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From 1870, Sophus Lies work put the theory of differential equations on a more satisfactory foundation. He showed that the integration theories of the older mathematicians can, by the introduction of what are now called Lie groups, be referred to a common source, and that ordinary differential equations that admit the same infinitesimal transformations present comparable difficulties of integration. He also emphasized the subject of transformations of contact. Lies group theory of differential equations has been certified, namely: (1) that it unifies the many ad hoc methods known for solving differential equations, and (2) that it provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations.[18]. A general approach to solve DEs uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions (Lie theory). Continuous group theory, Lie algebras, and differential geometry ...

From 1870, Sophus Lies work put the theory of differential equations on a more satisfactory foundation. He showed that the integration theories of the older mathematicians can, by the introduction of what are now called Lie groups, be referred to a common source, and that ordinary differential equations that admit the same infinitesimal transformations present comparable difficulties of integration. He also emphasized the subject of transformations of contact. Lies group theory of differential equations has been certified, namely: (1) that it unifies the many ad hoc methods known for solving differential equations, and (2) that it provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations.[18] A general approach to solve DEs uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions (Lie theory). Continuous group theory, Lie algebras, and differential geometry ...

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The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB , Mathematica , and MapleTM, A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics students field of study.Stressing applications wherever possible, the authors have written this text with the applied math, engineer, or science major in mind. It includes a number of modern topics that are not commonly found in a traditional sophomore-level text. For example, Chapter 2 covers direction fields, phase line techniques, and the Runge-Kutta method; another chapter discusses linear algebraic topics, such as transformations and eigenvalues. Chapter 6 considers linear and nonlinear systems of equations from a dynamical systems viewpoint and uses the linear algebra insights from the previous chapter; it also includes modern applications like epidemiological models

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Introduction to Ordinary Differential Equations from Korea Advanced Institute of Science and Technology. In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations ...

TY - JOUR. T1 - Mathematical equation of fusion index of tetanic contraction of skeletal muscles. AU - Watanabe, Shogo. AU - Kitawaki, T.. AU - Oka, Hisao. PY - 2010/4. Y1 - 2010/4. N2 - The fusion index (FI) is an index that can evaluate the tetanic progression of the skeletal muscles. Although the FI-frequency curve (FFC), which is obtained by changing the stimulation frequency, is greatly affected by muscle fiber type and fiber compositions, there are no reports of a mathematical equation that can express the FFC. In this study, the FFC was measured for the gastrocnemius, vastus intermedius, and soleus muscles of rats, and the mathematical equation (FFC-equation) was proposed. The FFC-equation (FI(f)) was proportional to the h-th power of f, and was in inverse proportion to the sum of the h-th power of k and the h-th power of f. f was the stimulation frequency, k was the stimulation frequency at 50% of FI, and h reflected the gradient of FFC. As a result, the approximated curve produced by ...

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Mechanistic within-host models integrating blood anti-malarial drug concentrations with the parasite-time profile provide a valuable decision tool for determining dosing regimens for anti-malarial treatments, as well as a formative component of population-level drug resistance models. We reviewed published anti-malarial pharmacokinetic-pharmacodynamic models to identify the challenges for these complex models where parameter estimation from clinical field data is limited. The inclusion of key pharmacodynamic processes in the mechanistic structure adopted varies considerably. These include the life cycle of the parasite within the red blood cell, the action of the anti-malarial on a specific stage of the life cycle, and the reduction in parasite growth associated with immunity. With regard to estimation of the pharmacodynamic parameters, the majority of studies simply compared descriptive summaries of the simulated outputs to published observations of host and parasite responses from clinical ...

Ionic polymer-metal composites (IPMCs) generate electrical potential under deformation and can be used as sensors. Recently, Zhu et al. have proposed a sensor model which describes distribution of cations, water molecules and electrical potential under bending deformation. In this paper, we discuss a simplification of the multi-physical sensor model, which is represented by a set of nonlinear partial differential equations. The nonlinear partial differential equations are simplified and approximated into a set of linear ordinary differential equations, i.e., a state-space equation model. At the end, the simplified model is validated by comparing the simulation results with those of the partial differential equation model ...

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor-ligand binding in the context of antibody-antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of an ordinary differential equation model and their microscopic equivalents as obtained from simulating the spatio-temporal binding kinetics by agent-based models. On the other hand, we investigate the impact of various receptor properties - such as their dimensionality of motion, morphology and binding valency - on the receptor-ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e. either as membrane-anchored receptors or as soluble receptors. The mapping of the

Recently, epigenetic-mediated mechanisms - which involve heritable changes in gene expression in the absence of alterations in DNA sequences - have been proposed as contributing to asthma. In this issue of the JCI, Hollingsworth and colleagues report on the effect of prenatal maternal dietary intake of methyl donors on the risk of allergic airway disease in offspring in mice and show that these effects involve epigenetic regulation (see the related article beginning on page 3462). Supplementation of the maternal diet with methyl donors was associated with greater airway allergic inflammation and IgE production in F1 and, to some extent, F2 progeny. Site-specific differences in DNA methylation and reduced transcriptional activity were detected. If these findings are confirmed, a new paradigm for asthma pathogenesis may be emerging. ...

Recently, epigenetic-mediated mechanisms - which involve heritable changes in gene expression in the absence of alterations in DNA sequences - have been proposed as contributing to asthma. In this issue of the JCI, Hollingsworth and colleagues report on the effect of prenatal maternal dietary intake of methyl donors on the risk of allergic airway disease in offspring in mice and show that these effects involve epigenetic regulation (see the related article beginning on page 3462). Supplementation of the maternal diet with methyl donors was associated with greater airway allergic inflammation and IgE production in F1 and, to some extent, F2 progeny. Site-specific differences in DNA methylation and reduced transcriptional activity were detected. If these findings are confirmed, a new paradigm for asthma pathogenesis may be emerging. ...

Abstract , References , Similar Articles , Additional Information Abstract: This paper considers the problem of stabilizing a control system governed by a combination of partial and ordinary differential equations. The partial differential equations govern the evolution of the system in the interior of some spatial domain, and the ordinary differential equations describe the evolution of the boundary data; the control enters through the boundary ordinary differential equations in a bilinear fashion. We provide sufficient conditions for feedback stabilization of such ``hybrid systems. Two examples to wave equations with dynamic boundary conditions are provided ...

TY - JOUR. T1 - Tumor growth dynamics with nutrient limitation and cell proliferation time delay. AU - Alsheri, Ahuod. AU - Alzahrani, Ebraheem O.. AU - Asiri, Asim. AU - El-Dessoky, Mohamed M.. AU - Kuang, Yang. PY - 2017/12/1. Y1 - 2017/12/1. N2 - It is known that avascular spherical solid tumors grow monotonically, often tends to a limiting final size. This is repeatedly confirmed by various mathematical models consisting of mostly ordinary differential equations. However, cell growth is limited by nutrient and its proliferation incurs a time delay. In this paper, we formulate a nutrient limited compartmental model of avascular spherical solid tumor growth with cell proliferation time delay and study its limiting dynamics. The nutrient is assumed to enter the tumor proportional to its surface area. This model is a modification of a recent model which is built on a two-compartment model of cancer cell growth with transitions between proliferating and quiescent cells. Due to the limitation of ...

Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic

Attempts to formulate realistic models of the development of the human oculomotor control system have led to the conclusion that evolutionary factors play a crucial role. Moreover, even rather coarse simulations of the biological evolutionary processes result in adaptable control systems that are considerably more efficient than those designed by human researchers. In this paper I shall describe some of the aspects of these biological models that are likely to be useful for building robot control systems. In particular, I shall consider the evolution of appropriate innate starting points for learning/adaptation, patterns of learning rates that vary across different system components, learning rates that vary during the systems lifetime, and the relevance of individual differences across the evolved populations.. ...

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Mathematics is a very helpful tool that can be used to describe naturally arising phenomena, quantity, structure, shape, change, and relationships.What constitutes the notion of useless anyway? Mathematical equations are simply there to state the relationship of two expressions. There is also an infinite amount of mathematical equations, so you could not possibly write all the useless ones here anyway. Because mathematical equations can be created indiscriminately, there will be infinite numbers of useless mathematical equations and infinite numbers of useful mathematical equations depending on your definition of useless ...

Mathematics is a very helpful tool that can be used to describe naturally arising phenomena, quantity, structure, shape, change, and relationships.What constitutes the notion of useless anyway? Mathematical equations are simply there to state the relationship of two expressions. There is also an infinite amount of mathematical equations, so you could not possibly write all the useless ones here anyway. Because mathematical equations can be created indiscriminately, there will be infinite numbers of useless mathematical equations and infinite numbers of useful mathematical equations depending on your definition of useless ...

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Membranes are the most common cellular structures in both plants and animals. They are now recognized as being involved in almost all aspects of cellular activity ranging from motility and food entrapment in simple unicellular organisms, to energy transduction, immunorecognition, nerve conduction and biosynthesis in plants and higher organisms. This functional diversity is reflected in the wide variety of lipids and particularly of proteins that compose different membranes. An understanding of the physical principles that govern the molecular organization of membranes is essential for an understanding of their physiological roles since structure and function are much more interdependent in membranes than in, say, simple chemical reactions in solution. We must recognize, however, that the word understanding means different things in different disciplines, and nowhere is this more apparent than in this multidisciplinary area where biology, chemistry and physics meet ...

The reconstruction of gene regulatory networks from time series gene expression data is one of the most difficult problems in systems biology. This is due to several reasons, among them the combinatorial explosion of possible network topologies, limited information content of the experimental data with high levels of noise, and the complexity of gene regulation at the transcriptional, translational and post-translational levels. At the same time, quantitative, dynamic models, ideally with probability distributions over model topologies and parameters, are highly desirable. We present a novel approach to infer such models from data, based on nonlinear differential equations, which we embed into a stochastic Bayesian framework. We thus address both the stochasticity of experimental data and the need for quantitative dynamic models. Furthermore, the Bayesian framework allows it to easily integrate prior knowledge into the inference process. Using stochastic sampling from the Bayes posterior distribution,

ABSTRACT:We consider a minimal cascade model previously proposed ~1 for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a bicyclic phosphorylation-dephosphorylation cascade involving cyclin and cdc2 kinase. By constructing stability diagrams showing domains of periodic behavior as a function of the maximum rates of the kinases and phosphatases involved in the two cycles of the cascade, we investigate the role of these converter enzymes in the oscillatory mechanism. Oscillations occur when the balance of kinase and phosphatase rates in each cycle is in a range bounded by two critical values. The results suggest ways to arrest the mitotic oscillator by altering the maximum rates of the converter enzymes. These results bear on the control of cell proliferation. The original paper reference is cited below: Arresting the mitotic oscillator and the control of cell proliferation: insights from a cascade model for cdc2 kinase activation, Goldbeter, A. and ...

Title: Stochastic and deterministic spatial models for complex systems Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge, which is fundamental in any multi-scale modeling approach for complex systems, is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE, in particular, why naively adding diffusion terms to ordinary differential equations might fail to account for spatial dynamics in population models. These connections also explain how ...

Title: Stochastic and deterministic spatial models for complex systems Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge, which is fundamental in any multi-scale modeling approach for complex systems, is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE, in particular, why naively adding diffusion terms to ordinary differential equations might fail to account for spatial dynamics in population models. These connections also explain how ...

Greaves, M. F. (2004) Biological models for leukaemia and lymphoma. In: Mechanisms of Carcinogenesis: Contributions of Molecular Epidemiology. IARC Scientific Publications, 157 . IARC Press, Lyon, France, pp. 351-372. ISBN 978-928322157-9 ...

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Multiscale modeling has emerged as a powerful approach to interpret and capitalize on the biological complexity underlying blood vessel growth. We present a multiscale model of angiogenesis that heralds the start of a large scale initiative to integrate related biological models. The goal of the integrative project is to better understand underlying biological mechanisms from the molecular level up through the organ systems level, and test new therapeutic strategies. Model methodology includes ordinary and partial differential equations, stochastic models, complex logical rules, and agent-based architectures. Current modules represent blood flow, oxygen transport, growth factor distribution and signaling, cell sensing, cell movement and cell proliferation. Challenges of integration lie in connecting modules that are diversely designed, seamlessly coordinating feedback, and representing spatial and time scales from ligand-receptor interactions and intracellular signaling, to cell-level movement ...

Madzvamuse, A. and Maini, P. K. and Wathen, A. J. (2005) A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains. Journal of Scientific Computing, 24 (2). pp. 247-262. Maini, P. K. (2005) Foreword, Cellular Automaton Modeling of Biological Pattern Formation. In: Cellular Automaton Modeling of Biological Pattern Formation. Birkhauser, Boston, vii-viii. ISBN 987654321 Maini, P. K. (2005) Morphogenesis, Biological, Encyclopedia of Nonlinear Science. Encyclopedia of Nonlinear Science, n/a (n/a). pp. 587-588. Maini, P. K. and Dallon, J. C. and Sherratt, J. A. (2005) A multiscale model for collagen alignment in wound healing. Journal of Physiology, 561P, . 5P. Meyer-Hermann, M. E. and Maini, P. K. (2005) Cutting edge: back to "one-way" germinal centers. The Journal of Immunology, 174 (5). pp. 2489-2493. Meyer-Hermann, M. E. and Maini, P. K. (2005) Interpreting two-photon imaging data of lymphocyte motility. Physical Review E, 71 (6). 061912-1. ...

Partial differential equations arise in the mathematical modeling of many physical, chemical, and biological phenomena. They play a crucial role in diverse subject areas, such as fluid dynamics, electromagnetism, material science, astrophysics, financial modeling, and hydrogeology, for example. This course is an introduction to partial differential equations with emphasis on the wave, diffusion and Laplace equations. The focus will be on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Methods of solutions include separation of variables using orthogonal series, transform methods, method of characteristics, and some numerical methods. 3 sh.. Prerequisites: MATH 420.. ...

Biological systems are inherently hierarchal and multiscale in time and space. A major challenge of systems biology is to describe biological systems as a computational model, which can be used to derive novel hypothesis and drive experiments leading to new knowledge. The constraint-based reconstruction and analysis approach has been successfully applied to metabolism and to the macromolecular synthesis machinery assembly. Here, we present the first integrated stoichiometric multiscale model of metabolism and macromolecular synthesis for Escherichia coli K12 MG1655, which describes the sequence-specific synthesis and function of almost 2000 gene products at molecular detail. We added linear constraints, which couple enzyme synthesis and catalysis reactions. Comparison with experimental data showed improvement of growth phenotype prediction with the multiscale model over E. colis metabolic model alone. Many of the genes covered by this integrated model are well conserved across enterobacters and ...

We mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative for a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). These models incorporate parameters that directly represent known physiological properties. Other parameters have been introduced to reproduce empirical observations. We used sensitivity analysis to investigate the influence of model parameters on the ODE solutions. In addition, we expanded an existing approach to treating initial conditions as parameters and to calculating second- order sensitivities. Furthermore, we used a global sensitivity analysis approach to include finite ranges of parameter values. Hence, a theoretician striving for model reduction could use the method for identifying particularly low sensitivities to detect superfluous parameters. An experimenter could use it for identifying particularly high sensitivities to improve parameter ...

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An accurate cell-integrated semi Lagrangian and semi-implicit scheme based on step-functions. A new and very accurate cell-integrated semi Lagrangian (CISL) two time level scheme has been formulated and tested for the shallow water equations in a plane channel model with realistic variation of the Coriolis-parameter and including topography. The implementation includes semi-implicit time stepping of the gravity wave terms. Furthermore, two-dimensional advection of passive tracers has been tested in idealized flows as well as in a fully general flow.. Regarding basic features, the new formulation is based on step-functions, which implicitly are advected with the flow across cell boundaries. The scheme is exact in case of passive advection by a flow that is constant in time and space. This means that the accuracy is of indefinite order. In addition to this attractive feature the scheme shows very small numerical dispersion in fully non-linear and divergent flows and in such flows the scheme is ...

Mathematical models are powerful tools in modern life sciences. Similar to experimental techniques, models facilitate the study of biological processes and hypothesis testing. Furthermore, models allow for the integrative assessment of multiple datasets as well as the prediction of latent variables and the design of future experiments. To achieve this, the model structure has to be defined and the unknown model parameters have to be estimated from experimental data. These tasks are challenging for a wide range of application problems. In this presentation, I will outline some of our work on data-driven mathematical modelling. Firstly, I will talk about the modelling of intracellular signalling using large-scale ordinary differential equations (ODEs). I will present a scalable optimization framework we developed to calibrate ODEs with thousands of state variables and parameters, and how our models outperform established statistical models. Secondly, I will talk about the modelling of ...

Computational cardiac models provide important insights into the underlying mechanisms of heart function. Parameter estimation in these models is an ongoing challenge with many existing models being overparameterised. Sensitivity analysis presents a key tool for exploring the parameter identifiability. While existing methods provide insights into the significance of the parameters, they are unable to identify redundant parameters in an efficient manner. We present a new singular value decomposition based algorithm for determining parameter identifiability in cardiac models. Using this local sensitivity approach, we investigate the Ten Tusscher 2004 rapid inward rectifier potassium and the Mahajan 2008 rabbit L-type calcium currents in ventricular myocyte models. We identify non-significant and redundant parameters and improve the models by reducing them to minimum ones that are validated to have only identifiable parameters. The newly proposed approach provides a new method for model validation and

Would you like to know how to customize the promotion of Actual Configuration Items (CIs) in SmartCloud Control Desk and Change and Configuration Management Database (CCMDB)? The new wiki article System Properties used by Actual CI Promotion describes several system properties and maxvars that you can use to affect the behavior of promotions. For example, you can define whether a promotion should create attributes even if the effective value is blank. This article is available on the SmartCloud Control Desk wiki and the Change and Configuration Management Database wiki .

What is experimental literature? How has experimentation affected the course of literary history, and how is it shaping literary expression today? Literary experiment has always been diverse and challenging, but never more so than in our age of digital…

Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behaviour of the model through asymptotic and local perturbation analysis, in which the role of the geometry is ...

The study of Complex Systems focuses on how interactions of constituents within a system, individually or grouped into clusters, produce behavioral patterns locally or globally and how these interact with the external environment. Over the last few decades the study of Complex Systems has gone through a growing rate of interest and today, given a sufficiently big set of data, we are able to construct comprehensive models describing emerging characteristics and properties of complex phenomena transcending the different domains of physical, biological and social sciences. The use of network theory has shown, amongst others, a particular t in describing statical and dynamical correlations of complex data sets because its ability to deal not only with deterministic quantities but also with probabilistic methods. A complex system is generally an open system flexible in adapting to variable external conditions in the way that it exchanges information with environment and adjusts its internal structure ...

Biological pattern formation often relies on self-organization, integrating biochemical with mechanical patterning processes. Such patterns are particularly important during embryogenesis, as they increase spatial complexity through a sequence of organizing processes that generally build upon previously established pre-patterns. How pre-patterns control self-organization remains unexplored. Here we investigate PAR polarity establishment in the C. elegans zygote, by combining measurements of the spatial distribution of protein numbers and fluxes with a physical theory. We characterize the handover from a pre-pattern to mechanochemical self-organization, and find that guiding cues from the centrosome steer the patterning system comprised of PAR proteins and the actomyosin cortex to a transition point beyond which the patterned state becomes self-organized. This mechanism of controlled pattern formation integrates mechanical and molecular aspects of biological pattern formation with guiding cues. ...

Article Estimation of total nitrogen transport and retention during flow in a catchment using a mass balance model incorporating the effects of land cover distribution and human activity information. The load of total nitrogen (TN) in stream water wa...

Brain cancer is a very complex and deadly disease. Traditional diagnoses and treatments of this disease are from in vitro experimental observations. Although biologists have developed many experimental data at the molecular, cellular, micro-environmental and tissue scales, only very few scientists have integrated these data into multi-scale models to study tumor response to treatment.. Cellular automata (CA) methods have been widely applied to model brain tumor growth [1, 2]. Although CA models are good at describing cell-cell and cell-microenvironment interactions, this type of discrete modelling approach falls short on investigating most fluid dynamic aspects of the tumor microenvironment. Alternatively, Continuum models employ systems of partial differential equations to simulate the solid tumor invasion by updating boundaries of different sub-domains of tumor based on the level-set method [3, 4]. It is, however, hard with this approach to describe cell-cell interactions, such as the ...

In this work, we develop a mathematical formalism based on a 3D in vitro model that is used to simulate the early stages of angiogenesis. The model treats cells as individual entities that are migrating as a result of chemotaxis and durotaxis. The phenotypes used here are endothelial cells that can be distinguished into stalk and tip (leading) cells. The model takes into account the dynamic interaction and interchange between both phenotypes. Next to the cells, the model takes into account several proteins such as vascular endothelial growth factor, delta-like ligand 4, urokinase plasminogen activator and matrix metalloproteinase, which are computed through the solution of a system of reaction-diffusion equations. The method used in the present study is classified into the hybrid approaches. The present study, implemented in three spatial dimensions, demonstrates the feasibility of the approach that is qualitatively confirmed by experimental results ...

MODULE 3: INTEGRAL CALCULUS. VTU Important Questions. Lecture 1: Review of Integral Calculus. Lecture 2: Evaluation of Multiple Integrals. Lecture 3: Evaluation of Double Integrals over the region. Lecture 4: Changing the Order of Integration. Lecture 5: Changing into Polar Coordinates. Lecture 6: Applications of Multiple Integrals. Lecture 7: Beta & Gamma functions - Properties. Lecture 8: Problems on Gamma function. Lecture 9: Problems on Beta functions. MODULE 4: DIFFERENTIAL EQUATIONS. VTU Important Questions. Lecture 1: Exact - Reducible to Exact D.E. - Problems. Lecture 2: Bernoullis Differential Equations. Lecture 3: Applications - Orthogonal Trajectories. Lecture 4: Applications - Newtons Law of Cooling Lecture 5: Applications - Electrical Circuits. Lecture 6: Nonlinear Differential Equations. Lecture 7: Clairauts Equation - Problems. Lecture 8: Reducible to Clairauts equation ...

In the last three decades, several models on the interaction of glucose and insulin have appeared in the literature, the mostly used one is generally known as the "minimal model" which was first published in 1979 and modified in 1986. Recently, this minimal model has been questioned by De Gaetano and Arino [4] from both physiological and modeling aspects. Instead, they proposed a new and mathematically more reasonable model, called "dynamic model". Their model makes use of certain simple and specific functions and introduces time delay in a particular way. The outcome is that the model always admits a globally asymptotically stable steady state. The objective of this paper is to find out if and how this outcome depends on the specific choice of functions and the way delay is incorporated. To this end, we generalize the dynamical model to allow more general functions and an alternative way of incorporating time delay. Our findings show that in theory, such models can possess unstable positive ...

The aim of this work is to study, by means of computational simulations, the induction and sustaining of nonsynaptic epileptiform activity.The computational model consists of a network of cellular bodies of neurons and glial cells connected to a three-dimensional (3D) network of juxtaposed extracellular compartments. the extracellular electrodiffusion calculation was used to simulate the extracellular potential. Each cellular body was represented in terms of the transmembrane ionic transports (Na(+)/K(+) pumps, ionic channels, and cotransport mechanisms), the intercellular electrodiffusion through gap-junctions, and the neuronal interaction by electric field and the variation of cellular volume.The computational model allows simulating the nonsynaptic epileptiform activity and the extracellular potential captured the main feature of the experimental measurements. the simulations of the concomitant ionic fluxes and concentrations can be used to propose the basic mechanisms involved in the ...

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Robustness of system behavior to parameter variation. Correlation between the time-binned PSTH of equally-spaced groups of neurons responding to the same object

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This workshop, closely related to DArcy Thompsons legacy, will focus on recent advances, mathematical challenges, and promising new directions in research on mathematical aspects of form in living systems. Stochastic models and topological approaches, including knot theory, have been employed to study shape evolution, for example the structure of the DNA. Cellular and developmental biology have recently seen a surge in the use of mathematical models and new conceptual frameworks for problems such as the self-organisation of the cytoskeleton or gradients of morphogens in embryos. However, the constitutive features of living systems pose unique technical and conceptual challenges. Some of these challenges concern construction a multiscale framework for agent-based models, and employing non-equilibrium physics to address non-conservative nature of living systems, using continuum models such as the (visco)elasticity of growing bodies.. Workshop details and registration will be available at ...

Many mathematical models have been proposed for the process of cell polarization. Some of these are functional models that capture a class of dynamical behaviour, whereas others are derived from features of signalling molecules. Some mechanistic models are detailed, and therefore complex, whereas others are simplified. Each type contributes to our understanding of cell polarization. However, the huge variety at different levels of detail makes comparisons challenging. Here, we provide examples of both elementary and more detailed models for polarization. We also display how a recent mathematical method, local perturbation analysis, can provide an appropriate tool for such comparisons. This technique simplifies and speeds up the model development process by revealing the effect of model extensions, parameter variations and in silico manipulations such as knock-out or over-expression of key molecules. Finally, simulations in both one dimension and two dimensions, and particularly in deforming two

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This paper presents a parametric study of the effects of radiation heat loss and non-constant heating on the measurement accuracy of thermal properties of micro/nanoscale

TY - JOUR. T1 - Influence of the nuclear membrane, active transport, and cell shape on the Hes1 and p53-Mdm2 pathways. T2 - Bulletin of Mathematical Biology. AU - Sturrock,Marc. AU - Terry,Alan J.. AU - Xirodimas,Dimitris P.. AU - Thompson,Alastair M.. AU - Chaplain,Mark A. J.. PY - 2012/7. Y1 - 2012/7. N2 - There are many intracellular signalling pathways where the spatial distribution of the molecular species cannot be neglected. These pathways often contain negative feedback loops and can exhibit oscillatory dynamics in space and time. Two such pathways are those involving Hes1 and p53-Mdm2, both of which are implicated in cancer.In this paper we further develop the partial differential equation (PDE) models of Sturrock et al. (J. Theor. Biol., 273:15-31, 2011) which were used to study these dynamics. We extend these PDE models by including a nuclear membrane and active transport, assuming that proteins are convected in the cytoplasm towards the nucleus in order to model transport along ...

The Membership Focal Points are a network of dedicated staff based in the IUCN regional and country Offices. Please note that in addition to the below list, there are a number of national Membership Focal Points.. Please contact the relevant Membership Focal Point below for any necessary assistance, who will of course let you know if there is a national focal point for your country/territory. N.B. The Membership Focal Points are listed according to Secretariats operational regions/areas, not the official Statutory regions.. ...

The Membership Focal Points are a network of dedicated staff based in the IUCN regional and country Offices. Please note that in addition to the below list, there are a number of national Membership Focal Points.. Please contact the relevant Membership Focal Point below for any necessary assistance, who will of course let you know if there is a national focal point for your country/territory. N.B. The Membership Focal Points are listed according to Secretariats operational regions/areas, not the official Statutory regions.. ...

Many processes in physics, the life sciences and technology that evolve in time are modeled by initial and boundary value problems for partial differential or integro-differential equations. The resulting mathematical theory of Evolution Equations involves tools from many fields of mathematical analysis, notably from functional analysis, operator theory and partial differential equations. This course is a self-contained introduction to the subject. It covers background materials like duality theory, the Bochner integral, vector-valued analytic functions, distributions and Fourier multipliers, vector-valued Laplace transforms, Tauberian theorems, asymptotic analysis, and spectral theory for closed operators on Banach spaces. The theory of Cauchy problems and operator semigroups will be developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, numerical approximation, and asymptotic behavior of solutions will be covered and diverse applications to concrete ...

This study examines two factors which affect the dimensions of the postcranial skeleton of Bovidae: physical constraints of increasing size and adaptations to particular habitats or modes of locomotion. Total limb lengths, lengths of proximal bones, diameters, and areas of long bones all scale more or less predictably with body size. All lengths scale with negative allometry, whereas areas and diameters vary from slightly negative to positive, depending on the bone. Comparisons of exponents of the scaling relationships to expectations of geometric and elastic scaling theory show that bovids do not scale geometrically, and in some dimensions seem to scale elastically. However, elastic factors cannot be the sole physical constraint governing scaling since many dimensions differ significantly from elastic theory. In addition, some limb elements show changes in gross morphology which violate the assumptions of elastic theory. Length of radius, metacarpal, and metatarsal do not scale predictably with ...

External Factors and their Influence on Gene ExpressionBy Jessica SaxtonAbstractThe discovery of DNA as the source of heredity and genetics opened countless doors for the development of more theories on genetics. Through the development of the known ge...

The effect of radiation on magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was studied. The governing system of partial differential equations was transformed into ordinary differential equations before being solved numerically by an implicit finite-difference method. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. It was found that the local heat transfer rate at the surface decreases with increasing values of the magnetic and radiation parameters ...

Thanks for your answers. Im not sure I was clear in my original post. Im trying to determine the basis or most fundamental principle associated with the principle of least action (or stationary action). The laws of motion can be derived from that principle. Since they can be derived from it, I dont have to rely on them being correct beforehand; thats the whole point of the principle of least action. I should be able to calculate the Lagrangian and the correct equations should just fall out. Feynman seemed to indicate that the most fundamental principle is that the proper laws of motion will follow curves with the smallest action (or stationary action). However, there is one other requirement according to his article -- for the curves to be valid, they must start and end at the same point ...

There a wide variety of biological theories of ageing from macro-level concepts such as evolutionary trade-offs and reliability theory to system-based theories of neuroendocrine and immune function and molecular and cellular theories such as the role of a biological clock. Animal studies can elegantly demonstrate the role of specific pathways such as insulin signalling but their relevance to human ageing remains controversial. Fundamentally, the loss of homeostatic control across a wide range of systems may suggest that no single pathway is necessary or sufficient for ageing. The new findings from GWAS studies of chronic diseases may also highlight commonality of pathways across phenotypes.. Within the context of the Halcyon programme we will present preliminary results around our work on telomeres, the hypothalamic pituitary axis and genetic variants on potential ageing traits. We will discuss future outputs as well the challenges of exploring these ideas within an epidemiological ...

A new two-dimensional surfactant flooding simulator for a three-component (water, petroleum, chemical), two-phase (aqueous, oleous) system in porous media is developed and analyzed. The compositional physical model is governed by a system of non-linear partial differential equations composed of Darcys and mass conservation equations. The system is then numerically solved by a finite difference method using the IMPEC (IMplicit Pressure and Explicit Concentration) scheme. Physical properties are described by a set of concentration-dependent algebraic equations. Additionally, a novel numerical stability analysis is presented in order to study the robustness of the new simulator. The oil recovery factor showed a strong dependency on the surfactant properties and phase behavior, which should be carefully evaluated. In order to achieve this, the new simulator utilizes and modifies a simplified ternary diagram to model accurately the component partitioning. Results showed that surfactant partitioning ...

Protected: How external factors can balloon your application GC pause times2017-03-132017-07-13https://www.jclarity.com/wp-content/uploads/2015/02/JClarity_logo_tagline3.pngjClarityhttps://www.jclarity.com/wp-content/uploads/2015/02/JClarity_logo_tagline3.png200px200px ...

Our approach to the problem of understanding the nonlinear-optical response of a material focuses on fundamental concepts, which are exact and lead to broad results that encompass all material systems. For example, one can calculate precisely and without approximation the fundamental limit of the efficiency
Organic nonlinear optics

Provides a broad spectrum of numerical techniques and real life applications of these techniques All fundamentally important aspects of numerical

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Abstract , References , Similar Articles , Additional Information Abstract: It is shown by means of some examples from the theories of linear algebraic equations, linear integral equations and nonlinear differential equations that the effectiveness of the method of expanding a solution in a power series in terms of a parameter may in many cases be greatly increased by expanding in terms of a suitably chosen function of the parameter. This is particularly the case when the physical setting of the problem allows only positive values of the parameter to enter ...

Heart ValvesRabkin, Elena, and Frederick J. Clinical Applications and Underlying PrinciplesLiu, Yanchun, Fuguo Chen, Wei Liu, Lei Cui, Qingxin Shang, Wangyao Xia, Jian Wang, Yimin Cui, Guanghui Yang, Deli Liu, Juanjuan Wu, Rong Xu, Samuel D. Mao, Jinshu, Liguo Zhao, Kang de Yao, Qingxin Shang, Guanghui Yang, and Yilin Cao. Wanga, Xiaohong, Jianbiao Ma, Qingling Feng, and Fuzhai Cui. China, and online CountriesMelkerson, M. This scaffolds one of over 2,200 animals on read Meaning in Absurdity: What bizarre phenomena can tell us about the nature. be people for this read Meaning in the cells modified along the cell. Edward P. Von der Porten 1933-2018 Hier kannst du read Meaning ß! Bitte immer completion geraten T Deutsch-Englisch-Ü bersetzung eintragen( Formatierung siehe Guidelines), primä fü mit fibrosis religion Beleg im Kommentarfeld. Du kannst depression means part way; manifest century, wenn du dich einloggst package relationship Vorschlä role im Contribute-Bereich epithelium; den; ...

Sprouting angiogenesis, where new blood vessels grow from pre-existing ones, is a complex process where biochemical and mechanical signals regulate endothelial cell proliferation and movement. It is relevant in determining the malignancy of several tumor lesions including glioblastomas. Mathematical descriptions of sprouting angiogenesis have to take into consideration biological signals as well as relevant physical processes, in particular the mechanical interplay between adjacent endothelial cells and the extracellular microenvironment. In this work, we introduce the first phase-field continuous model of sprouting angiogenesis capable of predicting sprout morphology as a function of the elastic properties of the tissues and the traction forces exerted by the cells. The model is very compact, only consisting of three coupled partial differential equations, and has the clear advantage of a reduced number of parameters. This model allows us to describe sprout growth as a function of the cell-cell ...

This paper is an introduction to biologically oriented computer laboratory projects using Excel. These projects help students develop mathematical and computational skills needed to pursue quantitatively oriented biological problems. Necessary Excel techniques and biological background will be provided. These projects are appropriate in calculus, biocalculus, modeling, and differential equations courses ...

How are muscles connected to bones at the cellular/tissue level? E.g., how are the ligaments and muscles attached to each other and the bone at the molecular level? Im trying to understand what "keeps them there". Thanks!!! ...

Cell signaling networks are complex systems that integrate information from the cellular environment (1-5). Maps of complex networks were derived by interconnecting the individual pathways obtained from experimental data (6, 7). These studies revealed that signaling networks contain numerous features, such as feedback and feedforward loops (8, 9), which render it virtually impossible for the human mind to decipher how signals are integrated within the pathways. Thus, computational approaches are needed to elucidate the regulatory properties of signaling networks (10-12).. Several groups have used ordinary differential equations (ODE) to analyze the dynamics of signaling networks and generate experimentally testable predictions (6, 13-17). The use of mass action ODE modeling, however, is impaired because of incomplete knowledge about the concentrations and kinetics of signaling intermediates.. Inferring the parameters for mass action modeling in signaling networks is challenging. The most common ...

Abstract: Techniques for modeling living biological systems include receiving constant values for multiple interaction factors w.sub.ij. A set of initial state values is received for state variables that indicate relevant properties of a living biological system. Also received is a set of trial values for perturbation variables that indicate factors that might affect one or more of the relevant properties of the biological system. A temporal change in a value for a particular state variable is determined based on a non-linear transformation of a sum of the trial value for the perturbation that affects the particular state added to a sum of all non-zero values for a product of w.sub.ij and a state variable over all state variables. In some embodiments, measurement-based values are received for a measurable subset of the state variables. Values for the constant interaction factors w.sub.ij are determined based on the measurement-based values ...

Comparative biochemistry demonstrates that the metabolites, complex biochemical networks, enzymes and regulatory mechanisms essential to all living cells are conserved in amazing detail throughout evolution. Thus, in order to evolve, an organism must overcome new adverse conditions without creating different but equally dangerous alterations in its ongoing successful metabolic relationship with its environment. Evidence suggests that stable long-term acquisitive evolution results from minor increases in mutation rates of genes related to a particular stress, with minimal disturbance to the balanced and resilient metabolism critical for responding to an unpredictable environment. Microorganisms have evolved specific biochemical feedback mechanisms that direct mutations to genes derepressed by starvation or other stressors in their environment. Transcription of the activated genes creates localized supercoiling and DNA secondary structures with unpaired bases vulnerable to mutation. The resulting ...

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BACKGROUND: Mathematic models and sensitivity analyses of biologic pathways have been used for exploring the dynamics and for detecting the key components of signaling pathways. METHODS: The authors previously developed a mathematic model of the epidermal growth factor receptor-extracellular signal-regulated protein kinase (EGFR-ERK) pathway using ordinary differential equations from existing EGFR-ERK pathway models. By using prolonged ERK activation as an indicator that may lead to cell proliferation under certain circumstances, in the current study, a pathway sensitivity analysis was performed to test its capability of detecting pro-proliferative activities through altered protein levels to examine the effects on ERK activation. RESULTS: The analysis revealed that 12 of 20 oncoproteins and 4 of 5 tumor suppressors were detected, consistent with reported experimental works. Because pathway dynamics depend on many factors, some of which were not included in the current models, failure to detect ...

The set of linear differential equations formulated by Bolie to describe the mechanism of homeostatic control of blood glucose are written as a vector equation of the form dXdt AX Ft, where the elements of the A matrix represent combinations of the ten independent parameters of the Bolie model. Parameter values are determined by minimizing the system cost function, which is defined as the integrated square of the difference between the model solution and the actual data. The Fletcher-Reeves function minimization technique is used with the linear model to find the minimum of the cost function and therefore establish the most likely values of the linear system parameters. This model is then extended to include all possible second-order nonlinear terms. Analytical expressions are derived for both models for the cost function and gradient of the cost function in the direction of some general perturbation matrix. The analysis of the results indicate that seven of the ten model parameters are invariant for

Essential knowledge 2.D.1: All biological systems from cells and organisms to populations, communities and ecosystems are affected by complex biotic and abiotic interactions involving exchange of matter and free ...

To understand this response, we constructed multiple models of the p53-Mdm2 negative feedback loop ranging in detail from a minimal 3-equation abstract model to a detailed, 25-equation mass-action model. These models vary both in their representations of the species, as well as their reactions with one another. In order to compare their mechanisms of operation, we are challenged to identify lumped parameters that can be computationally measured from each model. With such metrics in hand, it would be possible to compare their relationship to features of output trajectories across multiple models.. We have developed a small-signal technique to obtain two such metrics, and can compute the gain and transit time around feedback loops consisting of cascades of nonlinear chemical reactions. This method reduces to the lifetime of species in a reaction cascade under hypothesis that allow this lifetime to be computed. These particular metrics are motivated by the fact that many biological systems are ...

ABSTRACT: A total of 16 data sets on wild and cultivated fishes, crustaceans and molluscs were used to test and compare conventional growth curves (von Bertalanffy, Logistic, Gompertz and Richards) and a new growth model. Statistical properties for estimation of the models were evaluated and compared to determine suitability. The absolute value of the Hougaard measure of skewness of parameter estimates (h) was used as the criterion to evaluate statistical behavior of the models. For conventional curves, the cases where the estimates were severely skewed or contained considerable nonlinearity (h , 0.15) were: von Bertalanffy (93.5%), Logistic (87.5%), Gompertz (85.1%) and Richards (97.6%). Depending on the parameterization used in the new model, 87.5 to 91.6% had negligible skewness (h ≤ 0.1), indicating desirable close-to-linear behavior and better performance than conventional growth curves. The poor statistical properties for estimation of conventional growth curves call for a critical ...

View Notes - Lecture Week 1 & 2 from AHS 132 at Nassau CC. Homeostasis
Control or regulation of bodily processes at optimal levels Maintain normal values of heart rate, blood pressure, pH, blood

The development of neuroscience over the past 50 years has some similarities with the development of physics in the 17th century. Towards the beginning of that century, Bacon promoted the systematic gathering of experimental data and the induction of scientific truth; towards the end, Newton expressed his principles of gravitation and motion in a concise set of mathematical equations that made precise falsifiable predictions. This paper expresses the opinion that as neuroscience comes of age, it needs to move away from amassing large quantities of data about the brain, and adopt a popperian model in which theories are developed that can make strong falsifiable predictions and guide future experimental work ...

In many important physical systems involving both diffusion and nonlinearity it often occurs that initially diffusion is the dominant mechanism. The question then arises as to whether or not linearization provides a uniformly valid first approximation for large times. The author attempts to partially answer this question by examining a number of simple model equations, both deterministic and stochastic. Several of the models are physically important and have been treated incorrectly in recent works. A major part of the analysis involves constructing asymptotic expansions for an interesting class of multidimensional integrals. (Author)(*INTEGRAL EQUATIONS

... ON THE MECHANISM OF COMPETITION IN YEAST CELLS. (1) No mathematical theories can be accepted by biologists without a most careful experimental verification. We can but agree with the following remarks made in Nature (H. T. H. P. 31) concerning the mathematical theory of the struggle for existence developed by Vito Volterra: "This work is connected with Prof. Volterras researches on integro-differential equations and their applications to mechanics. In view of the simplifying hypothesis adopted, the results are not likely to be accepted by biologists until they have been confirmed experimentally, but this work has as yet scarcely begun." First of all, very reasonable doubts may arise whether the equations of the struggle for existence given in the preceding chapter express the essence of the processes of competition, or whether they are merely empirical expressions. everybody remembers the attempt to study from a purely formalistic viewpoint the phenomena of heredity by calculating ...

Much of the study of turbulence requires statistics and stochastic processes, simply because the instanteous motions are too complicated to understand. This should not be taken to mean that the govering equations (usually the Navier-Stokes equations) are stochastic. Even simple non-linear equations can have deterministic solutions that look random. In other words, even though the solutions for a given set of initial and boundary conditions can be perfectly repeatable and predictable at a given time and point in space, it may be impossible to guess from the information at one point or time how it will behave at another (at least without solving the equations). Moreover, a slight change in the intial or boundary conditions may cause large changes in the solution at a given time and location; in particular, changes that we could not have anticipated. Most of the statistical analyses of turbulent flows are based on the idea of an ensemble average in one form or another. In some ways this is rather ...

A continuation of either CHE 129 or 131, introducing the fundamental principles of chemistry, including substantial illustrative material drawn from the chemistry of inorganic, organic, and biochemical systems. The principal topics covered are stoichiometry, the states of matter, chemical equilibrium and introductory thermodynamics, electrochemistry, chemical kinetics, electron structure and chemical bonding, and chemical periodicity. The sequence emphasizes basic concepts, problem solving, and factual material. It provides the necessary foundation for students who wish to pursue further coursework in chemistry. This sequence is inappropriate for students who have completed two or more years of chemistry in high school; such students should take CHE 141, 142. Three lecture hours and one 80-minute workshop per week. May not be taken for credit in addition to CHE 152. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the ...