Relevant bibliographies by topics / Mathematics applied to the medical field

Academic literature on the topic 'Mathematics applied to the medical field'

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Published: 20 April 2024

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Journal articles on the topic "Mathematics applied to the medical field"

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Peksen, Ali, and Chat GPT. "Using ChatGPT in the Medical Field: A Narrative." Infectious Diseases and Clinical Microbiology 5, no. 1 (March 11, 2023): 66–68. http://dx.doi.org/10.36519/idcm.2023.227.

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This text was written by filtering the response of ChatGPT to our querries. ChatGPT has jumped into many fields including the scientific arena. It seems that there could be benefits of this application, however there is a huge area that could be misused. We optimistically focused on the positive sides to inform our readers, and decided to ask ChatGPT to talk about itself.
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Bellomo, Nicola, Elena De Angelis, and Luigi Preziosi. "Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy." Journal of Theoretical Medicine 5, no. 2 (2003): 111–36. http://dx.doi.org/10.1080/1027336042000288633.

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This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analyzed. Moreover, this paper deals with the modeling and optimization of therapeutical actions. The aim of the critical analysis and review consists in providing the background framework towards the development of research perspectives in this promising new field of applied mathematics.
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Yang, Zhuo, Yaohui Hou, and Lijun Wang. "P‐2.17: The Research Status And Prospect of Augmented Reality in Medical Field." SID Symposium Digest of Technical Papers 54, S1 (April 2023): 541–45. http://dx.doi.org/10.1002/sdtp.16351.

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With the explosion of metaverse, augmented reality technology (AR) has been well developed. Augmented reality is a technology that connects the real and virtual worlds. In recent years, as the global population aging problem intensifies, the elderly are more dependent on advanced and guaranteed medical technology, AR+ medical has been further developed, and has received investment from many technology giants. AR technology has changed the form of traditional medical treatment. Through the study of AR+ medical treatment, the author analyzed the research results of AR in medical education, hand rehabilitation, medical plastic surgery, clinical medicine and other fields. The future research of AR in the medical field is prospected.
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Golovko, Liudmyla, Olena Yara, Olena Uliutina, Tetiana Kondratiuk, and Halaidiuk Lidiia. "Responsibility in the Field of Providing Medical Services: The Experience of Slovakia." Revista de la Universidad del Zulia 14, no. 40 (May 4, 2023): 351–60. http://dx.doi.org/10.46925//rdluz.40.20.

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The purpose of the article is to identify the positive experience of Slovakia in the field of legal liability of medical workers, which has been successful in practice and therefore worth following, both in Ukraine and in other states. To achieve this purpose, general and special scientific research methods were used, in particular dialectical, historical-legal, systematic, and comparative legal methods. The legal regulation of liability for the provision of medical services constantly generates debate in scientific circles and in practical implementation. The legislation of Ukraine does not regulate concepts such as medical mistakes and medical crimes. The lack of regulatory criteria for medical mistakes and crimes, the difficulty in determining the cause and effect relationship, as well as the need for professional supervision in the provision of medical services, encourages the study of foreign experience, mainly the experience of the European Union Member States in this field.
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Yakobovskiy, M. V., and M. A. Kornilina. "Development of Supercomputer Technologies at the Institute of Mathematical Modelling and Keldysh Institute of Applied Mathematics of Russian Academy of Sciences." Computational Mathematics and Information Technologies 8, no. 1 (April 2, 2024): 12–28. http://dx.doi.org/10.23947/2587-8999-2024-8-1-12-28.

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A review scientific work in the field of supercomputer technologies at the Institute of Mathematical Modelling and Keldysh Institute of Applied Mathematics is presented. Progress in supercomputer technologies, programming tools and technique (such as hyperbolization, load balancing, fault tolerance, adaptive mesh refinement, rational mesh decomposition) and several supercomputer applications are presented.
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Wang, Hao, Jianwen Song, and Lijun Wang. "P‐2.18: Overview and Prospect of the Application of Digital Human in Medical Field." SID Symposium Digest of Technical Papers 54, S1 (April 2023): 546–49. http://dx.doi.org/10.1002/sdtp.16352.

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This article briefly describes the concept of digital human and the difference between it and virtual human and digital virtual human, summarizes the application status of digital human in the medical field, by analyzing the advantages and characteristics of digital human and applying it in the medical field, such as the construction of digital virtual human model, discusses the advantages and disadvantages of digital human in the medical field and its application prospects. It is of great significance to study the medical research mode, clinical teaching mode and clinical medical work mode in the digital age.
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Bregman, Alvan. "Alligation Alternate and the Composition of Medicines: Arithmetic and Medicine in Early Modern England." Medical History 49, no. 3 (July 1, 2005): 299–320. http://dx.doi.org/10.1017/s0025727300008899.

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Practical mathematics in the early modern period was applied to such fields as astronomy and navigation; cartography and surveying; engineering and military arts, including gunnery; and especially banking and mercantile trade. Those who have written about practical mathematics make no mention of medical applications in their surveys, although there were many cases where physicians set up as mathematical practitioners. This article examines medical applications found in practical mathematical literature up to the end of the seventeenth century in England.
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KALTENBACHER, MANFRED. "COMPUTATIONAL ACOUSTICS IN MULTI-FIELD PROBLEMS." Journal of Computational Acoustics 19, no. 01 (March 2011): 27–62. http://dx.doi.org/10.1142/s0218396x11004286.

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We present physical/mathematical models base on partial differential equations (PDEs) and efficient numerical simulation schemes based on the Finite Element (FE) method for multi-field problems, where the acoustic field is the field of main interest. Acoustics, the theory of sound, is an emerging scientific field including disciplines from physics over engineering to medical science. We concentrate on the following three topics: vibro-acoustics, aero-acoustics and high intensity focused ultrasound. For each topic, we discuss the physical/mathematical modeling, efficient numerical schemes and provide practical applications.
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Cárceles, Salvador Barranco, Andreas Kyritsakis, Veronika Zadin, Aquila Mavalankar, and Ian Underwood. "27‐2: Field Emission Beyond Information Displays." SID Symposium Digest of Technical Papers 54, no. 1 (June 2023): 366–69. http://dx.doi.org/10.1002/sdtp.16568.

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Field emission is at the heart of a wide range of research areas and technologies. The commercialisation of some of these technologies has been limited due to the challenges to achieve emission uniformity, yield, and lifetime within the tolerances that the industry demands. The recent advances in simulation tools and nanofabrication have enabled the effective design and production of field emitter enabled technologies. Here, we present the construction, functionalities, and limitations of our computational tool for field emission design and analysis, along with relevant examples ranging from 3D portable medical imaging to novel cancer therapy.
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Sitaula, Sanjeeta, Hira Nath Dahal, Manisha Dahal, Rajeev Ojha, and Ananda Kumar Sharma. "Visual field defects in neuro-ophthalmological diseases at a tertiary hospital in Nepal." Nepal Journal of Neuroscience 20, no. 2 (July 21, 2023): 49–56. http://dx.doi.org/10.3126/njn.v20i2.53901.

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Purpose: This retrospective study aims to describe the pattern of visual field defects among patients presenting with neuro-ophthalmological diseases in a tertiary hospital of Kathmandu. Materials and Methods: Medical records of patients undergoing Goldmann visual fields (GVF) for neuro-ophthalmological diseases from July 2019 to June 2021 were retrospectively reviewed. Patient demographics, laterality of the disease, clinical diagnosis and pattern of visual field defect were evaluated and entered and analyzed using SPSS version 20 using descriptive univariate and bivariate analysis. Results: A total of 216 subjects (378 eyes) with the mean age 34.52±14.80 years were included in the study. The visual field defects were divided 4 categories: optic nerve disorders (76.4%, n=165), chiasmal disorders (17.6%, n=38), retrochiasmal disorders (2.8%, n=6) and miscellaneous (3.2%, n=7). Disc edema/papilledema was the most common diagnosis in optic nerve disorders with enlarged blind spot (79.1%) and constriction of visual fields (18.3%) as pattern of visual field defects followed by optic neuritis. Common lesions affecting the chiasma in our study were craniopharyngioma on whom 50% had the classical temporal field involvement (bitemporal-20%, inferotemporal-20% and superotemporal-10%) and pituitary lesions where 30% showed constriction of peripheral fields, 57.5% showed temporal field defects (mostly superotemporal) in both eyes. Retrochiasmal lesions were less common but all showed a bilateral and homonymous pattern of visual field defect. Conclusion: Optic nerve disorders were the most common group of conditions undergoing visual fields. Understanding the varied patterns of visual field defects can aid in early diagnosis and guide timely treatment of common neuro-ophthalmological diseases.
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Dissertations / Theses on the topic "Mathematics applied to the medical field"

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Ambrose, Joseph Paul. "Dynamic field theory applied to fMRI signal analysis." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2035.

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In the field of cognitive neuroscience, there is a need for theory-based approaches to fMRI data analysis. The dynamic neural field model-based approach has been developing to meet this demand. This dissertation describes my contributions to this approach. The methods and tools were demonstrated through a case study experiment on response selection and inhibition. The experiment was analyzed via both the standard behavioral approach and the new model-based method, and the two methods were compared head to head. The methods were quantitatively comparable at the individual-level of the analysis. At the group level, the model-based method reveals distinct functional networks localized in the brain. This validates the dynamic neural field model-based approach in general as well as my recent contributions.
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Whalen, Patrick. "Full Field Propagation Models And Methods For Extreme Nonlinear Optics." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/347238.

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This dissertation examines models, methods, and applications of electric field pulse propagation in nonlinear optics. Standard nonlinear optical propagation models such as the NLS equation are derived using a procedure invoking a slowly-varying wave approximation which amounts to discarding second order derivatives in the propagation direction. This work follows a more intuitive procedure emphasizing unidirectionality, the core trait of laser light propagation, by projecting a nonlinear wave system onto a unidirectional subspace. The projection method is discussed as a general theory and then applied to a series of different electric field configurations. Two important full-field propagation models are examined. The unidirectional pulse propagation equations (UPPE's) are generated from Maxwell's equations with the sole approximation being that of unidirectionality. The second model studied is the MKP equation which is a canonical full-field propagation equation particularly amenable to mathematical analysis due to its status as a conserved system. Applications unique to full-field propagation including electric field shock and harmonic walk-off induced collapse arrest are studied through numerical simulations. An emphasis is placed on the mid-infrared to long-infrared wavelength regime where significant differences between envelope models and electric field models manifest as a result of extremely weak dispersion. Presented are the first embedded Runge-Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In the stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations including the standard z-propagated UPPE.
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Kahle, A. "Cosmic microwave background anisotropies in the presence of a weak magnetic field." Master's thesis, University of Cape Town, 2003. http://hdl.handle.net/11427/4894.

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Bibliography: leaves 87-90.
One of the questions cosmology still has not satisfactorily resolved is the origin of magnetic fields in the universe. These have been observed at all scales where man has c:evised means to observe them, from stellar scales, to intergalactic and intercluster scales. Indeed, there is no reason to believe that they are not present, at some level, at even larger scales. However, a satisfactory explanation for their origin is yet to be found. The two most popular theories for the creation of these magnetic fields, namely the Galactic dynamo, and primordial field amplification, both rely on the presence of a seed field, which they then amplify. However, the galactic dynamo requires a far weaker seed field compared to primordial field amplification. It would thus be helpful, in trying to understand magnetogenesis, if one could discover some means to detect such a seed field. One way to do so would be to search for a signature that such a magnetic field might leave on the CMB, and then look for the presence of this signature in CMB observations. This is the principal aim of this thesis.
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Murugan, Jeffrey. "Geometrical and nonperturbative aspects of low dimensional field theories." Master's thesis, University of Cape Town, 2000. http://hdl.handle.net/11427/7681.

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Bibliography: leaves 84-88
We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model.
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Kuehn, T. "Approximation of anisotropic and advected mean curvature flows by phase field models." Thesis, University of Sussex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318501.

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Webber, Matthew. "Stochastic neural field models of binocular rivalry waves." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:c444a73e-20e3-454d-85ae-bbc8831fdf1f.

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Binocular rivalry is an interesting phenomenon where perception oscillates between different images presented to the two eyes. This thesis is primarily concerned with modelling travelling waves of visual perception during transitions between these perceptual states. In order to model this effect in such a way that we retain as much analytical insight into the mechanisms as possible we employed neural field theory. That is, rather than modelling individual neurons in a neural network we treat the cortical surface as a continuous medium and establish integro-differential equations for the activity of a neural population. Our basic model which has been used by many previous authors both within and outside of neural field theory is to consider a one dimensional network of neurons for each eye. It is assumed that each network responds maximally to a particular feature of the underlying image, such as orientation. Recurrent connections within each network are taken to be excitatory and connections between the networks are taken to be inhibitory. In order for such a topology to exhibit the oscillations found in binocular rivalry there needs to be some form of slow adaptation which weakens the cross-connections under continued firing. By first considering a deterministic version of this model, we will show that, in fact, this slow adaptation also serves as a necessary "symmetry breaking" mechanism. Using this knowledge to make some mild assumptions we are then able to derive an expression for the shape of a travelling wave and its wave speed. We then go on to show that these predictions of our model are consistent not only with numerical simulations but also experimental evidence. It will turn out that it is not acceptable to completely ignore noise as it is a fundamental part of the underlying biology. Since methods for analyzing stochastic neural fields did not exist before our work, we first adapt methods originally intended for reaction-diffusion PDE systems to a stochastic version of a simple neural field equation. By regarding the motion of a stochastic travelling wave as being made up of two distinct components, firstly, the drift-diffusion of its overall position, secondly, fast fluctuations in its shape around some average front shape, we are able to derive a stochastic differential equation for the front position with respect to time. It is found that the front position undergoes a drift-diffusion process with constant coefficients. We then go on to show that our analysis agrees with numerical simulation. The original problem of stochastic binocular rivalry is then re-visited with this new toolkit and we are able to predict that the first passage time of a perceptual wave hitting a fixed barrier should be an inverse Gaussian distribution, a result which could potentially be experimentally tested. We also consider the implications of our stochastic work on different types of neural field equation to those used for modelling binocular rivalry. In particular, for neural fields which support pulled fronts propagating into an unstable state, the stochastic version of such an equation has wave fronts which undergo subdiffusive motion as opposed to the standard diffusion in the binocular rivalry case.
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Michlin, Tracie L. "Using wavelet bases to separate scales in quantum field theory." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5572.

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This thesis investigates the use of Daubechies wavelets to separate scales in local quantum field theory. Field theories have an infinite number of degrees of freedom on all distance scales. Quantum field theories are believed to describe the physics of subatomic particles. These theories have no known mathematically convergent approximation methods. Daubechies wavelet bases can be used separate degrees of freedom on different distance scales. Volume and resolution truncations lead to mathematically well-defined truncated theories that can be treated using established methods. This work demonstrates that flow equation methods can be used to block diagonalize truncated field theoretic Hamiltonians by scale. This eliminates the fine scale degrees of freedom. This may lead to approximation methods and provide an understanding of how to formulate well-defined fine resolution limits.
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Loubaton, Rodolphe. "Modélisation des effets d’une intervention dans un programme génique temporel." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0322.

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Les cellules cancéreuses peuvent présenter des anomalies de l'expression de certains gènes qui altèrent le fonctionnement normal des programmes de fonctionnement cellulaire, provoquant une prolifération incontrôlée de ces cellules. Ces programmes cellulaires sont constitués de l'expression de milliers de gènes qui s'activent et interagissent de façon concertée. Ces interactions peuvent être représentées sous forme d'un réseau de régulation de gènes. L'objectif général de cette thèse, qui s'inscrit dans la continuité des travaux de Vallat et al (2021) consiste à modéliser un programme cellulaire à partir de données temporelles d'expression de gènes. Le modèle construit permettra d'identifier des gènes cibles dont la diminution d'expression pourrait diminuer la prolifération cellulaire dans un but thérapeutique. Dans le premier chapitre, nous faisons une revue des modèles de réseaux de gènes existant afin de justifier le choix de notre modèle qui est détaillé dans le deuxième chapitre. Ce modèle (appelé modèle LiRE) est un modèle statistique paramétrique gaussien qui permet de prendre en compte la dynamique d'expression de gènes à l'aide de paramètres décrivant, entre autres, les interactions entre les gènes. Les différentes propriétés théoriques de notre modèle nous ont permis de développer un algorithme itératif pour inférer les paramètres en combinant des étapes de régressions linéaires pénalisées lasso et régressions avec contraintes de positivité et contraintes sur la somme des coefficients. Nous menons également dans ce chapitre une étude numérique de ce modèle pour étudier sa performance sur des données simulées. Dans le troisième chapitre, nous décrivons des méthodes qui permettent de modéliser et prédire les résultats d'expériences d'interventions biologiques modifiant l'expression de certains gènes, afin de prédire les meilleurs gènes cibles dont il faudrait diminuer l'expression dans le programme cellulaire pour diminuer la prolifération des cellules cancéreuses. Nous donnons des résultats théoriques sur différents modèles y compris notre modèle LiRE. Dans le dernier chapitre, nous détaillons notre package R MultiRNAflow qui nous a permis de réaliser des analyses statistiques de données dynamiques et complexes d'expressions de gènes afin de caractériser les gènes retenus pour l'inférence de notre modèle LiRE
Cancer cells can exhibit abnormalities in the expression of certain genes that alter the normal functioning of cellular programs, causing them to proliferate uncontrollably. These cellular programs are made up of the expression of thousands of genes that activate and interact in a concerted fashion. These interactions can be represented as a gene regulatory network. The general objective of this thesis, which follows on from the work of Vallat et al (2021), is to model a cellular program using temporal gene expression data. The model constructed will make it possible to identify target genes whose reduced expression could reduce cell proliferation for therapeutic purposes. In the first chapter, we review existing gene network models in order to justify the choice of our model, which is detailed in the second chapter. This model (called the LiRE model) is a Gaussian parametric statistical model that allows us to take into account gene expression dynamics using parameters describing, among other things, the interactions between genes. The various theoretical properties of our model have enabled us to develop an iterative algorithm for inferring parameters, combining steps of penalized linear regressions lasso and regressions with positivity constraints and constraints on the sum of coefficients. In this chapter, we also carry out a numerical study of this model to investigate its performance on simulated data. In the third chapter, we describe methods for modeling and predicting the results of biological intervention experiments modifying the expression of certain genes, in order to predict the best target genes whose expression should be decreased in the cellular program to reduce cancer cell proliferation. We give theoretical results on different models including our LiRE model. In the final chapter, we detail our R package MultiRNAflow, which enabled us to perform statistical analyses of dynamic and complex gene expression data in order to characterize the genes selected for inference in our model LiRE
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Verma, Vishash. "Improved Slope Estimation in Organic Field-Effect Transistor Mobility Estimation." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618703169092189.

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Cairns, Melissa Ann. "Weak Anchoring Effects on Magnetic Field Induced Transitions of a Cholesteric Liquid Crystal Filmwith Negative Magnetic Anisotropy." Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1563550315014445.

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Books on the topic "Mathematics applied to the medical field"

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Dennis, Cynthia A. Applied radiographic calculations. Philadelphia: W.B. Saunders, 1993.

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Tai, Chen-to. Generalized vector and dyadic analysis: Applied mathematics in field theory. 2nd ed. New York: IEEE Press, 1997.

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Tai, Chen-to. Generalized vector and dyadic analysis: Applied mathematics in field theory. New York: Institute of Electrical and Electronics Engineers, 1992.

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Mergenthaler, Erhard. Textbank systems: Computer science applied in the field of psychoanalysis. Berlin: Springer-Verlag, 1985.

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T, Robinson Elizabeth, and Tolley Elizabeth E, eds. Qualitative methods in public health: A field guide for applied research. San Francisco, CA: Jossey-Bass, 2005.

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H, Zwinderman Aeilko, and Cleophas Toine F, eds. Statistics applied to clinical trials. Dordrecht: Kluwer Academic Publishers, 2000.

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H, Zwinderman Aeilko, and Cleophas Toine F, eds. Statistics applied to clinical trials. 2nd ed. Dordrecht: Kluwer Academic Publishers, 2002.

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Peace, Karl E., 1941- author, ed. Applied meta-analysis with R. Boca Raton: CRC Press, 2013.

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Jones, M. N. Spherical Harmonics and Tensors for Classical Field Theory: (Electronic & Electrical Engineering Research Studies: Applied & Engineering Mathematics). Letchworth, Hertfordshire, England: Research Studies Press Letchword., 1985.

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IUTAM Symposium on Field Analyses for Determination of Material Parameters-- Experimental and Numerical Aspects (2000 Kiruna, Sweden). IUTAM Symposium on Field Analyses for Determination of Material Parameters-- Experimental and Numerical Aspects. Boston: Kluwer Academic Publishers, 2003.

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Book chapters on the topic "Mathematics applied to the medical field"

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Abraham, Ralph, and Michael Nivala. "Emergent Periodicity in a Field of Chaos." In Applied Mathematics, 1–8. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2547-8_1.

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Chattopadhyay, Surajit, and Sudipto Roy. "Dependence of Brans–Dicke Parameter on Scalar Field." In Applied Mathematics, 177–82. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2547-8_16.

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Torquato, Salvatore. "Cell and Random-Field Models." In Interdisciplinary Applied Mathematics, 188–209. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-6355-3_8.

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Kiss, István Z., Joel C. Miller, and Péter L. Simon. "Mean-field approximations for homogeneous networks." In Interdisciplinary Applied Mathematics, 117–64. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50806-1_4.

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Kiss, István Z., Joel C. Miller, and Péter L. Simon. "Mean-field approximations for heterogeneous networks." In Interdisciplinary Applied Mathematics, 165–205. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50806-1_5.

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Ván, Peter. "Entropy Production in Phase Field Theories." In Applied Wave Mathematics II, 365–70. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29951-4_16.

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Epstein, Charles L. "Medical Imaging." In Encyclopedia of Applied and Computational Mathematics, 881–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_66.

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Krejčí, P., J. Sprekels, and S. Zheng. "Existence and Asymptotic Behaviour in Phase-Field Models with Hysteresis." In Lectures on Applied Mathematics, 77–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-59709-1_6.

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Cancès, Eric. "Self-Consistent Field (SCF) Algorithms." In Encyclopedia of Applied and Computational Mathematics, 1310–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_256.

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Dunn, W. L., A. M. Yacout, and F. O’Foghludha. "The Use of Single-Scatter Models in Medical Radiation Applications." In Applied and Industrial Mathematics, 335–42. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-009-1908-2_28.

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Conference papers on the topic "Mathematics applied to the medical field"

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Xu, Tongzhou. "Review of NIR spectroscopy applications in medical field." In 7TH INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION: Mathematics of Quantum Computing. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0112957.

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Khalil, Shuker Mahmood, and Nadia M. Ali Abbas. "On nano with their applications in medical field." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027374.

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Moloney, J. V. "Applied Mathematics Perspectives of Nonlinear Guided Wave Optics: Stability, Propagation and Soliton Aspects." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/nlgwp.1989.fc1.

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Traditionally nonlinear optical waveguide theory has evolved as a natural extension of linear waveguiding concepts. In this picture, low-power guided waves are supported by discontinuities or gradations in material refractive indices and the optical nonlinearity plays a rather passive role, modifying slightly the mode propagation constant. Linear coupled mode analysis, when extended to incorporate nonlinear effects, predicts a variety of novel switching effects such as nonlinear directional coupling or bistable response in feedback geometries. The theoretical observation that at higher incident power, a single interface (planar waveguide) could support novel stationary nonlinear surface (guided) waves, if at least one of the bounding dielectric media displayed a positive nonlinear optical response to the applied electromagnetic field, has led to an explosive growth of the literature on nonlinear waveguides [1]. Parallel studies have employed the beam propagation method (BPM) to study the asymptotic states of self-focused channels incident at oblique angles to a nonlinear interface [2]. More recently the BPM has been used as a computational tool to investigate stability of the above analytically computed stationary nonlinear surface (NSW) or guided (NGW) waves [3].
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Kotov, Yurij Borisovich, Vera Maratovna Guryeva, and Tatiana Alekseevna Semenova. "Cognitive investigation of the complex systems behavior using medical objects as an example." In 5th International Conference “Futurity designing. Digital reality problems”. Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/future-2022-11.

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The article gives a brief review of mathematical methods developed to study the behavior of open and nonequilibrium physical systems. Some results of these methods are used in medical field. Three-valued logic, nonparametric and nonnumerical statistics applied to medical data processing. To compare nonnumerical sets, the authors have introduced a measure of their proximity, called indistinguishability. The proposed data processing method in open systems, the “logical symptoms method”, is provided by the author's computer programs complex and can be used in other fields of science.
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Cavoretto, Roberto, and Alessandra De Rossi. "A Local IDW Transformation Algorithm for Medical Image Registration." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991098.

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Bender, Carl M., Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "PT-Symmetric Quantum Field Theory." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636813.

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Chara, Zdenek, Bohus Kysela, and Pavel Vlasak. "Velocity field around a falling particle." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756080.

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Gocheva-Ilieva, Snezhana G., Iliycho P. Iliev, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Mathematical Modeling Of The Electric Field In Copper Bromide Laser." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790197.

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Kozma, Robert, Marko Puljic, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Neural Population Dynamics Modeled by Mean-Field Graphs." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637870.

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Colli, Pierluigi. "Modelling and Analysis of a Class of Phase Field Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990877.

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Reports on the topic "Mathematics applied to the medical field"

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Olsen and Willson. L51916 Pressure Based Parametric Emission Monitoring Systems (PEMS). Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), April 2002. http://dx.doi.org/10.55274/r0010181.

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The natural gas industry operates over 8000 stationary large bore (bore greater than 14 in) natural gas engines for natural gas compression on pipelines and power generation. As emissions regulations become increasingly more stringent, the need for low cost methods for compliance demonstration arises. A PEMS model is one such approach. Research in this area has increased significantly during the last decade. PEMS models for this application utilize parameters commonly measured on industrial engines in the field to predict engine-out emissions. Monitoring emissions in this manner represents a significant cost savings over the periodic use of chemiluminescence NOX analyzers, which are not standard equipment in natural gas compressor stations. PEMS model accuracy is dependent on the quality of the input data, both the training NOX measurements and the selection of input parameters. Hence, it is important to have both reliable data measurement methods and an understanding of engine operating parameters relation to NOX. This work is part of the body of work referred to as the Integrated Test Plan (ITP), performed at the Engines and Energy Conversion Laboratory (EECL). This report details an investigation into Parametric Emissions Monitoring System (PEMS) models. It is the final document to be delivered under the ITP program. Much of the work performed under the ITP program focused on Hazardous Air Pollutants (HAPs) research. However, the emphasis of the PEMS work is on the prediction of oxides of nitrogen (NOX) emissions from large bore natural gas engines. In this work two different PEMS models are developed, a semi-empirical model and a neural network model. The semi-empirical model is based on general relationships between NOX emissions and engine parameters, but contains empirical constants that are determined based on the best fit to engine experimental data. The neural network model utilizes a similar set of input parameters, but relies on the neural network code to determine the relationships between input parameters and measured NOX emissions. The neural network model also contains empirical constants. The mathematics involved in both models is described. A single term semi-empirical model, which has been utilized in the literature as a PEMS model, is applied for comparative purposes.
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