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Differential equation

Xiangnan Zhong, Haibo He, Ding Wang, Zhen Ni
In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with H∞ optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively...
July 17, 2017: IEEE Transactions on Cybernetics
Xiulan Lai, Avner Friedman
BACKGROUND: The B-raf gene is mutated in up to 66% of human malignant melanomas, and its protein product, BRAF kinase, is a key part of RAS-RAF-MEK-ERK (MAPK) pathway of cancer cell proliferation. BRAF-targeted therapy induces significant responses in the majority of patients, and the combination BRAF/MEK inhibitor enhances clinical efficacy, but the response to BRAF inhibitor and to BRAF/MEK inhibitor is short lived. On the other hand, treatment of melanoma with an immune checkpoint inhibitor, such as anti-PD-1, has lower response rate but the response is much more durable, lasting for years...
July 19, 2017: BMC Systems Biology
P Magal, A Noussair, J Pasquier, P Zongo, F Le Foll
In this paper, we consider a direct protein transfer process between cells in co-culture. Assuming that cells continually encounter each other, and from some hypotheses on cell-to-cell rules of transfer, we derive discrete and continuous Boltzmann-like integro-differential equations. The novelty of this model is to take into account multiple transfer rules. This new transfer model is used to fit the experimental data of cell-to-cell protein transfer in breast cancer.
July 18, 2017: Bulletin of Mathematical Biology
Xiaojing Wang, Yangyang Shi, Zhilan Feng, Jingan Cui
Many mathematical models for the disease transmission dynamics of Ebola have been developed and studied, particularly during and after the 2014 outbreak in West Africa. Most of these models are systems of ordinary differential equations (ODEs). One of the common assumptions made in these ODE models is that the duration of disease stages, such as latent and infectious periods, follows an exponential distribution. Gamma distributions have also been used in some of these models. It has been demonstrated that, when the models are used to evaluate disease control strategies such as quarantine or isolation, the models with exponential and Gamma distribution assumptions may generate contradictory results (Feng et al...
July 18, 2017: Bulletin of Mathematical Biology
Ping Li, Benjamin Schloss, D Jake Follmer
In this article we report a computational semantic analysis of the presidential candidates' speeches in the two major political parties in the USA. In Study One, we modeled the political semantic spaces as a function of party, candidate, and time of election, and findings revealed patterns of differences in the semantic representation of key political concepts and the changing landscapes in which the presidential candidates align or misalign with their parties in terms of the representation and organization of politically central concepts...
July 17, 2017: Behavior Research Methods
Daniel McNeish
Studies on small sample properties of multilevel models have become increasingly prominent in the methodological literature in response to the frequency with which small sample data appear in empirical studies. Simulation results generally recommend that empirical researchers employ restricted maximum likelihood estimation (REML) with a Kenward-Roger correction with small samples in frequentist contexts to minimize small sample bias in estimation and to prevent inflation of Type-I error rates. However, simulation studies focus on recommendations for best practice, and there is little to no explanation of why traditional maximum likelihood (ML) breaks down with smaller samples, what differentiates REML from ML, or how the Kenward-Roger correction remedies lingering small sample issues...
July 17, 2017: Multivariate Behavioral Research
Javier Cervera, Salvador Meseguer, Salvador Mafe
We have studied theoretically the microRNA (miRNA) intercellular transfer through voltage-gated gap junctions in terms of a biophysically-grounded system of coupled differential equations. Instead of modeling a specific system, we use a general approach describing the interplay between the genetic mechanisms and the single-cell electric potentials. The dynamics of the multicellular ensemble are simulated under different conditions including spatially-inhomogeneous transcription rates and local intercellular transfer of miRNAs...
July 17, 2017: Journal of Physical Chemistry. B
Y H Ding, S X Hu
Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm(3) and temperature T = 2000 to 10(8) K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models...
June 2017: Physics of Plasmas
Yuting Shi, Jin Wang, Shumin Li, Bo Yan, Hui Xu, Ke Zhang, Yukou Du
In this work, a sensitive and novel method for determining uric acid (UA) has been developed, in which the glassy carbon electrode (GCE) was modified with electrodeposition Au nanoparticles and used to monitor the concentration of UA with the assistant of visible light illumination. The morphology of the Au nanoparticles deposited on GCE surface were characterized by scanning electron microscope (SEM) and the nanoparticles were found to be well-dispersed spheres with the average diameter approaching 26.1 nm...
December 2017: Nanoscale Research Letters
Hiroyasu Katsuno, Makio Uwaha
We study the effect of chiral impurities on Viedma ripening using a simple reaction model. The exponential amplification of the enantiomeric excess (EE) is greatly accelerated by a smaller growth rate of solids with monomers caused by the chiral impurities. From the analysis of the model, it is found that the time evolution of the EE is essentially described by a second-order differential equation. The effect of chiral impurities is that the unstable fixed point is shifted from the racemic point, which leads to the linear amplification behavior observed experimentally...
June 2017: Physical Review. E
Sergio Bordel
Thermodynamic systems can be defined as composed by many identical interacting subsystems. Here it is shown how the dynamics of relaxation toward equilibrium of a thermodynamic system is closely related to the symmetry group of the Hamiltonian of the subsystems of which it is composed. The transitions between states driven by the interactions between identical subsystems correspond to elements of the root system associated to the symmetry group of their Hamiltonian. This imposes constraints on the relaxation dynamics of the complete thermodynamic system, which allow formulating its evolution toward equilibrium as a system of linear differential equations in which the variables are the thermodynamic forces of the system...
June 2017: Physical Review. E
AmirAli Farokhniaee, Edward W Large
Many neurons in the auditory system of the brain must encode periodic signals. These neurons under periodic stimulation display rich dynamical states including mode locking and chaotic responses. Periodic stimuli such as sinusoidal waves and amplitude modulated sounds can lead to various forms of n:m mode-locked states, in which a neuron fires n action potentials per m cycles of the stimulus. Here, we study mode-locking in the Izhikevich neurons, a reduced model of the Hodgkin-Huxley neurons. The Izhikevich model is much simpler in terms of the dimension of the coupled nonlinear differential equations compared with other existing models, but excellent for generating the complex spiking patterns observed in real neurons...
June 2017: Physical Review. E
De-Ming Deng, Yi-Ta Lu, Cheng-Hung Chang
The legality of using simple kinetic schemes to determine the stochastic properties of a complex system depends on whether the fluctuations generated from hierarchical equivalent schemes are consistent with one another. To analyze this consistency, we perform lumping processes on the stochastic differential equations and the generalized fluctuation-dissipation theorem and apply them to networks with the frequently encountered Arrhenius-type transition rates. The explicit Langevin force derived from those networks enables us to calculate the state fluctuations caused by the intrinsic and extrinsic noises on the free energy surface and deduce their relations between kinetically equivalent networks...
June 2017: Physical Review. E
David Müller, Andreas Otto, Günter Radons
In this paper, we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore, we introduce an operator theoretic framework, where the solution operator of the delay system is decomposed into the Koopman operator describing the delay access and an operator similar to the solution operator known from systems with constant delay...
June 2017: Physical Review. E
Richard J McMurtrey
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have ignited investigation into important aspects of molecular diffusion in 3D cellular architectures. This paper describes fundamental mechanics of diffusion with equations for modeling these dynamic processes under a variety of scenarios in 3D cellular tissue constructs. The effects of these diffusion processes and resultant concentration gradients are described in the context of the major molecular signaling pathways in stem cells that both mediate and are influenced by gas and nutrient concentrations, including how diffusion phenomena can affect stem cell state, cell differentiation, and metabolic states of the cell...
July 14, 2017: Stem Cells and Development
Eleonora Molinaro, Cristina Romei, Agnese Biagini, Elena Sabini, Laura Agate, Salvatore Mazzeo, Gabriele Materazzi, Stefano Sellari-Franceschini, Alessandro Ribechini, Liborio Torregrossa, Fulvio Basolo, Paolo Vitti, Rossella Elisei
Anaplastic thyroid carcinoma (ATC) is a rare malignancy, accounting for 1-2% of all thyroid cancers. Although rare, ATC accounts for the majority of deaths from thyroid carcinoma. ATC often originates in a pre-existing thyroid cancer lesion, as suggested by the simultaneous presence of areas of differentiated or poorly differentiated thyroid carcinoma. ATC is characterized by the accumulation of several oncogenic alterations, and studies have shown that an increased number of oncogenic alterations equates to an increased level of dedifferentiation and aggressiveness...
July 14, 2017: Nature Reviews. Endocrinology
Cole Zmurchok, Tim Small, Michael J Ward, Leah Edelstein-Keshet
Molecular motors such as kinesin and dynein are responsible for transporting material along microtubule networks in cells. In many contexts, motor dynamics can be modelled by a system of reaction-advection-diffusion partial differential equations (PDEs). Recently, quasi-steady-state (QSS) methods have been applied to models with linear reactions to approximate the behaviour of the full PDE system. Here, we extend this QSS reduction methodology to certain nonlinear reaction models. The QSS method relies on the assumption that the nonlinear binding and unbinding interactions of the cellular motors occur on a faster timescale than the spatial diffusion and advection processes...
July 13, 2017: Bulletin of Mathematical Biology
Andrea Beaghton, Pantelis John Beaghton, Austin Burt
BACKGROUND: The introduction of new malaria control interventions has often led to the evolution of resistance, both of the parasite to new drugs and of the mosquito vector to new insecticides, compromising the efficacy of the interventions. Recent progress in molecular and population biology raises the possibility of new genetic-based interventions, and the potential for resistance to evolve against these should be considered. Here, population modelling is used to determine the main factors affecting the likelihood that resistance will evolve against a synthetic, nuclease-based driving Y chromosome that produces a male-biased sex ratio...
July 14, 2017: Malaria Journal
David C Cicero, Elizabeth A Martin, Alexander Krieg
The Wisconsin Schizotypy Scales, including their brief versions, are among the most commonly used self-report measures of schizotypy. Although they have been used extensively in many ethnic groups, few studies have examined their differential item functioning (DIF) across groups. The current study included 1,056 Asian, 408 White, 476 Multiethnic, and 372 Hispanic undergraduates. Unidimensional models of the brief Magical Ideation Scale and Perceptual Aberration Scales fit the data well. For both scales, global tests of measurement invariance provided mixed evidence, but few of the items displayed DIF across ethnicities or between sexes within a multiple indicator multiple causes model...
July 1, 2017: Assessment
Jyothi S Prabhu, Aruna Korlimarla, C E Anupama, Annie Alexander, Rohini Raghavan, Roma Kaul, Krisha Desai, Savitha Rajarajan, Suraj Manjunath, Marjorrie Correa, R Raman, Anjali Kalamdani, Msn Prasad, Shekar Patil, K S Gopinath, B S Srinath, T S Sridhar
Hormone receptor positive (HR+) breast cancers are a heterogeneous class with differential prognosis. Although more than half of Indian women present with advanced disease, many such patients do well. We have attempted identification of biologically indolent tumors within HR+HER2- tumors based on gene expression using histological grade as a guide to tumor aggression. 144 HR+HER2- tumors were divided into subclasses based on scores derived by using transcript levels of multiple genes representing survival, proliferation, and apoptotic pathways and compared to classification by Ki-67 labeling index (LI)...
July 11, 2017: Translational Oncology
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