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Differential equation

Thorsten Tjardes, Markus Luecking
Introduction: To achieve the aim of zero preventable deaths on the battlefield a deeper understanding of uncontrolled hemorrhage from junctional or proximal extremity sources is mandatory. While tourniquet application to the extremities has drastically reduced morbidity and mortality, there is still room for improvement regarding the timing of tourniquet placement as the available evidence clearly points out a tight correlation between timing of tourniquet application and outcome. To save as many lives as possible the "point of no return" regarding the circulatory breakdown due to hemorrhage, colloquially addressed as platinum 5 min, needs to be determined...
March 14, 2018: Military Medicine
Joseph Páez Chávez, Dirk Jungmann, Stefan Siegmund
The paper presents a comprehensive numerical study of mathematical models used to describe complex biological systems in the framework of integrated pest management. Our study considers two specific ecosystems that describe the application of control mechanisms based on pesticides and natural enemies, implemented in an impulsive and periodic manner, due to which the considered models belong to the class of impulsive differential equations. The present work proposes a numerical approach to study such type of models in detail, via the application of path-following (continuation) techniques for nonsmooth dynamical systems, via the novel continuation platform COCO (Dankowicz and Schilder)...
December 2018: Journal of Biological Dynamics
Kyung Duk Min, Sung Il Cho
BACKGROUND: The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease. METHODS: We developed mathematical models of ordinary differential equations including human, rodent and mite groups...
March 19, 2018: Journal of Korean Medical Science
Stephen Smith, Neil Dalchau
Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted to systems of two or three chemical species, for which equations are tractable. However, when models seek to combine descriptions of intercellular signal diffusion and intracellular biochemistry, plausible genetic networks can consist of dozens of interacting species...
March 2018: Journal of the Royal Society, Interface
Antonella Succurro, Oliver Ebenhöh
Understanding microbial ecosystems means unlocking the path toward a deeper knowledge of the fundamental mechanisms of life. Engineered microbial communities are also extremely relevant to tackling some of today's grand societal challenges. Advanced meta-omics experimental techniques provide crucial insights into microbial communities, but have been so far mostly used for descriptive, exploratory approaches to answer the initial 'who is there?' QUESTION: An ecosystem is a complex network of dynamic spatio-temporal interactions among organisms as well as between organisms and the environment...
March 14, 2018: Biochemical Society Transactions
Andreja Goršek, Jožef Ritonja, Darja Pečar
BACKGROUND: Milk fermentation takes place in the presence of various micro-organisms, whereby a variety of dairy products is produced. The oldest among them is kefir, which is usually produced by fermentation of milk with kefir grains. Carbon dioxide (CO2 ), as one of the process products, also contributes to the characteristic flavor of kefir. The amount of CO2 generated during fermentation depends on bioprocessing conditions and may change, which is not desirable at the industrial level...
March 12, 2018: Journal of the Science of Food and Agriculture
Huifang Luo, Jierui Wang, Shuang Zhang, Congbo Mi
The frontal sinus, due to its unique anatomical features, has become an important element in research for individual identification. Previous studies have demonstrated the use of frontal sinus as an indicator for sex discrimination; however, the sex discrimination rate using frontal sinus was lower compared to that using the traditional morphological methods. In order to improve the sex discrimination percentage, we developed a new method involving the measurement of the frontal sinus index and frontal sinus area from lateral cephalogram radiographs...
January 3, 2018: Journal of Forensic and Legal Medicine
Benjamin J I Schellenberg, Jérémie Verner-Filion, Patrick Gaudreau, Daniel S Bailis, Marc-André K Lafrenière, Robert J Vallerand
OBJECTIVE: Passion research has focused extensively on the unique effects of both harmonious passion and obsessive passion (Vallerand, 2015). We adopted a quadripartite approach (Gaudreau & Thompson, 2010) to test whether physical and psychological well-being are distinctly related to subtypes of passion with varying within-person passion combinations: pure harmonious passion, pure obsessive passion, mixed passion, and non-passion. METHOD: In four studies (total N = 3122), we tested if passion subtypes were differentially associated with self-reported general health (Study 1), health symptoms in video gamers (Study 2), global psychological well-being (Study 3), and academic burnout (Study 4) using latent moderated structural equation modeling...
March 10, 2018: Journal of Personality
Yi Ern Cheah, Jamey D Young
Typically,13 C flux analysis relies on assumptions of both metabolic and isotopic steady state. If metabolism is steady but isotope labeling is not allowed to fully equilibrate, isotopically nonstationary metabolic flux analysis (INST-MFA) can be used to estimate fluxes. This requires solution of differential equations that describe the time-dependent labeling of network metabolites, while iteratively adjusting the flux and pool size parameters to match the transient labeling measurements. INST-MFA holds a number of unique advantages over approaches that rely solely upon steady-state isotope enrichments...
March 6, 2018: Current Opinion in Biotechnology
Ryan Nikin-Beers, Julie C Blackwood, Lauren M Childs, Stanca M Ciupe
Dengue virus causes worldwide concern with nearly 100 million infected cases reported annually. The within-host dynamics differ between primary and secondary infections, where secondary infections with a different virus serotype typically last longer, produce higher viral loads, and induce more severe disease. We build upon the variable within-host virus dynamics during infections resulting in mild dengue fever and severe dengue hemorrhagic fever. We couple these within-host virus dynamics to a population-level model through a system of partial differential equations creating an immuno-epidemiological model...
March 6, 2018: Journal of Theoretical Biology
Suzanne Bartle-Haring, Megan Ferriby, Randal Day
The purpose of this investigation was to determine whether differentiation at the couple level would act as a moderator or a mediator in the association between marital satisfaction and depressive symptoms over time. In a sample of 412 couples, a latent profile analysis was performed to determine how couple differentiation scores were clustered. An Actor/Partner Interdependence Model was then estimated via a group comparison procedure in structural equation modeling. There was no evidence of a moderating effect of differentiation...
March 9, 2018: Journal of Marital and Family Therapy
Nancy L Fleischer, Paula Lozano, Yun-Hsuan Wu, James W Hardin, Gang Meng, Angela D Liese, Geoffrey T Fong, James F Thrasher
OBJECTIVE: To examine how point-of-sale (POS) display bans, tobacco retailer density and tobacco retailer proximity were associated with smoking cessation and relapse in a cohort of smokers in Canada, where provincial POS bans were implemented differentially over time from 2004 to 2010. METHODS: Data from the 2005 to 2011 administrations of the International Tobacco Control (ITC) Canada Survey, a nationally representative cohort of adult smokers, were linked via residential geocoding with tobacco retailer data to derive for each smoker a measure of retailer density and proximity...
March 8, 2018: Tobacco Control
J F Sánchez-Pérez, F Marín, J L Morales, M Cánovas, F Alhama
Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables...
2018: PloS One
L Iess, W M Folkner, D Durante, M Parisi, Y Kaspi, E Galanti, T Guillot, W B Hubbard, D J Stevenson, J D Anderson, D R Buccino, L Gomez Casajus, A Milani, R Park, P Racioppa, D Serra, P Tortora, M Zannoni, H Cao, R Helled, J I Lunine, Y Miguel, B Militzer, S Wahl, J E P Connerney, S M Levin, S J Bolton
The gravity harmonics of a fluid, rotating planet can be decomposed into static components arising from solid-body rotation and dynamic components arising from flows. In the absence of internal dynamics, the gravity field is axially and hemispherically symmetric and is dominated by even zonal gravity harmonics J2n that are approximately proportional to qn , where q is the ratio between centrifugal acceleration and gravity at the planet's equator. Any asymmetry in the gravity field is attributed to differential rotation and deep atmospheric flows...
March 7, 2018: Nature
Meysam Hashemi, Axel Hutt, Laure Buhry, Jamie Sleigh
Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems...
March 7, 2018: Neuroinformatics
Srivatsa Bhat K, Ranjan Ganguli
In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam...
February 2018: Royal Society Open Science
G Röst, Z Vizi, I Z Kiss
We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Anna Ghazaryan, Stephane Lafortune, Vahagn Manukian
Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i...
April 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Margaret Beck, Anastasia Doikou, Simon J A Malham, Ioannis Stylianidis
We develop a method for generating solutions to large classes of evolutionary partial differential systems with non-local nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogous to the Marchenko integral equation in integrable systems. We show explicitly how this can be achieved through several examples, including reaction-diffusion systems with non-local quadratic nonlinearities and the nonlinear Schrödinger equation with a non-local cubic nonlinearity...
April 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Haitao Xu, Jesús Cuevas-Maraver, Panayotis G Kevrekidis, Anna Vainchtein
In this work, we revisit a criterion, originally proposed in Friesecke & Pego (Friesecke & Pego 2004 Nonlinearity 17 , 207-227. (doi:10.1088/0951715/17/1/013)), for the stability of solitary travelling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of this criterion from the point of view of stability theory, both at the level of the spectral analysis of the advance-delay differential equations in the co-travelling frame, as well as at that of the Floquet problem arising when considering the travelling wave as a periodic orbit modulo shift...
April 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
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