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Littérature scientifique sur le sujet « Mathematical biology in general »

Auteur : Grafiati

Publié le 4 juin 2021

Mis à jour le 31 juillet 2024

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Articles de revues sur le sujet "Mathematical biology in general"

Maini, P. K. « Essential Mathematical Biology ». Mathematical Medicine and Biology 20, n^o 2 (1 juin 2003) : 225–26. http://dx.doi.org/10.1093/imammb/20.2.225.

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Logan, J. David, Elizabeth S. Allman et John A. Rhodes. « Mathematical Models in Biology ». American Mathematical Monthly 112, n^o 9 (1 novembre 2005) : 847. http://dx.doi.org/10.2307/30037621.

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Sanft, Rebecca, et Anne Walter. « Experimenting with Mathematical Biology ». PRIMUS 26, n^o 1 (9 juillet 2015) : 83–103. http://dx.doi.org/10.1080/10511970.2015.1064050.

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Deem, Michael W. « Mathematical adventures in biology ». Physics Today 60, n^o 1 (1 janvier 2007) : 42–47. http://dx.doi.org/10.1063/1.2709558.

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Vasieva, Olga, Manan'Iarivo Rasolonjanahary et Bakhtier Vasiev. « Mathematical modelling in developmental biology ». REPRODUCTION 145, n^o 6 (juin 2013) : R175—R184. http://dx.doi.org/10.1530/rep-12-0081.

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In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

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Laubenbacher, Reinhard. « Algebraic Methods in Mathematical Biology ». Bulletin of Mathematical Biology 73, n^o 4 (12 mars 2011) : 701–5. http://dx.doi.org/10.1007/s11538-011-9643-7.

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Kraikivski, Pavel. « Mathematical Modeling in Systems Biology ». Entropy 25, n^o 10 (25 septembre 2023) : 1380. http://dx.doi.org/10.3390/e25101380.

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Ali Lashari, Abid, et Faiz Ahmad. « False mathematical reasoning in biology ». Journal of Theoretical Biology 307 (août 2012) : 211. http://dx.doi.org/10.1016/j.jtbi.2012.05.006.

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Shelah, Saharon, et Lutz Strüngmann. « Infinite combinatorics in mathematical biology ». Biosystems 204 (juin 2021) : 104392. http://dx.doi.org/10.1016/j.biosystems.2021.104392.

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Krumbeck, Yvonne, Tim Rogers et George Constable. « An Invitation to Stochastic Mathematical Biology ». Notices of the American Mathematical Society 68, n^o 11 (1 décembre 2021) : 1. http://dx.doi.org/10.1090/noti2381.

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Thèses sur le sujet "Mathematical biology in general"

Modhara, Sunny. « Mathematical modelling of vascular development in zebrafish ». Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/29125/.

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The Notch signalling pathway is pivotal in ensuring that the processes of arterial specification, angiogenic sprouting and haematopoietic stem cell (HSC) specification are correctly carried out in the dorsal aorta (DA), a primary arterial blood vessel in developing vertebrate embryos. Using the zebrafish as a model organism, and additional experimental observations from mouse and cell line models to guide mathematical modelling, this thesis aims to better understand the mechanisms involved in the establishment of a healthy vasculature in the growing embryo. We begin by studying arterial and HSC specification in the zebrafish DA. Mathematical models are used to analyse the dose response of arterial and HSC genes to an input Notch signal. The models determine how distinct levels of Notch signalling may be required to establish arterial and HSC identity. Furthermore, we explore how Delta-Notch coupling, which generates salt-and-pepper patterns, may drive the average gene expression levels higher than their homogeneous levels. The models considered here can qualitatively reproduce experimental observations. Using laboratory experiments, I was able to isolate DA cells from transgenic zebrafish embryos and generate temporal gene expression data using qPCR. We show that it is possible to fit ODE models to such data but more reliable data and a greater number of replicates at each time point is required to make further progress. The same VEGF-Delta-Notch signalling pathway is involved in tip cell selection in angiogenic sprouting. Using an ODE model, we rigourously study the dynamics of a VEGF-Delta-Notch feedback loop which is capable of amplifying differences betwen cells to form period-2 spatial patterns of alternating tip and stalk cells. The analysis predicts that the feeback strengths of Delta ligand and VEGFR-2 production dictate the onset of patterning in the same way, irrespective of the parameter values used. This model is extended to incorporate feedback from filopodia, growing in a gradient of extracellular VEGF, which are capable of facilitating tip cell selection by amplifying the resulting patterns. Lastly, we develop a PDE model which is able to properly account for VEGF receptor distributions in the cell membrane and filopodia. Receptors can diffuse and be advected due to domain growth, defined by a constitutive law, in this model. Our analysis and simulations predict that when receptor diffusivity is large, the ODE model for filopodia growth is an excellent approximation to the PDE model, but that for smaller diffusivity, the PDE model provides valuable insight into the pattern forming potential of the system.

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Cherkaoui, Rbati Mohammed. « Mathematical and physical systems biology : application to pharmacokinetic drug-drug interactions and tumour growth ». Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33719/.

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In this thesis, a multi-scale approach is provided to a pharmacokinetic and a pharmacodynamic problem. The first part of this research provides a realistic mathematical physiological model of the liver to predict drug drug interactions (DDIs). The model describes the geometry of a lobule (liver unit) and integrates the exchange processes, diffusion and active transport, between the hepatocytes and the blood and possible drug-drug interactions such as; reversible inhibition, mechanistic based inhibition (MBI) and enzyme induction. The liver model is subsequently integrated into a PBPK model with 7 compartments (artery blood, venous blood, gut, liver, kidney, lung, rest of the body). To assess the efficiency of the model to predict DDIs, 77 clinical DDI studies were compared to the model. These 77 clinical studies represent 5 victim drugs (midazolam, simvastatin, triazolam, cerivastatin and nifedipine) and 30 perpetrator drugs. The reversible inhibition, MBI and induction parameters for the majority of the perpetrators were estimated with in vitro experiments and adjusted for the human liver size. The PK parameters, such as clearance and absorption rate, and the physiological parameters were obtained from the literature. The DDIs were measured as the ratio of the AUC (Area Under the Curve of the blood concentration) or the ratio of the maximum concentration Cmax of the victim drug administered with and without the perpetrator drug. The predicted ratios were compared with the clinical observation by calculating the geometric fold error GMFE. The GMFE for AUCratio and Cmax,ratio were calculated to be 1.54 and 1.34, respectively. Moreover, the PBPK model excluding the gut compartment under-predicts both inhibition (lower AUCratio) and induction (higher AUCratio) which strongly suggests that the gut DDI component can not be neglected for accurate clinical prediction. However, the static combined model by Fahmi et al. [1, 2] without the gut component fortuitously predicts the clinical AUCratio better than inclusion with the gut component. To conclude, the model predicts DDIs relatively well as it is in the lower range of errors reported in the literature (1.47-2.00 [1, 2]). Moreover, the model is able to predict the pharmacokinetics of drugs and provides a dynamic description of the DDIs, such as the enzyme level and spatial distribution within a lobule. Furthermore, the perpetrator dose regimen can be changed or the error in the in vitro parameters can be integrated to observe their influences on the AUC ratio. The second part of this research explored the Warburg effect in a avascular tumour growth model incorporating a cell shedding term to account for tumour shrinkage. The tumour model was based on an extension of the Ward and King model [3], where two sub-populations; living cells and dead cells are considered. Three diffusion equations for glucose, lactate and the drug are considered and included into the model for growth rate, natural death rate and a death rate due to the drug. The simulation of the model without a drug shows similar behaviour to the original model by Ward and King despite the presence of the shedding term and predicts an extracellular pH of 6.8. However, when a drug treatment is added, the model is able to simulate the shrinkage of the tumour unlike the original model. Moreover, two scenarios with a basic, neutral and acidic drug were explored, assuming similar efficiency at physiological pH to assess the effect of changes in the extracellular pH. Acidic or weak base drugs seem to be more efficient in low pH environment as the fraction of neutral form is greater and therefore more drug is available to cross the cell membrane to reach its target.

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Handley, Kelly. « Statistical analysis of proteomic mass spectrometry data ». Thesis, University of Nottingham, 2007. http://eprints.nottingham.ac.uk/10287/.

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This thesis considers the statistical modelling and analysis of proteomic mass spectrometry data. Proteomics is a relatively new field of study and tried and tested methods of analysis do not yet exist. Mass spectrometry output is high-dimensional and so we firstly develop an algorithm to identify peaks in the spectra in order to reduce the dimensionality of the datasets. We use the results along with a variety of classification methods to examine the classification of new spectra based on a training set. Another method to reduce the complexity of the problem is to fit a parametric model to the data. We model the data as a mixture of Gaussian peaks with parameters representing the peak locations, heights and variances, and apply a Bayesian Markov chain Monte Carlo (MCMC) algorithm to obtain their estimates. These resulting estimates are used to identify m/z values where differences are apparent between groups, where the m/z value of an ion is its mass divided by its charge. A multilevel modelling framework is also considered to incorporate the structure in the data and locations exhibiting differences are again obtained. We consider two mass spectrometry datasets in detail. The first consists of mass spectra from breast cancer cells which either have or have not been treated with the chemotherapeutic agent Taxol. The second consists of mass spectra from melanoma cells classified as stage I or stage IV using the TNM system. Using the MCMC and multilevel techniques described above we show that, in both datasets, small subsets of the available m/z values can be identified which exhibit significant differences in protein expression between groups. Also we see that good classification of new data can also be achieved using a small number of m/z values and that the classification rate does not fall greatly when compared with results from the complete spectra. For both datasets we compare our results with those in the literature which use other techniques on the same data. We conclude by discussing potential areas for further research.

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Young, Gregory D. « Image segmentation and paired shapes asymmetry quantification| An application in a Drosophila wing image set ». Thesis, California State University, Long Beach, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1589666.

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The current process to identify wing pair shape asymmetry in Drosophila wing images contains multiple layers of potential measurement error. The image segmentation routine is a low-level method performed on a low resolution image set, and is prone to inaccurate edge detection in finding the wing's interior vascular structure and the exterior wing edge. An automated splining procedure on the segmentation result which yields the locations of several landmark points on the wing itself has several erroneous spline control points. The process to correct errors in the data requires both parameter tuning in the algorithm as well as manual correction of the segmentation and splining results. The in-production measures of asymmetry between Drosophila wing pairs are shown to be sensitive to these measurement errors. To reduce error in the segmentation step, several image segmentation methods are analyzed for use in developing a robust, efficient and automated segmentation algorithm for Drosophila wing image sets. Evaluation of the accuracy and efficiency of the methods is discussed, with a focus on the performance of multi-scale methods. A Frangi multi-scale segmentation is shown to more accurately locate the wing's interior vascular network. Additionally, an alternative principal components analysis of the variance structure in the image set is developed to isolate and quantify wing pair shape variation across the data set. This analysis replaces the splining process to identify locations of landmark points. Alternative measures of wing pair shape asymmetry are created from this analysis and an alternative measure of Directional Asymmetry (DA) is shown to reproduce existing benchmark measures of DA.

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Manthey, Seth. « Assessing Current Instructional Practices In General Biology One (Bio1010) And Arguing For A Model-Centered Curriculum ». FIU Digital Commons, 2015. http://digitalcommons.fiu.edu/etd/2211.

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This collected papers dissertation focused on the argument for the need to adapt and develop a model-centered General Biology I course through the analyses of current instructional practices at a large, public, Hispanic-serving university. This dissertation included a comparison of General Biology I course sections taught in two differing formats, one is a traditional lecture with face-to-face meetings and the other is an online instruction setting. The comparison of these sections was accomplished through the use of a conceptual inventory, student attitude survey, drop-fail-withdraw (DFW) rates, and Social Network Analysis. This comparison found that there was no detectible significant difference between course type for both the conceptual understanding and formation of student-to-student networks. It was also found that there was a significant difference between course type when looking at students’ attitudes towards Biology and success in the two course types. Additionally in a second study the project used a phenomoenographic analysis of student interviews that explored the students’ use of scientific models when asked about plant cells and animal cells. It was found that during the analysis of students’ ideas that students predominantly used a single model function. The cell types of focus in the second study were two models that were identified, in a third study, through a coded analysis of faculty interviews and textbook analysis. These models are viewed as essential for students to possess an understanding of upon completion of General Biology I. The model-based course that this study argued for is based on a curricular framework initially developed for use in introductory physics courses. University Modeling Instruction courses in physics (UMI-P) have been linked to improved student conceptual understanding positive attitudinal shifts, and decreased DFW rates. UMI, however, has not been expanded for implementation within the other science disciplines. Drawing from the success of UMI within physics this dissertation focused on the argument for the need for the adaptation and development of UMI for introductory biology.

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Huntley, Miriam. « Quantitative Methods for Analyzing Structure in Genomes, Self-Assembly, and Random Matrices ». Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493360.

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This dissertation presents my graduate work analyzing biological structure. My research spans three different areas, which I discuss in turn. First I present my work studying how the genome folds. The three-dimensional structure of the genome inside of the nucleus is a matter of great biological importance, yet there are many questions about just how the genetic material is folded up. To probe this, we performed Hi-C experiments to create the highest resolution dataset (to date) of genome-wide contacts in the nucleus. Analysis of this data uncovered an array of fundamental structures in the folded genome. We discovered approximately 10,000 loops in the human genome, which each bring a pair of loci far apart along the DNA strand (up to millions of basepairs away) into close proximity. We found that contiguous stretches of DNA are segregated into self-associating contact domains. These domains are associated with distinct patterns of histone marks and segregate into six nuclear subcompartments. We found that these spatial structures are deeply connected to the regulation of the genome and cell function, suggesting that understanding and characterizing the 3D structure of the genome is crucial for a complete description of biology. Second, I present my work on self-assembly. Many biological structures are formed via `bottom-up' assembly, wherein a collection of subunits assemble into a complex arrangement. In this work we developed a theory which predicts the fundamental complexity limits for these types of systems. Using an information theory framework, we calculated the capacity, the maximum amount of information that can be encoded and decoded in systems of specific interactions, giving possible future directions for improvements in experimental realizations of self-assembly. Lastly, I present work examining the statistical structure of noisy data. Experimental datasets are a combination of signal and randomness, and data analysis algorithms, such as Principal Component Analysis (PCA), all seek to extract the signal. We used random matrix theory to demonstrate that even in situations where the dataset contains too much noise for PCA to be successful, the signal can be still be recovered with the use of prior information.
Engineering and Applied Sciences - Applied Math

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Kondrashov, Dmitry A. « Protein control of a ligand : Modeling nitric oxide release in nitrophorin 4 ». Diss., The University of Arizona, 2005. http://hdl.handle.net/10150/280770.

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The nitric oxide (NO) transport protein nitrophorin 4 (Np4) is able to modulate NO release rates by two orders of magnitude in response to pH change, and the rates are much slower than in the classic transport protein myoglobin. Experiments have shown that a large conformational change in two loops near the heme binding site from a closed state at pH 5 to an open pocket at pH 7 is apparently responsible for controlling NO release. The mechanism of protein control of ligand escape was investigated using atomic-resolution X-ray crystallography, molecular dynamics simulations, and stochastic modeling. Crystal structures at pH 5 and pH 7 with and without NO revealed that the loops exhibit a mixture of conformations under all the conditions, suggesting they are not a static barrier to NO escape. Molecular dynamics simulations at both pH 5 and pH 7 were performed to observe NO migration as a function of protein conformation. The simulations agree closely with the X-ray structures, and show the loops opening and NO escaping at pH 7, while at pH 5 the loops remain closed and NO never leaves the binding pocket. A stochastic model was based on these observations, modeling the loops as a gate fluctuating between open and closed states and NO as a diffusing particle inside the protein, where it can rebind to the heme or escape out of the protein. An analytical solution of NO escape rates as a function of loop opening and closing rates demonstrates that in the appropriate regime the escape rate is determined by the probability of ligand rebinding to the heme. This indicates the reason for the difference in off rates between Np4 and Mb: Np4 encourages rebinding, while Mb provides internal space for ligand migration. Similarly, pH dependence of Np4 off rates is attributed to a greater rebinding fraction in the closed state at pH 5. However, the source of multiple rates in the experimental kinetics remains unclear, and the model will need to be extended to capture this complexity.

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Yates, Christian. « Comparing stochastic discrete and deterministic continuum models of cell migration ». Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:6f9cb70e-937c-441f-83c3-50e37e1cb420.

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Multiscale mathematical modelling is one of the major driving forces behind the systems biology revolution. The inherently interdisciplinary nature of its study and the multiple spatial and temporal scales which characterise its dynamics make cell migration an ideal candidate for a systems biology approach. Due to its ease of analysis and its compatibility with the type of data available, phenomenological continuum modelling has long been the default framework adopted by the cell migration modelling community. However, in recent years, with increased computational power, complex, discrete, cell-level models, able to capture the detailed dynamics of experimental systems, have become more prevalent. These two modelling paradigms have complementary advantages and disadvantages. The challenge now is to combine these two seemingly disparate modelling regimes in order to exploit the benefits offered by each in a comprehensive, multiscale equivalence framework for modelling cell migration. The main aim of this thesis is to begin with an on-lattice, individual-based model and derive a continuum, population-based model which is equivalent to it in certain limits. For simple models this is relatively easy to achieve: beginning with a one-dimensional, discrete model of cell migration on a regular lattice we derive a partial differential equation for the evolution of cell density on the same domain. We are also able to simply incorporate various signal sensing dynamics into our fledgling equivalence framework. However, as we begin to incorporate more complex model attributes such as cell proliferation/death, signalling dynamics and domain growth we find that deriving an equivalent continuum model requires some innovative mathematics. The same is true when considering a non-uniform domain discretisation in the one-dimensional model and when determining appropriate domain discretisations in higher dimensions. Higher-dimensional simulations of individual-based models bring with them their own computational challenges. Increased lattice sites in order to maintain spatial resolution and increased cell numbers in order to maintain consistent densities lead to dramatic reductions in simulation speeds. We consider a variety of methods to increase the efficiency of our simulations and derive novel acceleration techniques which can be applied to general reaction systems but are especially useful for our spatially extended cell migration algorithms. The incorporation of domain growth in higher dimensions is the final hurdle we clear on our way to constructing a complex discrete-continuum modelling framework capable of representing signal-mediated cell migration on growing (possibly non-standard) domains in multiple dimensions.

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Ortiz, Lugo Alvaro A. Sr. « Qualitative Analysis of Pathogen Dynamics within Cyclic and Time-Varying Water Networks ». University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563872208710325.

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Gjini, Erida. « Bridging between parasite genomic data and population processes : trypanosome dynamics and the antigenic archive ». Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3375/.

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Antigenic variation processes play a central role in parasite invasion and chronic infectious disease, and are likely to respond to host immune mechanisms and epidemiological characteristics. Whether changes in antigenic variation strategies lead to net positive or negative effects for parasite fitness is unclear. To improve our understanding of pathogen evolution, it is important to investigate the mechanisms by which pathogens regulate antigenic variant expression. This involves consideration of the complex interactions that occur between parasites and their hosts, and top-down and bottom-up factors that might drive changes in the genetic architecture of their antigenic archives. Increasing availability of pathogen genomic data offers new opportunities to understand the fundamental mechanisms of immune evasion and pathogen population dynamics during chronic infection. Motivated by the growing knowledge on the antigenic variation system of the sleeping sickness parasite, the African trypanosome, in this thesis, we present different models that analyze antigenic variation of this parasite at different biological scales, ranging from the within-host level, to between-host transmission, and finally the parasite genetics level. First, we describe mechanistically how the structure of the antigenic archive impacts the parasite population dynamics within a single host, and how it interplays with other within-host processes, such as parasite density-dependent differentiation into transmission life-stages and specific host immune responses. Our analysis focuses first on a single parasitaemia peak and then on the dynamics of multiple peaks that rely on stochastic switching between groups of parasite variants. We show that the interplay between the two types of parasite control within the host: specific and general, depends on the modular structure of the parasite antigenic archive. Our modelling reveals that the degree of synchronization in stochastic variant emergence (antigenic block size) determines the relative dominance of general over specific control within a single peak, and can divide infection scenarios into stationary and oscillatory regimes. A requirement for multiple-peak dynamics is a critical switch rate between blocks of antigenic variants, which depends on host characteristics, such as the immune delay, and implies constraints on variant surface glycoprotein (VSG) archive genetic diversification. Secondly, we study the interactions between the structure and function of the antigenic archive at the transmission level. By using nested modelling, we show that the genetic architecture of the archive has important consequences for pathogen fitness within and between hosts. We find host-dependent optimality criteria for the antigenic archive that arise as a result of typical trade-offs between parasite transmission and virulence. Our analysis suggests that different traits of the host population can select for different aspects of the antigenic archive, reinforcing the importance of host heterogeneity in the evolutionary dynamics of parasites. Variant-specific host immune competence is likely to select for larger antigenic block sizes. Parasite tolerance and host life-span are likely to select for whole archive expansion as more archive blocks provide the parasite with a fitness advantage. Within-host carrying capacity, resulting from density-dependent parasite regulation, is likely to impact the evolution of between-block switch rates in the antigenic archive. Our study illustrates the importance of quantifying the links between parasite genetics and within-host dynamics, and suggests that host body size might play a significant role in the evolution of trypanosomes. In Chapters 4 and 5 we consider the genetics behind trypanosome antigenic variation. Antigen switch rates are thought to depend on a range of genetic features, among which, the genetic identity between the switch-off and switch-on gene. The subfamily structure of the VSG archive is important in providing the conditions for this type of switching to occur. We develop a hidden Markov model to describe and estimate evolutionary processes generating clustered patterns of genetic identity between closely related gene sequences. Analysis of alignment data from high-identity VSG genes in the silent antigen gene archive of the African trypanosome identifies two scales of subfamily diversification: local clustering of sequence mismatches, a putative indicator of gene conversion events with other lower-identity donor genes in the archive, and the sparse scale of isolated mismatches, likely to arise from independent point mutations. In addition to quantifying the respective rates of these two processes, our method yields estimates for the gene conversion tract length distribution and the average diversity contributed locally by conversion events. Model fitting is conducted for a range of models using a Bayesian framework. We find that gene conversion events with lower-identity partners are at least 5 times less common than point mutations for VSG pairs, and the average imported conversion tract is short. However, due to the high frequency of mismatches in converted segments, the two processes have almost equal impact on the rate of sequence diversification between VSG sub-family members. We are able to disentangle the most likely locations of point mutations vs. conversions on each aligned gene pair. Finally we model VSG archive diversification at the global scale, as a result of opposing evolutionary forces: point mutation, which induces diversification, and gene conversion, which promotes global homogenization. By adopting stochastic simulation and theoretical approaches such as population genetics and the diffusion approximation, we find how the stationary identity configuration of the archive depends on mutation and conversion parameters. By fitting the theoretical form of the distribution to the current VSG archive configuration, we estimate the global rates of gene conversion and point mutation. The relative dominance of mutation as an evolutionary force quantifies the high divergence propensity of VSG genes in response to host immune pressures. The success of our models in describing realistic infection patterns and making predictions about the fitness consequences of the parasite antigenic archive illustrates the advantage of using integrative approaches that bridge between different biological scales. Even though quantifying the genetic signatures of antigenic variation remains a challenging task, cross-disciplinary analyses and mechanistic modelling of parasite genomic data can help in this direction, to better understand parasite evolution.

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Livres sur le sujet "Mathematical biology in general"

Allman, Elizabeth Spencer. Mathematical models in biology : An introduction. New York : Cambridge University Press, 2004.

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L, Casti J., et Karlqvist Anders, dir. Cooperation and conflict in general evolutionary processes. New York : Wiley, 1995.

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Murray, J. D. Mathematical biology : Spatial models and biomedical applications. 3^e éd. New York : Springer, 2003.

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Thom, René. Structural stability and morphogenesis : An outline of a general theory of models. Redwood City, Calif : Addison-Wesley, Advanced Book Program, 1989.

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Thom, René. Structural stability and morphogenesis : An outline of a general theory of models. Reading, Mass : Addison-Wesley Pub., 1989.

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Raven, Peter H. Understanding biology. 3^e éd. Dubuque, IA : W.C.Brown, 1995.

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Raven, Peter H. Biology. 5^e éd. Boston : WCB/McGraw-Hill, 1999.

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Raven, Peter H. Biology. 3^e éd. Dubuque, Iowa : Wm. C. Brown Publishers, 1995.

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Raven, Peter H. Biology. 2^e éd. St. Louis : Times Mirror/Mosby College Pub., 1989.

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Raven, Peter H. Biology. 4^e éd. Dubuque, IA : Wm. C. Brown Publishers, 1996.

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Chapitres de livres sur le sujet "Mathematical biology in general"

La Rosa, Massimo, Antonino Fiannaca, Riccardo Rizzo et Alfonso Urso. « DNA Barcode Classification Using General Regression Neural Network with Different Distance Models ». Dans Mathematical Models in Biology, 119–32. Cham : Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23497-7_9.

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Kuznetsov, Vladimir A. « Mathematical Modeling of Avidity Distribution and Estimating General Binding Properties of Transcription Factors from Genome-Wide Binding Profiles ». Dans Methods in Molecular Biology, 193–276. New York, NY : Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7027-8_9.

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Klingensmith, William C. « General Concepts in Nuclear Medicine ». Dans The Mathematics and Biology of the Biodistribution of Radiopharmaceuticals - A Clinical Perspective, 3–13. Cham : Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26704-3_1.

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Kovanic, Pavel. « General Relations ». Dans Mathematical Gnostics, 281–306. Boca Raton : CRC Press, 2023. http://dx.doi.org/10.1201/9780429441196-25.

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Flügge, S. « Mathematical Methods ». Dans General Index / Generalregister, 1–17. Berlin, Heidelberg : Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-82502-6_1.

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Tucker, Craig S., et Edwin H. Robinson. « General Biology ». Dans Channel Catfish Farming Handbook, 9–18. Boston, MA : Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-1376-3_2.

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Dubey, J. P., A. Hemphill, R. Calero-Bernal et G. Schares. « General Biology ». Dans Neosporosis in Animals, 7–114. Boca Raton : Taylor & Francis, 2017. : CRC Press, 2017. http://dx.doi.org/10.1201/9781315152561-3.

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Whiteley, Jonathan. « More General Elliptic Problems ». Dans Mathematical Engineering, 143–60. Cham : Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49971-0_8.

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Knickmeier, Katrin, Anja Reckendorf et Dennis Brennecke. « How to Become a Marine Mammal Scientist ». Dans Marine Mammals, 79–89. Cham : Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-06836-2_6.

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AbstractMany young students dream about a career working with marine mammals. Although marine mammal jobs are limited and highly competitive, there are several ways to obtaining them. But, there is no magic formula to pursue a career in marine mammal science. We describe various skill sets and experiences that can improve your chances. Not the least, it is important to actively work towards your career goals and believe in your strengths. We interview marine mammal researchers to inspire students to follow their passion and pursue a career in natural sciences, which may lead to work on marine mammals. In times of climate change, pollution, habitat and biodiversity loss, there is a huge need for students interested in science, technology, biology, engineering and mathematics, to provoke a general change for the better.

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Pallaschke, Diethard, et Stefan Rolewicz. « General Optimality ». Dans Foundations of Mathematical Optimization, 1–55. Dordrecht : Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-1588-1_1.

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Actes de conférences sur le sujet "Mathematical biology in general"

AL-DARABSAH, ISAM, et YUAN YUAN. « DYNAMICS ON A GENERAL STAGE STRUCTURED N PARALLEL FOOD CHAINS ». Dans International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814602228_0004.

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LASKOWSKI, MAREK, et SEYED M. MOGHADAS. « A GENERAL FRAMEWORK FOR AGENT-BASED MODELLING WITH APPLICATIONS TO INFECTIOUS DISEASE DYNAMICS ». Dans International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814602228_0019.

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BARBAROSSA, M. V., et G. RÖST. « MATHEMATICAL MODELS FOR VACCINATION, WANING IMMUNITY AND IMMUNE SYSTEM BOOSTING : A GENERAL FRAMEWORK ». Dans International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814667944_0012.

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Grabarnik, P., et M. Myllymäki. « The generic envelope test and its modifications ». Dans Mathematical Biology and Bioinformatics. Pushchino : IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.111.

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Vagts, Steffen, et Josef Schlattmann. « General Systems Theory in a Horizontal and Vertical Action Process for Cross-Disciplinary Knowledge Transfer ». Dans ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64235.

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Biomimetic product development builds a bridge between the scientific disciplines engineering and biology and represents a cross-disciplinary knowledge circulation, which can produce highly innovative advancements in technology. The methodological support for such projects was initiated by the VDI guideline 6220 by 2012 [1] and still requires further research. The method presented in this abstract tries to provide a significant contribution to the successful transfer of knowledge across disciplines, to convey innovative solutions from biology to technology. The central idea of the method called Heli-Act (an acronym of Helix and Action) described here is based on the system-theoretical analysis of the action and the action carrier, the action circle and the action line under the relevant aspects of the socio-technical integration of methods and tools that will support the action carrier in the biomimetic development process. As a cross-common “language” general systems theory is used, which also includes the mathematical modeling system for both action as well as for object systems, which allows a computer-assisted method implementation. For the association of specialized terminology of the disciplines involved in the cross-disciplinary communication a semantic network is used to derive a translation tool in the Ontology World Language (OWL). Practical application experiences from a current project are presented, which describes the tribological optimization of a technical joint by awareness from the analysis of insects joints.

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Dzhimak, S. S., M. I. Drobotenko, A. A. Svidlo et A. A. Elkina. « INFLUENCE OF THE 2H/1H ISOTOPE COMPOSITION OF A MEDIUM ON THE PROBABILITY OF BROKENING OF HYDROGEN BONDS BETWEEN BASE PAIRS IN A DNA MOLECULE ». Dans NOVEL TECHNOLOGIES IN MEDICINE, BIOLOGY, PHARMACOLOGY AND ECOLOGY. Institute of information technology, 2022. http://dx.doi.org/10.47501/978-5-6044060-2-1.95-101.

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In this work, the role of single substitutions of protium for deuterium in the formation of bub-bles of open states is studied by mathematical modeling methods. It is shown that the proba-bility of formation of bubbles of a certain length (from 12 to 27 nucleotides) depends on the localization of the deuterium atom in the DNA molecule and may differ significantly from the probability of open states in general.

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Diego, Xavier, Eugenio On˜ate et Wing Kam Liu. « Rho-GTPase Regulation by GEFs, GAPs and GDIs in Cell Migration ». Dans ASME 2010 First Global Congress on NanoEngineering for Medicine and Biology. ASMEDC, 2010. http://dx.doi.org/10.1115/nemb2010-13165.

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The family of small RhoGTPases plays a crucial role in the spatial and temporal coordination cell migration. GEFs, GAPs and GDIs are the enzymes that regulate their activity, although the mechanism is poorly understood. Regulation models proposed to date have focused on GEFs as the main modulators of RhoGTPase activity, leaving a passive role to GAPs and GDIs. In this work we show that this assumption leads to models with properties that may be inconsistent with observations, more precisely, appearance of Turing instabilities and reduced sensitivity to secondary stimuli. The mathematical basis of this behavior is established, and a general class of interaction schemes that bypass it by including GAP and GDI regulation, which is supported by experimental evidence, is proposed.

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MIHĂLACHE, Lilia, Natalia JOSU et Teodora VASCAN. « Abordări didactice privind elaborarea și implementarea proiectului STEAM "Enigma inter/transdisciplinară a pomului de Crăciun" în sistemul învățământului general ». Dans Inter/transdisciplinary approaches in the teaching of the real sciences, (STEAM concept) = Abordări inter/transdisciplinare în predarea ştiinţelor reale, (concept STEAM). Ion Creangă Pedagogical State University, 2023. http://dx.doi.org/10.46727/c.steam-2023.p334-338.

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This article proposes different didactic approaches to initiate, develop, and implement a STEAM project in the general education system. The completion of the project with the title „The Inter/Transdisciplinary Analysis of the Christmas Tree” involves the study and examination of the Christmas tree from multiple interdisciplinary perspectives, highlighting the connections between biology, mathematics, computer science, programming, 3D modelling, and the use of 3D printing. All the objectives proposed for the project involve following specific steps, and upon completing these steps, they cultivate knowledge and develop skills and abilities in the students participating in the implementation of the project. All the inter/transdisciplinary mechanisms triggered within this project contribute to guiding students toward choosing a STEAM career and subsequent involvement in some of the branches of the real economy.

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Filipov, Mia, et Ozrenka Meštrović. « Pupils’ Perspective on Video-Based Classroom Research ». Dans 81th International Scientific Conference of the University of Latvia. University of Latvia Press, 2023. http://dx.doi.org/10.22364/htqe.2023.18.

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This case study was part of a practical action research aimed at planning, carrying out and evaluating a video-based professional development program for mathematics and biology teachers. The teachers involved in the research were tasked with implementing elements of effective teaching and their lessons were video-recorded. The research lasted two pandemic school years, from early 2020 to mid-2021. During this period, the recorded lessons were analysed in online learning communities and on Moodle forums. There, the teachers could engage in video-based learning, allowing for a discussion on teaching practices while ensuring collaborative reflection and critical friendship with pedagogues and mathematics or biology teacher educators. However, their pupils were involved in the research only indirectly: they were the objects of recorded lessons with no active role in the process. In addition to analysing recorded lessons, we conducted two group interviews with pupils in order to understand their perspective on the video-based classroom research. Pupils stated that their taking part in video-based classroom research led to some positive changes in themselves, mainly improved attitude towards Mathematics and Biology as school subjects and their self-esteem. However, pupils did not understand why the lessons were video-recorded. They did not understand the positive and negative aspects of recording lessons, which is why their activity decreased during the lessons and they expressed their fear of the camera. Since pupils are at the centre of education, it is necessary to ensure their active involvement in the process of planning, implementing and evaluating changes in teaching, especially since these changes are aimed at improving their learning in general.

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Kelasidi, Eleni, Gard Elgenes et Henrik Kilvær. « Fluid Parameter Identification for Underwater Snake Robots ». Dans ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-78070.

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Nowadays different types of unmanned underwater vehicles (UUVs), such as remotely operated vehicles (ROVs) and autonomous underwater vehicles (AUVs), are widely used for sub-sea inspection, maintenance, and repair (IMR) operations in the oil and gas industry, archaeology, oceanography and marine biology. Also, lately, the development of underwater snake robots (USRs) shows promising results towards extending the capabilities of conventional UUVs. The slender and multi-articulated body of USRs allows for operation in tight spaces where other traditional UUVs are incapable of operating. However, the mathematical model of USRs is more challenging compared to models of ROVs and AUVs, because of its multi-articulated body. It is important to develop accurate models for control design and analysis, to ensure the desired behaviour and to precisely investigate the locomotion efficiency. Modelling the hydrodynamics poses the major challenge since it includes complex and non-linear hydrodynamic effects. The existing analytical models for USRs consider theoretical values for the fluid coefficients and thus they only provide a rough prediction of the effects of hydrodynamics on swimming robots. In order to obtain an accurate prediction of the hydrodynamic forces acting on the links of the USRs, it is necessary to obtain the fluid coefficients experimentally. This paper determines the drag and added mass co-efficients of a general planar model of USRs. In particular, this paper presents methods for identifying fluid parameters based on both computational fluid dynamic (CFD) simulations and several experimental approaches. Additionally, in this paper, we investigate variations of the drag force modelling, providing more accurate representations of the hydrodynamic drag forces. The obtained fluid coefficients are compared to the existing estimates of fluid coefficients for a general model of USRs.

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Rapports d'organisations sur le sujet "Mathematical biology in general"

Wilder, Michael. Improving Hypothesis Testing Skills : Evaluating a General Purpose Classroom Exercise with Biology Students in Grade 9. Portland State University Library, janvier 2000. http://dx.doi.org/10.15760/etd.427.

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Kriegel, Francesco. Learning General Concept Inclusions in Probabilistic Description Logics. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.220.

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Probabilistic interpretations consist of a set of interpretations with a shared domain and a measure assigning a probability to each interpretation. Such structures can be obtained as results of repeated experiments, e.g., in biology, psychology, medicine, etc. A translation between probabilistic and crisp description logics is introduced and then utilised to reduce the construction of a base of general concept inclusions of a probabilistic interpretation to the crisp case for which a method for the axiomatisation of a base of GCIs is well-known.

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Borchmann, Daniel, Felix Distel et Francesco Kriegel. Axiomatization of General Concept Inclusions from Finite Interpretations. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.219.

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Description logic knowledge bases can be used to represent knowledge about a particular domain in a formal and unambiguous manner. Their practical relevance has been shown in many research areas, especially in biology and the semantic web. However, the tasks of constructing knowledge bases itself, often performed by human experts, is difficult, time-consuming and expensive. In particular the synthesis of terminological knowledge is a challenge every expert has to face. Because human experts cannot be omitted completely from the construction of knowledge bases, it would therefore be desirable to at least get some support from machines during this process. To this end, we shall investigate in this work an approach which shall allow us to extract terminological knowledge in the form of general concept inclusions from factual data, where the data is given in the form of vertex and edge labeled graphs. As such graphs appear naturally within the scope of the Semantic Web in the form of sets of RDF triples, the presented approach opens up the possibility to extract terminological knowledge from the Linked Open Data Cloud. We shall also present first experimental results showing that our approach has the potential to be useful for practical applications.

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Frantseva, Anastasiya. The video lectures course "Elements of Mathematical Logic" for students enrolled in the Pedagogical education direction, profile Primary education. Frantseva Anastasiya Sergeevna, avril 2021. http://dx.doi.org/10.12731/frantseva.0411.14042021.

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The video lectures course is intended for full-time and part-time students enrolled in "Pedagogical education" direction, profile "Primary education" or "Primary education - Additional education". The course consists of four lectures on the section "Elements of Mathematical Logic" of the discipline "Theoretical Foundations of the Elementary Course in Mathematics" on the profile "Primary Education". The main lecture materials source is a textbook on mathematics for students of higher pedagogical educational institutions Stoilova L.P. (M.: Academy, 2014.464 p.). The content of the considered mathematics section is adapted to the professional needs of future primary school teachers. It is accompanied by examples of practice exercises from elementary school mathematics textbooks. The course assumes students productive learning activities, which they should carry out during the viewing. The logic’s studying contributes to the formation of the specified profile students of such professional skills as "the ability to carry out pedagogical activities for the implementation of primary general education programs", "the ability to develop methodological support for programs of primary general education." In addition, this section contributes to the formation of such universal and general professional skills as "the ability to perform searching, critical analysis and synthesis of information, to apply a systematic approach to solving the assigned tasks", "the ability to participate in the development of basic and additional educational programs, to design their individual components". The video lectures course was recorded at Irkutsk State University.

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Reuss, Luis, Jr Russell, Jennings John M. et Michael L. Molecular Biology and Functions of Carrier Proteins. Annual Symposium (46th) of the Society of General Physiologists held in Woods Hole, Massachusetts on September 10-13, 1992. Volume 48. Fort Belvoir, VA : Defense Technical Information Center, septembre 1993. http://dx.doi.org/10.21236/ada269599.

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Modlo, Yevhenii O., Serhiy O. Semerikov, Ruslan P. Shajda, Stanislav T. Tolmachev et Oksana M. Markova. Methods of using mobile Internet devices in the formation of the general professional component of bachelor in electromechanics competency in modeling of technical objects. [б. в.], juillet 2020. http://dx.doi.org/10.31812/123456789/3878.

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The article describes the components of methods of using mobile Internet devices in the formation of the general professional component of bachelor in electromechanics competency in modeling of technical objects: using various methods of representing models; solving professional problems using ICT; competence in electric machines and critical thinking. On the content of learning academic disciplines “Higher mathematics”, “Automatic control theory”, “Modeling of electromechanical systems”, “Electrical machines” features of use are disclosed for Scilab, SageCell, Google Sheets, Xcos on Cloud in the formation of the general professional component of bachelor in electromechanics competency in modeling of technical objects. It is concluded that it is advisable to use the following software for mobile Internet devices: a cloud-based spreadsheets as modeling tools (including neural networks), a visual modeling systems as a means of structural modeling of technical objects; a mobile computer mathematical system used at all stages of modeling; a mobile communication tools for organizing joint modeling activities.

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Gottlieb, Yuval, Bradley Mullens et Richard Stouthamer. investigation of the role of bacterial symbionts in regulating the biology and vector competence of Culicoides vectors of animal viruses. United States Department of Agriculture, juin 2015. http://dx.doi.org/10.32747/2015.7699865.bard.

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Symbiotic bacteria have been shown to influence host reproduction and defense against biotic and abiotic stressors, and this relates to possible development of a symbiont-based control strategy. This project was based on the hypothesis that symbionts have a significant impact on Culicoides fitness and vector competence for animal viruses. The original objectives in our proposal were: 1. Molecular identification and localization of the newly-discovered symbiotic bacteria within C. imicola and C. schultzei in Israel and C. sonorensis in California. 2. Determination of the prevalence of symbiotic bacteria within different vector Culicoides populations. 3. Documentation of specific symbiont effects on vector reproduction and defense: 3a) test for cytoplasmic incompatibility in Cardinium-infected species; 3b) experimentally evaluate the role of the symbiont on infection or parasitism by key Culicoides natural enemies (iridescent virus and mermithid nematode). 4. Testing the role(s) of the symbionts in possible protection against infection of vector Culicoides by BTV. According to preliminary findings and difficulties in performing experimental procedures performed in other insect symbiosis systems where insect host cultures are easily maintained, we modified the last two objectives as follows: Obj. 3, we tested how symbionts affected general fitness of Israeli Culicoides species, and thoroughly described and evaluated the correlation between American Culicoides and their bacterial communities in the field. We also tried alternative methods to test symbiont-Culicoides interactions and launched studies to characterize low-temperature stress tolerances of the main US vector, which may be related to symbionts. Obj. 4, we tested the correlation between EHDV (instead of BTV) aquisition and Cardinium infection. Culicoides-bornearboviral diseases are emerging or re-emerging worldwide, causing direct and indirect economic losses as well as reduction in animal welfare. One novel strategy to reduce insects’ vectorial capacity is by manipulating specific symbionts to affect vector fitness or performance of the disease agent within. Little was known on the bacterial tenants occupying various Culicoides species, and thus, this project was initiated with the above aims. During this project, we were able to describe the symbiont Cardinium and whole bacterial communities in Israeli and American Culicoides species respectively. We showed that Cardinium infection prevalence is determined by land surface temperature, and this may be important to the larval stage. We also showed no patent significant effect of Cardinium on adult fitness parameters. We showed that the bacterial community in C. sonorensis varies significantly with the host’s developmental stage, but it varies little across multiple wastewater pond environments. This may indicate some specific biological interactions and allowed us to describe a “core microbiome” for C. sonorensis. The final set of analyses that include habitat sample is currently done, in order to separate the more intimately-associated bacteria from those inhabiting the gut contents or cuticle surface (which also could be important). We were also able to carefully study other biological aspects of Culicoides and were able to discriminate two species in C. schultzei group in Israel, and to investigate low temperature tolerances of C. sonorensis that may be related to symbionts. Scientific implications include the establishment of bacterial identification and interactions in Culicoides (our work is cited in other bacteria-Culicoides studies), the development molecular identification of C. schultzei group, and the detailed description of the microbiome of the immature and matched adult stages of C. sonorensis. Agricultural implications include understanding of intrinsic factors that govern Culicoides biology and population regulation, which may be relevant for vector control or reduction in pathogen transmission. Being able to precisely identify Culicoides species is central to understanding Culicoides borne disease epidemiology.

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Hlushak, Oksana M., Svetlana O. Semenyaka, Volodymyr V. Proshkin, Stanislav V. Sapozhnykov et Oksana S. Lytvyn. The usage of digital technologies in the university training of future bachelors (having been based on the data of mathematical subjects). [б. в.], juillet 2020. http://dx.doi.org/10.31812/123456789/3860.

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This article demonstrates that mathematics in the system of higher education has outgrown the status of the general education subject and should become an integral part of the professional training of future bachelors, including economists, on the basis of intersubject connection with special subjects. Such aspects as the importance of improving the scientific and methodological support of mathematical training of students by means of digital technologies are revealed. It is specified that in order to implement the task of qualified training of students learning econometrics and economic and mathematical modeling, it is necessary to use digital technologies in two directions: for the organization of electronic educational space and in the process of solving applied problems at the junction of the branches of economics and mathematics. The advantages of using e-learning courses in the educational process are presented (such as providing individualization of the educational process in accordance with the needs, characteristics and capabilities of students; improving the quality and efficiency of the educational process; ensuring systematic monitoring of the educational quality). The unified structures of “Econometrics”, “Economic and mathematical modeling” based on the Moodle platform are the following ones. The article presents the results of the pedagogical experiment on the attitude of students to the use of e-learning course (ELC) in the educational process of Borys Grinchenko Kyiv University and Alfred Nobel University (Dnipro city). We found that the following metrics need improvement: availability of time-appropriate mathematical materials; individual approach in training; students’ self-expression and the development of their creativity in the e-learning process. The following opportunities are brought to light the possibilities of digital technologies for the construction and research of econometric models (based on the problem of dependence of the level of the Ukrainian population employment). Various stages of building and testing of the econometric model are characterized: identification of variables, specification of the model, parameterization and verification of the statistical significance of the obtained results.

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Sokolyuk, O. M., N. P. Dement, O. P. Pinchuk et O. V. Slobodyanyk. Features of the use of computer simulations in the school physics course. NAES of Ukraine, 2019. http://dx.doi.org/10.33407/lib.naes.717235.

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The article is devoted to the problem of increasing the methodological level of teaching subjects of the natural mathematical cycle, in particular physics, in institutions of general secondary education. It is noted that the formation of basic competencies in the natural sciences and technologies is possible through the active use of computer-oriented technical means in the educational process. Working with computer models in physics lessons creates the conditions for the realization of cognitive activity of students, positively affects the formation of both the motivational and the substantive-process component of the subject competence of students.

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Alarcon Lopez, Luis Guillermo. The Impact of Obligations in Spectrum Value. Inter-American Development Bank, juillet 2017. http://dx.doi.org/10.18235/0007977.

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Radiofrequency spectrum is an essential asset for mobile network operators. Governments set its value to organize competitive frequency auctions and define recurrent payments, such as taxes and right of use. This publication sustains that governments should value radio frequency spectrum as a function of the intended frequency use policy and corresponding obligations. A mathematical formula is proposed to articulate, quantitatively, the relationship between spectrum value and regulatory obligations, including promoting new market entrants, conditioning of wholesale obligations, definition of coverage goals, and requirement to support public safety and first respondent services. This paper targets, in general, the telecommunication ministries, national regulatory authorities, and government entities that address the topic of valuing radio frequency spectrum.

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