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The Consolidated Standards of Reporting Trials (CONSORT) statement is a guideline designed to improve the transparency and quality of the reporting of randomised controlled trials (RCTs). In this article we present an extension to that statement for randomised pilot and feasibility trials conducted in advance of a future definitive RCT. The checklist applies to any randomised study in which a future definitive RCT, or part of it, is conducted on a smaller scale, regardless of its design (eg, cluster, factorial, crossover) or the terms used by authors to describe the study (eg, pilot, feasibility, trial, study). The extension does not directly apply to internal pilot studies built into the design of a main trial, non-randomised pilot and feasibility studies, or phase II studies, but these studies all have some similarities to randomised pilot and feasibility studies and so many of the principles might also apply.The development of the extension was motivated by the growing number of studies described as feasibility or pilot studies and by research that has identified weaknesses in their reporting and conduct. We followed recommended good practice to develop the extension, including carrying out a Delphi survey, holding a consensus meeting and research team meetings, and piloting the checklist.The aims and objectives of pilot and feasibility randomised studies differ from those of other randomised trials. Consequently, although much of the information to be reported in these trials is similar to those in randomised controlled trials (RCTs) assessing effectiveness and efficacy, there are some key differences in the type of information and in the appropriate interpretation of standard CONSORT reporting items. We have retained some of the original CONSORT statement items, but most have been adapted, some removed, and new items added. The new items cover how participants were identified and consent obtained; if applicable, the prespecified criteria used to judge whether or how to proceed with a future definitive RCT; if relevant, other important unintended consequences; implications for progression from pilot to future definitive RCT, including any proposed amendments; and ethical approval or approval by a research review committee confirmed with a reference number.This article includes the 26 item checklist, a separate checklist for the abstract, a template for a CONSORT flowchart for these studies, and an explanation of the changes made and supporting examples. We believe that routine use of this proposed extension to the CONSORT statement will result in improvements in the reporting of pilot trials.Editor’s note: In order to encourage its wide dissemination this article is freely accessible on the BMJ and Pilot and Feasibility Studies journal websites.

Mathematical modeling is the process of trying to precisely define a nonmathematical situation, real-life phenomena of changing world and the relationships between the situations in the language of mathematics, and finding out mathematical formulations or patterns within these situations and phenomena. Mathematical modelingin terms of nonlinear dynamic equations is described as a conversion activity of realproblems in amathematicalform. The interactions between the mathematical and biological sciences have been increasing rapidly in recent years. Both traditional topics, such as population and disease modeling, and new ones, such as those in genomics arising from the accumulation of DNA sequence data, have made mathematical modeling in biomathematics an exciting field. The best predictions of numerous individuals and scientific communities have suggested that this growing area will continue to be one of the most dominating and fascinating driving factors to capture the global change phenomena and design a sustainable management for a better world. Frontiers in Mathematical Modelling Research provides the most recent and up-to-date developments in the mathematical analysis of real world problems arising in engineering, biology, economics, geography, planning, sociology, psychology, medicine and epidemiology of infectious diseases. Mathematical modeling and analysis are important, not only to understand disease progression, but also to provide predictions about the evolution of the disease and insights about the dynamics of the transmission rate and the effectiveness of control measures. One of the main focuses of the book is the transmission dynamics of emerging and re-emerging infectious diseases and the implementation of intervention strategies. It also discusses optimal control strategies like pharmaceutical and non-pharmaceutical interventions and their potential effectiveness on the control of infections with the help of compartmental mathematical models in epidemiology. This book also covers a wide variety of topics like dynamic models in robotics, chemical process, biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of diagnosis rate effects and prediction of zoonotic viruses, data-driven dynamic simulation and scenario analysis of the spread of diseases. Frontiers in Mathematical Modelling Research will play a pivotal role as helpful resource for mathematical biologists and ecologists, epidemiologists, epidemic modelers, virologists, researchers, mathematical modelers, robotic scientists and control engineers and others engaged in the analysis of the transmission, prevention, and control of infectious diseases and their impact on human health. It is expected that this self-contained edited book can also serve undergraduate and graduate students, young scholars and early career researchers as the basis for meaningful directives of current trends of research in mathematical biology.

Provides an overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world and how its contribution will be even more vital in the years ahead. Explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.

The Consolidated Standards of Reporting Trials (CONSORT) statement is a guideline designed to improve the transparency and quality of the reporting of randomised controlled trials (RCTs). In this article we present an extension to that statement for randomised pilot and feasibility trials conducted in advance of a future definitive RCT. The checklist applies to any randomised study in which a future definitive RCT, or part of it, is conducted on a smaller scale, regardless of its design (eg, cluster, factorial, crossover) or the terms used by authors to describe the study (eg, pilot, feasibility, trial, study). The extension does not directly apply to internal pilot studies built into the design of a main trial, non-randomised pilot and feasibility studies, or phase II studies, but these studies all have some similarities to randomised pilot and feasibility studies and so many of the principles might also apply. The development of the extension was motivated by the growing number of studies described as feasibility or pilot studies and by research that has identified weaknesses in their reporting and conduct. We followed recommended good practice to develop the extension, including carrying out a Delphi survey, holding a consensus meeting and research team meetings, and piloting the checklist. The aims and objectives of pilot and feasibility randomised studies differ from those of other randomised trials. Consequently, although much of the information to be reported in these trials is similar to those in randomised controlled trials (RCTs) assessing effectiveness and efficacy, there are some key differences in the type of information and in the appropriate interpretation of standard CONSORT reporting items. We have retained some of the original CONSORT statement items, but most have been adapted, some removed, and new items added. The new items cover how participants were identified and consent obtained; if applicable, the prespecified criteria used to judge whether or how to proceed with a future definitive RCT; if relevant, other important unintended consequences; implications for progression from pilot to future definitive RCT, including any proposed amendments; and ethical approval or approval by a research review committee confirmed with a reference number. This article includes the 26 item checklist, a separate checklist for the abstract, a template for a CONSORT flowchart for these studies, and an explanation of the changes made and supporting examples. We believe that routine use of this proposed extension to the CONSORT statement will result in improvements in the reporting of pilot trials. Editor’s note: In order to encourage its wide dissemination this article is freely accessible on the BMJ and Pilot and Feasibility Studies journal websites.

This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines.

This article has been published in a revised form in Journal of fluid mechanics, http://dx.doi.org/10.1017/jfm.2019.341. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2019

We provide an analytical tool based on a variational Bayesian treatment of hidden Markov models to combine the information from thousands of short single-molecule trajectories of intracellularly diffusing proteins. The method identifies the number of diffusive states and the state transition rates. Using this method we have created an objective interaction map for Hfq, a protein that mediates interactions between small regulatory RNAs and their mRNA targets. This paper reports an analytical method for single-particle tracking data. It identifies diffusive states of intracellular proteins and the rates of transition between them.