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Differential equation

Eva Doka, Gabor Lente
This works present a rigorous mathematical study of the effect of unavoidable inhomogeneities in laser flash photolysis experiments. There are two different kinds of inhomegenities: the first arises from diffusion, whereas the second one has geometric origins (the shapes of the excitation and detection light beams). Both of these are taken into account in our reported model, which gives rise to a set of reaction-diffusion type partial differential equations. These equations are solved by a specially developed finite volume method...
March 23, 2017: Journal of Physical Chemistry. A
James W Beck, Abigail A Scholer, Jeffrey Hughes
Disturbances are factors outside of a person's control that influence goal progress. Although disturbances are typically included in theoretical accounts of goal pursuit, relatively little empirical research has explicitly considered the effects of disturbances on the goal-striving process. We address this gap in the literature by examining the effects that disturbances have on the emotional experience of goal pursuit. More importantly, we differentiate between distance disturbances (changes to the amount of progress made) and velocity disturbances (changes to the rate of progress made)...
March 23, 2017: Journal of Applied Psychology
Indrikis A Krams, Petri T Niemelä, Giedrius Trakimas, Ronalds Krams, Gordon M Burghardt, Tatjana Krama, Aare Kuusik, Marika Mänd, Markus J Rantala, Raivo Mänd, Jukka Kekäläinen, Ilkka Sirkka, Severi Luoto, Raine Kortet
The causes and consequences of among-individual variation and covariation in behaviours are of substantial interest to behavioural ecology, but the proximate mechanisms underpinning this (co)variation are still unclear. Previous research suggests metabolic rate as a potential proximate mechanism to explain behavioural covariation. We measured the resting metabolic rate (RMR), boldness and exploration in western stutter-trilling crickets, Gryllus integer, selected differentially for short and fast development over two generations...
March 29, 2017: Proceedings. Biological Sciences
Himansu Kumar, Swapnil Tichkule, Utkarsh Raj, Saurabh Gupta, Swati Srivastava, Pritish Kumar Varadwaj
Chronic myeloid leukemia (CML) is a hematopoietic stem-cell disorder which proliferates due to abnormal growth of basophil cells. Several proangiogenic molecules have been reported to be associated in CML progression, including the hepatocyte growth factor (HGF). However, detail mechanism about the cellular distribution and function of HGF in CML is yet to be revealed. The proliferation of hematopoietic cells are regulated by some of the growth factors like interleukin 3 (IL-3), IL-6, erythropoietin, thrombopoietin, etc...
June 2016: 3 Biotech
Julie Wood, Zita Oravecz, Nina Vogel, Lizbeth Benson, Sy-Miin Chow, Pamela Cole, David E Conroy, Aaron L Pincus, Nilam Ram
Objectives: Life-span theories of aging suggest improvements and decrements in individuals' ability to regulate affect. Dynamic process models, with intensive longitudinal data, provide new opportunities to articulate specific theories about individual differences in intraindividual dynamics. This paper illustrates a method for operationalizing affect dynamics using a multilevel stochastic differential equation (SDE) model, and examines how those dynamics differ with age and trait-level tendencies to deploy emotion regulation strategies (reappraisal and suppression)...
March 2, 2017: Journals of Gerontology. Series B, Psychological Sciences and Social Sciences
Mitra Shojania Feizabadi
BACKGROUND: Drug-induced resistance is one the major obstacles that may lead to therapeutic failure during cancer treatment. Different genetic alterations occur when tumor cells divide. Among new generations of tumor cells, some may express intrinsic resistance to a specific chemotherapeutic agent. Also, some tumor cells may carry a gene that can develop resistance induced by the therapeutic drug. The methods by which the therapeutic approaches need to be revised in the occurrence of drug induced resistance is still being explored...
March 21, 2017: Theoretical Biology & Medical Modelling
Michael MacGillivray, Amy Ko, Emily Gruber, Miranda Sawyer, Eivind Almaas, Allen Holder
Constraint-based optimization, such as flux balance analysis (FBA), has become a standard systems-biology computational method to study cellular metabolisms that are assumed to be in a steady state of optimal growth. The methods are based on optimization while assuming (i) equilibrium of a linear system of ordinary differential equations, and (ii) deterministic data. However, the steady-state assumption is biologically imperfect, and several key stoichiometric coefficients are experimentally inferred from situations of inherent variation...
March 21, 2017: Scientific Reports
D A Irosh P Fernando
A preliminary model for exploring the pathogenesis of depression that involves genetic and environmental factors is described using a system of linear differential equation. The influence of environmental factors essentially involves random life events, which are modelled using a stochastic differential equation. Different scenarios, including the trajectory of the pathogenesis of depression and immunity, are described by model simulation.
August 2016: Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society
F Ortega, J Marcazzó, F Spano, M Santiago, P Molina, E Caselli
Analysis of phosphorescence curves is an alternative procedure to glow curve analysis in order to find the parameters characterizing trap and recombination centers of thermoluminescence materials. In this article a new algorithm to analyze phosphorescence curves is reported, which is derived from the set of coupled differential equation describing the carrier traffic without resorting to approximations. The new algorithm has been employed to analyze the phosphorescence curves of the K2YF5:Pr compound.
March 6, 2017: Applied Radiation and Isotopes
P J Witbooi
We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue [Formula: see text] of the basic reproduction number [Formula: see text] of the underlying deterministic model, with [Formula: see text]...
March 21, 2017: Acta Biotheoretica
Peter Ashcroft, Cassandra E R Smith, Matthew Garrod, Tobias Galla
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we decouple competition from reproduction; competition follows a birth-death process and is governed by an evolutionary game, while growth is determined by an externally controlled branching rate. In stochastic simulations we find non-monotonic behaviour of the fixation probability of mutants as the speed of growth is varied; the right amount of growth can lead to a higher success rate...
March 16, 2017: Journal of Theoretical Biology
D Bazeia, M B P N Pereira, A V Brito, B F de Oliveira, J G G S Ramos
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior...
March 21, 2017: Scientific Reports
Thomas Matthews, Kun Wang, Cuiping Li, Neb Duric, Mark Anastasio
Ultrasound computed tomography (USCT) holds great promise for breast cancer screening. Waveform inversionbased image reconstruction methods account for higher-order diffraction effects and can produce high-resolution USCT images, but are computationally demanding. Recently, a source encoding technique was combined with stochastic gradient descent to greatly reduce image reconstruction times. However, this method bundles the stochastic data fidelity term with the deterministic regularization term. This limitation can be overcome by replacing stochastic gradient descent (SGD) with a structured optimization method, such as the regularized dual averaging (RDA) method, that exploits knowledge of the composition of the cost function...
March 14, 2017: IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Markus F Weber, Erwin Frey
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations...
April 2017: Reports on Progress in Physics
Matthew J Simpson, Kai-Yin Lo, Yung-Shin Sun
BACKGROUND: Directed cell migration can be driven by a range of external stimuli, such as spatial gradients of: chemical signals (chemotaxis); adhesion sites (haptotaxis); or temperature (thermotaxis). Continuum models of cell migration typically include a diffusion term to capture the undirected component of cell motility and an advection term to capture the directed component of cell motility. However, there is no consensus in the literature about the form that the advection term takes...
March 17, 2017: BMC Systems Biology
Radu Herbei, Rajib Paul, L Mark Berliner
We examine the performance of a strategy for Markov chain Monte Carlo (MCMC) developed by simulating a discrete approximation to a stochastic differential equation (SDE). We refer to the approach as diffusion MCMC. A variety of motivations for the approach are reviewed in the context of Bayesian analysis. In particular, implementation of diffusion MCMC is very simple to set-up, even in the presence of nonlinear models and non-conjugate priors. Also, it requires comparatively little problem-specific tuning. We implement the algorithm and assess its performance for both a test case and a glaciological application...
2017: PloS One
Katharina Prochazka, Gero Vogl
Many of the world's around 6,000 languages are in danger of disappearing as people give up use of a minority language in favor of the majority language in a process called language shift. Language shift can be monitored on a large scale through the use of mathematical models by way of differential equations, for example, reaction-diffusion equations. Here, we use a different approach: we propose a model for language dynamics based on the principles of cellular automata/agent-based modeling and combine it with very detailed empirical data...
March 15, 2017: Proceedings of the National Academy of Sciences of the United States of America
M Saeedian, M Khalighi, N Azimi-Tafreshi, G R Jafari, M Ausloos
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives...
February 2017: Physical Review. E
Clóves G Rodrigues, Carlos A B Silva, José G Ramos, Roberto Luzzi
A family of what can be so-called Maxwell times which arises in the context of higher-order generalized hydrodynamics (HOGH; also called mesoscopic hydrothermodynamics) is evidenced. This is done in the framework of a HOGH built within a statistical formalism in terms of a nonequilibrium statistical ensemble formalism. It consists in a description in terms of the densities of particles and energy and their fluxes of all orders, with the motion described by a set of coupled nonlinear integro-differential equations involving them...
February 2017: Physical Review. E
Ivan B Coulamy, Andreia Saguia, Marcelo S Sarandy
We investigate the excitation dynamics at a first-order quantum phase transition (QPT). More specifically, we consider the quench-induced QPT in the quantum search algorithm, which aims at finding out a marked element in an unstructured list. We begin by deriving the exact dynamics of the model, which is shown to obey a Riccati differential equation. Then, we discuss the probabilities of success by adopting either global or local adiabaticity strategies. Moreover, we determine the disturbance of the quantum criticality as a function of the system size...
February 2017: Physical Review. E
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