disease is identified by declension of the inflamed and bleeding of vascular tissues of the anal canal. Traditionally, haemorrhoids are associated with chronic constipation and the most common symptoms are irritation in anus region, pain and discomfort, swelling around anus, tender lumps around the anus and rectal bleeding (depending upon the grade of haemorrhoid). Among the several conventional treatment procedures (commonly mentioned as, rubber band litigation, sclerotherapy and electrotherapy), laser haemorrhoidoplasty is an out-patient and less-invasive laparoscopic procedure...

Humans and other animals are able to perceive and represent a number of objects present in a scene, a core cognitive ability thought to underlie the development of mathematics. However, the perceptual mechanisms that underpin this capacity remain poorly understood. Here, we show that our visual sense of number derives from a visual system designed to efficiently encode the location of objects in scenes. Using a mathematical model, we demonstrate that an efficient but information-limited encoding of objects' locations can explain many key aspects of number psychophysics, including subitizing, Weber's law, underestimation, and effects of exposure time...

Diffusion is a mass transport phenomenon caused by chaotic thermal movements of molecules. Studying the transport in specific domain is simplified by using evolutionary differential equations for local concentration of the molecules instead of complete information on molecular paths [1]. Compounds in a fluid mixture tend to smooth out its spatial concentration inhomogeneities by diffusion. Rate of the transport is proportional to the concentration gradient and coefficient of diffusion of the compound in ordinary diffusion...

Q-matrix is an important component of most cognitive diagnosis models (CDMs); however, it mainly relies on subject matter experts' judgements in empirical studies, which introduces the possibility of misspecified q-entries. To address this, statistical Q-matrix validation methods have been proposed to aid experts' judgement. A few of these methods, including the multiple logistic regression-based (MLR-B) method and the Hull method, can be applied to general CDMs, but they are either time-consuming or lack accuracy under certain conditions...

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts...

As living standards rise, more and more people are paying attention to their own health, especially issues such as cerebral thrombosis, cerebral infarction, and other cerebral blood flow problems. An accurate simulation of blood flow within cerebral vessels has emerged as a crucial area of research. In this study, we focus on microcirculatory blood flow in ischemic brain tissue and employ a 0D-1D geometric multi-scale coupled model to characterize this process. Given the intricate nature of human cerebral vessels, we apply a numerical method combining the finite element method and the third-order Runge-Kutta method to resolve the coupled model...

BACKGROUND: Insulin-naive subjects with type 2 diabetes (T2D) start basal insulin titration from a low initial insulin dose (IID), which is adjusted weekly or twice per week based on fasting plasma glucose (FPG) measurement as recommended by the American Diabetes Association (ADA). The procedure to reach the optimal insulin dose (OID) is time-consuming, especially in subjects with high insulin needs (HIN). The aim of this study is to provide a fast and effective, but still safe, insulin titration algorithm in insulin-naive T2D subjects with HIN...

Low-cost air pollution sensors, offering hyper-local characterization of pollutant concentrations, are becoming increasingly prevalent in environmental and public health research. However, low-cost air pollution data can be noisy, biased by environmental conditions, and usually need to be field-calibrated by collocating low-cost sensors with reference-grade instruments. We show, theoretically and empirically, that the common procedure of regression-based calibration using collocated data systematically underestimates high air pollution concentrations, which are critical to diagnose from a health perspective...

The field of theranostics is rapidly advancing, driven by the goals of enhancing patient care. Recent breakthroughs in artificial intelligence (AI) and its innovative theranostic applications have marked a critical step forward in nuclear medicine, leading to a significant paradigm shift in precision oncology. For instance, AI-assisted tumor characterization, including automated image interpretation, tumor segmentation, feature identification, and prediction of high-risk lesions, improves diagnostic processes, offering a precise and detailed evaluation...

Lactation curves, which describe the production pattern of milk-related traits over time, provide insightful information about individual cow health, resilience, and milk production efficiency. Key functional traits can be derived through lactation curve modeling, such as lactation peak and persistency. Furthermore, novel traits such as resilience indicators can be derived based on the variability of the deviations of observed milk yield from the expected lactation curve fitted for each animal. Lactation curve parameters are heritable, indicating that one can modify the average lactation curve of a population through selective breeding...

The design and use of superhydrophobic surfaces have gained special attentions due to their superior performances and advantages in many flow systems, e.g., in achieving specific goals including drag reduction and flow/droplet handling and manipulation. In this work, we conduct a brief review of shear flows over superhydrophobic surfaces, covering the classic and recent studies/trends for both Newtonian and non-Newtonian fluids. The aim is to mainly review the relevant mathematical and numerical modeling approaches developed during the past 20 years...

BACKGROUND: Throughout the SARS-CoV-2 pandemic, policymakers have had to navigate between recommending voluntary behaviour change and policy-driven behaviour change to mitigate the impact of the virus. While individuals will voluntarily engage in self-protective behaviour when there is an increasing infectious disease risk, the extent to which this occurs and its impact on an epidemic is not known. METHODS: This paper describes a deterministic disease transmission model exploring the impact of individual avoidance behaviour and policy-mediated avoidance behaviour on epidemic outcomes during the second wave of SARS-CoV-2 infections in Ontario, Canada (September 1, 2020 to February 28, 2021)...