Recent Advances In Mathematical Modeling Research Articles

Pitfalls of Using Multinomial Regression Analysis to Identify Class-Structure-Relevant Variables in Biomedical Data Sets: Why a Mixture of Experts (MOE) Approach Is Better

Recent advances in mathematical modeling and artificial intelligence have challenged the use of traditional regression analysis in biomedical research. This study examined artificial data sets and biomedical data sets from cancer research using binomial and multinomial logistic regression. The results were compared with those obtained with machine learning models such as random forest, support vector machine, Bayesian classifiers, k-nearest neighbors, and repeated incremental clipping (RIPPER). The alternative models often outperformed regression in accurately classifying new cases. Logistic regression had a structural problem similar to early single-layer neural networks, which limited its ability to identify variables with high statistical significance for reliable class assignments. Therefore, regression is not per se the best model for class prediction in biomedical data sets. The study emphasizes the importance of validating selected models and suggests that a “mixture of experts” approach may be a more advanced and effective strategy for analyzing biomedical data sets.

Mathematical modeling, analysis and control in soft robotics: a survey

This paper reviews some recent advances in mathematical modeling, analysis and control, both from the theoretical and numerical viewpoints, in the emergent field of soft robotics. The presentation is not focused on specific prototypes of soft robots, but in a more general description of soft smart materials. The goal is to provide a unified and rigorous mathematical approach to open-loop control strategies for soft materials that hopefully might lay the seeds for future research in this field.

A Review on Drug-Induced Nephrotoxicity: Pathophysiological Mechanisms, Drug Classes, Clinical Management, and Recent Advances in Mathematical Modeling and Simulation Approaches.

A variety of marketed drugs belonging to various therapeutic classes are known to cause nephrotoxicity. Nephrotoxicity can manifest itself in several forms depending on the specific site involved as well as the underlying pathophysiological mechanisms. As they often coexist with other pathophysiological conditions, the steps that can be taken to treat them are often limited. Thus, drug-induced nephrotoxicity remains a major clinical challenge. Prior knowledge of risk factors associated with special patient populations and specific classes of drugs, combined with early diagnosis, therapeutic drug monitoring with dose adjustments, as well as timely prospective treatments are essential to prevent and manage them better. Most incident drug-induced renal toxicity is reversible only if diagnosed at an early stage and treated promptly. Hence, diagnosis at an early stage is the need of the hour to counter it. Significant recent advances in the identification of novel early biomarkers of nephrotoxicity are not beyond limitations. In such a scenario, mathematical modeling and simulation (M&S) approaches may help to better understand and predict toxicities in a clinical setting. This review summarizes pathophysiological mechanisms of drug-induced nephrotoxicity, classes of nephrotoxic drugs, management, prevention, and diagnosis in clinics. Finally, it also highlights some of the recent advancements in mathematical M&S approaches that could be used to better understand and predict drug-induced nephrotoxicity.

Inferring efficiency of translation initiation and elongation from ribosome profiling

One of the main goals of ribosome profiling is to quantify the rate of protein synthesis at the level of translation. Here, we develop a method for inferring translation elongation kinetics from ribosome profiling data using recent advances in mathematical modelling of mRNA translation. Our method distinguishes between the elongation rate intrinsic to the ribosome’s stepping cycle and the actual elongation rate that takes into account ribosome interference. This distinction allows us to quantify the extent of ribosomal collisions along the transcript and identify individual codons where ribosomal collisions are likely. When examining ribosome profiling in yeast, we observe that translation initiation and elongation are close to their optima and traffic is minimized at the beginning of the transcript to favour ribosome recruitment. However, we find many individual sites of congestion along the mRNAs where the probability of ribosome interference can reach n}{}50%. Our work provides new measures of translation initiation and elongation efficiencies, emphasizing the importance of rating these two stages of translation separately.

多孔質体内熱流動のモデリングの進展

Recent advances in mathematical modeling of heat and fluid flow in porous media were discussed starting from an introduction of volume averaging theory and leading to various engineering applications. Mathematical interpretations of tortuosity, thermal dispersion and interstitial heat transfer are provided with their models based on solvable volume averaged quantities. A useful concept “effective porosity” was introduced to account for the tortuosity. Moreover, an inverse relationship between the interstitial heat transfer coefficient and thermal dispersion coefficient was explained, which enables us to estimate the thermal dispersion simply by measuring the interstitial heat transfer using a single blow method. Engineering applications based on the local space sharing concept will be discussed ranging from bioheat transfer to ion transport through a membrane.

Review of “ mathematical models for neglected tropical diseases: essential tools for control and elimination, part A ” edited by Roy M. Anderson and Maria-Gloria Basáñez

Review This volume in Advances in Parasitology, which summarises recent advances in mathematical modelling of Neglected Tropical Disease (NTDs), marks 30 years since the publication of a landmark review by Anderson and May on `Helminth infections of humans: mathematical models, population dynamics, and control’ in the same journal. The remit of the current review has been expanded to cover not just helminths, but NTDs in general, in response to the focus on NTDs since the World Health Organization’s 2020 Roadmap on NTDs, and the 2012 London declaration (http://unitingtocombatntds.org/). Most of the chapters review recent developments in the mathematical models of particular diseases (leprosy, human African trypanosomiasis, lymphatic filariasis, Chagas disease), although there are also chapters on the Allee effect, helminth egg count data, molecular epidemiology, and economic evaluation. So, what developments have there been in the intervening years since the original review? Perhaps the most significant developments are related to improvements in computer power. One is the increasing use of micro-simulation models to model disease transmission. Unlike traditional models that track changes in the population, micro-simulation models track changes in the individual, and are therefore better able to account for differences between individuals e.g., in their susceptibility to disease or compliance to treatment. Two good examples of the approach, reviewed in this volume, are the LYMFASIM model of lymphatic filariasis and the SIMCOLEP model of leprosy. Algorithms for fitting models to data have also advanced considerably over the last couple of decades. As with micro-simulation, this has been facilitated by improvements in computing power. The process of fitting a model to data is useful for estimating parameters and validating the model. An excellent example is provided by Gambhir and colleagues who use a recently developed Bayesian algorithm to fit their model of lymphatic filariasis to data on microfilarial prevalence in different age groups. Despite improvements in methodologies, it can still be difficult to fit models to data, and examples like this are useful for improving best practice. The way that models are used has also changed. Anderson and May used models to establish general conditions under which a disease is able to persist in a population. This type of analysis is still done (e.g. in the chapter on the Allee effect), but increasingly models are used to evaluate specific scenarios, which are often to do with different strategies of intervention. In the current volume, models are used, for example, to find out how long mass drug administration should be continued to eliminate filariasis; to evaluate whether leprosy can be controlled by giving chemoprophylaxis to contacts of a case; and to optimise the timing of vector control campaigns for Chagas disease. Given that models are now frequently used to explore different scenarios for disease control or elimination, it is disappointing that they have had limited impact on policy (a point made by several authors in this volume). Perhaps this is because we are not providing policy makers with the information they need. The authors of Correspondence: christian.bottomley@lshtm.ac.uk MRC Tropical Epidemiology Group, London School of Hygiene & Tropical Medicine, Keppel Street, London WC1E 7HT, UK

A Review of Pharmacological Treatment Options for Lung Cancer: Emphasis on Novel Nanotherapeutics and Associated Toxicity.

Lung cancer remains a leading cause of death. Current treatment options are generally ineffective, highlighting the dire need for novel approaches. While numerous biologically-active chemotherapeutics have been discovered in the last two decades, biological barriers including minimal water solubility, stability, and cellular resistance hinder in vivo effectiveness. To overcome these limitations, nanoparticles have been designed to deliver chemotherapeutics selectively to cancerous tissue while minimizing pharmacokinetics hindrance. Numerous studies are underway analyzing the efficacy of nanoparticles in drug delivery, theranostic applications, and photothermal therapy. However, while nanoparticles have shown efficacy in treating some cancers, their potential toxicity and lack of targeting may hinder clinical potential. With the aim to help sort through these issues, we conduct a review to describe recent applications of nanotherapeutics for the treatment and diagnosis of lung cancer. We first provide a detailed background of statistics, etiology, histological classification, staging, diagnosis, and current treatment options. This is followed by a description of current applications of nanotherapeutics, focusing primarily on results published during the past five years. The potential toxicity associated with nanoparticles is evaluated, revealing inconclusive information which highlights the need for further studies. Lastly, recent advances in mathematical modeling and computational simulation have shown potential in predicting tumor response to nanotherapeutics. Thus, although nanoparticles have shown promise in treating lung cancer, further multi-disciplinary studies to quantify optimal dosages and assess possible toxicity are still needed. To this end, nanotherapeutic options currently in clinical trials offer hope to help address some of these critical issues.

Forecasting Influenza Epidemics in Hong Kong.

Recent advances in mathematical modeling and inference methodologies have enabled development of systems capable of forecasting seasonal influenza epidemics in temperate regions in real-time. However, in subtropical and tropical regions, influenza epidemics can occur throughout the year, making routine forecast of influenza more challenging. Here we develop and report forecast systems that are able to predict irregular non-seasonal influenza epidemics, using either the ensemble adjustment Kalman filter or a modified particle filter in conjunction with a susceptible-infected-recovered (SIR) model. We applied these model-filter systems to retrospectively forecast influenza epidemics in Hong Kong from January 1998 to December 2013, including the 2009 pandemic. The forecast systems were able to forecast both the peak timing and peak magnitude for 44 epidemics in 16 years caused by individual influenza strains (i.e., seasonal influenza A(H1N1), pandemic A(H1N1), A(H3N2), and B), as well as 19 aggregate epidemics caused by one or more of these influenza strains. Average forecast accuracies were 37% (for both peak timing and magnitude) at 1-3 week leads, and 51% (peak timing) and 50% (peak magnitude) at 0 lead. Forecast accuracy increased as the spread of a given forecast ensemble decreased; the forecast accuracy for peak timing (peak magnitude) increased up to 43% (45%) for H1N1, 93% (89%) for H3N2, and 53% (68%) for influenza B at 1-3 week leads. These findings suggest that accurate forecasts can be made at least 3 weeks in advance for subtropical and tropical regions.

Space traffic hazards from orbital debris mitigation strategies

The paper gives coverage of recent advances in mathematical modeling of long term orbital debris evolution within the frames of continua approach. Under the approach the evolution equations contain a number of source terms responsible for the variations of quantities of different fractions of orbital debris population due to fragmentations and collisions. Mechanisms of hypervelocity collisions of debris fragments with pressurized vessels are investigated. The spacecraft shield honeycomb concept is suggested based on principles of impact energy conversion and redistribution and consumption by destroyable structures. The paper is devoted to the 100th anniversary of the founder of space debris research in Moscow State University Prof. G.A. Tyulin.

Recent Advances in Mathematical Modeling and Simulation of DNA Replication Process.

DNA replication is the basis for biological inheritance, involving a series of sophisticated biochemical processes. Over the past decades, numerous in vitro or in vivo experiments have been implemented among a variety of organisms. While these resource-intensive techniques may always be costly, time-consuming or unable to measure the replication process on a global scale. Recently, mathematical modeling and computational simulation of biochemical processes that can be used for rapid testing of biology hypotheses have attracted considerable attention. In this review, we outline some key mathematical and computational works proposed recently for DNA replication process, with emphasis on the modeling and simulation of the replication origin identification and characterization, the replication process initiation and regulation, and the genome-wide profiling of DNA replication. Although many excellent works have been done, for a deeper insight into the DNA replication process, further iteration of mathematical modeling and biochemical experiment are still needed, and the prospective and possible research directions are discussed herein.

Computational fluid dynamics models and congenital heart diseases

Mathematical modeling is a powerful tool to investigate hemodynamics of the circulatory system. With improving imaging techniques and detailed clinical investigations, it is now possible to construct patient-specific models of reconstructive surgeries for the treatment of congenital heart diseases. These models can help clinicians to better understand the hemodynamic behavior of different surgical options for a treated patient. This review outlines recent advances in mathematical modeling in congenital heart diseases, the discoveries and limitations these models present, and future directions that are on the horizon.

Mathematical Modelling in Measurement and Instrumentation

This paper presents a brief outline of the use of mathematical modelling techniques in measurement and instrumentation systems and sub-systems. Following an overview of various models, it illustrates some of the recent advances in mathematical modelling of sensors and instrument transducers. This is illustrated in two case studies describing the use of numerical finite element (FE) modelling techniques for CAD and performance modelling of capacitive sensors and torque motor actuators.

Natural interaction in intelligent spaces: Designing for architecture and entertainment

The rapid evolution of computers' processing power, progress in projection and display technology, and their low cost, accompanied by recent advances in mathematical modeling, make available to space designers today sophisticated technologies which were once accessible only to research institutions or large companies. Thanks to wireless sensing techniques it is possible to endow a space with perceptual intelligence, and make it aware of how people use it, move in it, or react to it. Intelligent Spaces are relevant for several applications or tasks which range from surveillance to entertainment, from medical rehabilitation to artistic performance, from museum exhibit design to commerce. The author's work focuses on Narrative Spaces which are storytellers, able to articulate an informative or entertaining audio-visual narration for people interactively. Narrative Spaces communicate by use of large scale coordinated projections, sounds and displays whose contents are choreographed by the natural body movements or physical gestures of the people in them. This paper describes the guiding principles and modeling approaches that, according to the author, enable a robust modeling of user input and communication strategies for digital content presentation in Intelligent Narrative Spaces. It then provides examples of applications built according to the specified criteria.

Developing Mathematical Models of Neurobehavioral Performance for the “Real World”

Work-related operations requiring extended wake durations, night, or rotating shifts negatively affect worker neurobehavioral performance and health. These types of work schedules are required in many industries, including the military, transportation, and health care. These industries are increasingly using or considering the use of mathematical models of neurobehavioral performance as a means to predict the neurobehavioral deficits due to these operational demands, to develop interventions that decrease these deficits, and to provide additional information to augment existing decision-making processes. Recent advances in mathematical modeling have allowed its application to real-world problems. Developing application-specific expertise is necessary to successfully apply mathematical models, in part because development of new algorithms and methods linking the models to the applications may be required. During a symposium, "Modeling Human Neurobehavioral Performance II: Towards Operational Readiness," at the 2006 SIAM-SMB Conference on the Life Sciences, examples of the process of applying mathematical models, including model construction, model validation, or developing model-based interventions, were presented. The specific applications considered included refining a mathematical model of sleep/wake patterns of airline flight crew, validating a mathematical model using railroad operations data, and adapting a mathematical model to develop appropriate countermeasure recommendations based on known constraints. As mathematical models and their associated analytical methods continue to transition into operational settings, such additional development will be required. However, major progress has been made in using mathematical model outputs to inform those individuals making schedule decisions for their workers.

Quantifying HTLV‐I dynamics

Despite significant advances in our understanding of the immune response to persistent viruses like human T-cell lymphotropic virus type I (HTLV-I), many important questions remain unanswered. Mathematical modelling enables us to interpret and synthesise diverse experimental data in new ways and thus can contribute to our understanding. Here, we review recent advances in mathematical modelling of HTLV-I infection and illustrate how mathematics has enabled us to identify factors that determine an individual's viral burden and risk of developing HTLV-I-associated diseases.

Magnetic Micro- and Nano-Particle-Based Targeting for Drug and Gene Delivery

The use of magnetic micro- and nano-particles as carriers for in vivo targeting of therapeutic compounds was first proposed over 25 years ago. Since then, a variety of animal studies have demonstrated the efficacy of the technique, however, only a handful of Phase I/II clinical trials have taken place. While the theoretical underpinnings have been lacking, recent advances in mathematical modeling of magnetic targeting, as well as the development of novel magnetic nanoparticle carriers and implantable magnets, show promise in progressing this technology from the laboratory to the clinic.

Science and cycling: current knowledge and future directions for research

In this holistic review of cycling science, the objectives are: (1) to identify the various human and environmental factors that influence cycling power output and velocity; (2) to discuss, with the aid of a schematic model, the often complex interrelationships between these factors; and (3) to suggest future directions for research to help clarify how cycling performance can be optimized, given different race disciplines, environments and riders. Most successful cyclists, irrespective of the race discipline, have a high maximal aerobic power output measured from an incremental test, and an ability to work at relatively high power outputs for long periods. The relationship between these characteristics and inherent physiological factors such as muscle capilliarization and muscle fibre type is complicated by inter-individual differences in selecting cadence for different race conditions. More research is needed on high-class professional riders, since they probably represent the pinnacle of natural selection for, and physiological adaptation to, endurance exercise. Recent advances in mathematical modelling and bicycle-mounted strain gauges, which can measure power directly in races, are starting to help unravel the interrelationships between the various resistive forces on the bicycle (e.g. air and rolling resistance, gravity). Interventions on rider position to optimize aerodynamics should also consider the impact on power output of the rider. All-terrain bicycle (ATB) racing is a neglected discipline in terms of the characterization of power outputs in race conditions and the modelling of the effects of the different design of bicycle frame and components on the magnitude of resistive forces. A direct application of mathematical models of cycling velocity has been in identifying optimal pacing strategies for different race conditions. Such data should, nevertheless, be considered alongside physiological optimization of power output in a race. An even distribution of power output is both physiologically and biophysically optimal for longer ( >4km) time-trials held in conditions of unvarying wind and gradient. For shorter races (e.g. a 1km time-trial), an‘all out’ effort from the start is advised to‘save’ time during the initial phase that contributes most to total race time and to optimize the contribution of kinetic energy to race velocity. From a biophysical standpoint, the optimum pacing strategy for road time-trials may involve increasing power in headwinds and uphill sections and decreasing power in tailwinds and when travelling downhill. More research, using models and direct power measurement, is needed to elucidate fully how much such a pacing strategy might save time in a real race and how much a variable power output can be tolerated by a rider. The cyclist's diet is a multifactorial issue in itself and many researchers have tried to examine aspects of cycling nutrition (e.g. timing, amount, composition) in isolation. Only recently have researchers attempted to analyse interrelationships between dietary factors (e.g. the link between pre-race and in-race dietary effects on performance). The thermal environment is a mediating factor in choice of diet, since there may be competing interests of replacing lost fluid and depleted glycogen during and after a race. Given the prevalence of stage racing in professional cycling, more research into the influence of nutrition on repeated bouts of exercise performance and training is required.

Multivariate data analysis as a tool in advanced quality monitoring in the food production chain

This paper summarizes some recent advances in mathematical modeling of relevance in advanced quality monitoring in the food production chain. Using chemometrics – multivariate data analysis – it is illustrated how to tackle problems in food science more efficiently and, moreover, solve problems that could not otherwise be handled before. The different mathematical models are all exemplified by food related subjects to underline the generic use of the models within the food chain. Applications will be given from meat storage, vegetable characterization, fish quality monitoring and industrial food processing, and will cover areas such as analysis of variance, monitoring and handling of sampling variation, calibration, exploration/data mining and hard modeling.

Recent Advances in Mathematical Modeling of Flow and Heat Transfer Phenomena in Glass Furnaces

This paper reviews significant advances in the mathematical modeling of flow and heat transfer phenomena in glass furnaces during the period 1996–2000. It describes developments in both the fundamental/scientific and practical aspects of modeling. The topics reviewed include developments in (a) model formulation and modeling techniques, (b) postprocessing modeling of glass quality and environmental emissions, (c) measurement of thermodynamic and transport properties of melt relevant to modeling, and (d) incorporation of model‐based knowledge into process control schemes. These developments are critically examined and assessed from an industrial perspective, and topics needing further research and development efforts are identified.

Measurement of alpha-tocopherol turnover in plasma and in lipoproteins using stable isotopes and gas chromatography/mass spectrometry.

Burton and Daroszewska (16) have presented an excellent method for quantifying alpha-tocopherol in human and animal tissues. The present paper expands that method by including the theory and calculations for alpha-tocopherol turnover in human plasma and lipoprotein fractions. Recent advances in mathematical modeling in experimental nutrition (22) have been aided by the increased availability of labeled isotopes and sensitive analytical methods. Applied to the study of alpha-tocopherol, these techniques will allow the characterization of the kinetic behavior of this micronutrient in vivo and expand the understanding of this key nutrient's role in preventing disease.