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- Title
- An Efficient And Long-time Accurate Third-order Algorithm For The Stokes-darcy System.
- Creator
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Chen, Wenbin, Gunzburger, Max, Sun, Dong, Wang, Xiaoming
- Abstract/Description
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A third-order in time numerical IMEX-type algorithm for the Stokes-Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams-Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled...
Show moreA third-order in time numerical IMEX-type algorithm for the Stokes-Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams-Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. The scheme is also unconditionally stable and, with a mild time-step restriction, long-time accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. To the authors' knowledge, the novel algorithm is the first third-order accurate numerical scheme for the Stokes-Darcy system possessing its favorable efficiency, stability, and accuracy properties.
Show less - Date Issued
- 2016-12
- Identifier
- FSU_libsubv1_wos_000386770800006, 10.1007/s00211-015-0789-3
- Format
- Citation
- Title
- Analytical Results on the Role of Flexibility in Flapping Propulsion.
- Creator
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Moore, Nicholas
- Abstract/Description
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Wing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop small-amplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing's emergent pitching motions, along with...
Show moreWing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop small-amplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing's emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviours and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. The simple robust estimates afforded by our theory may prove valuable even in situations where details of the flapping motion and wing geometry differ.
Show less - Date Issued
- 2014
- Identifier
- FSU_migr_math_faculty_publications-0002, 10.1017/jfm.2014.533
- Format
- Citation
- Title
- Automatic stage identification of Drosophila egg chamber based on DAPI images.
- Creator
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Jia, Dongyu, Xu, Qiuping, Xie, Qian, Mio, Washington, Deng, Wu-Min
- Abstract/Description
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The Drosophila egg chamber, whose development is divided into 14 stages, is a well-established model for developmental biology. However, visual stage determination can be a tedious, subjective and time-consuming task prone to errors. Our study presents an objective, reliable and repeatable automated method for quantifying cell features and classifying egg chamber stages based on DAPI images. The proposed approach is composed of two steps: 1) a feature extraction step and 2) a statistical...
Show moreThe Drosophila egg chamber, whose development is divided into 14 stages, is a well-established model for developmental biology. However, visual stage determination can be a tedious, subjective and time-consuming task prone to errors. Our study presents an objective, reliable and repeatable automated method for quantifying cell features and classifying egg chamber stages based on DAPI images. The proposed approach is composed of two steps: 1) a feature extraction step and 2) a statistical modeling step. The egg chamber features used are egg chamber size, oocyte size, egg chamber ratio and distribution of follicle cells. Methods for determining the on-site of the polytene stage and centripetal migration are also discussed. The statistical model uses linear and ordinal regression to explore the stage-feature relationships and classify egg chamber stages. Combined with machine learning, our method has great potential to enable discovery of hidden developmental mechanisms.
Show less - Date Issued
- 2016-01-06
- Identifier
- FSU_libsubv1_wos_000368658200001, 10.1038/srep18850
- Format
- Citation
- Title
- Automatic stage identification of Drosophila egg chamber based on DAPI images.
- Creator
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Jia, Dongyu, Xu, Qiuping, Xie, Qian, Mio, Washington, Deng, Wu-Min
- Abstract/Description
-
The Drosophila egg chamber, whose development is divided into 14 stages, is a well-established model for developmental biology. However, visual stage determination can be a tedious, subjective and time-consuming task prone to errors. Our study presents an objective, reliable and repeatable automated method for quantifying cell features and classifying egg chamber stages based on DAPI images. The proposed approach is composed of two steps: 1) a feature extraction step and 2) a statistical...
Show moreThe Drosophila egg chamber, whose development is divided into 14 stages, is a well-established model for developmental biology. However, visual stage determination can be a tedious, subjective and time-consuming task prone to errors. Our study presents an objective, reliable and repeatable automated method for quantifying cell features and classifying egg chamber stages based on DAPI images. The proposed approach is composed of two steps: 1) a feature extraction step and 2) a statistical modeling step. The egg chamber features used are egg chamber size, oocyte size, egg chamber ratio and distribution of follicle cells. Methods for determining the on-site of the polytene stage and centripetal migration are also discussed. The statistical model uses linear and ordinal regression to explore the stage-feature relationships and classify egg chamber stages. Combined with machine learning, our method has great potential to enable discovery of hidden developmental mechanisms.
Show less - Date Issued
- 2016-01-06
- Identifier
- FSU_pmch_26732176, 10.1038/srep18850, PMC4702167, 26732176, 26732176, srep18850
- Format
- Citation
- Title
- Ca2+ Effects on ATP Production and Consumption Have Regulatory Roles on Oscillatory Islet Activity.
- Creator
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McKenna, Joseph P, Ha, Joon, Merrins, Matthew J, Satin, Leslie S, Sherman, Arthur, Bertram, Richard
- Abstract/Description
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Pancreatic islets respond to elevated blood glucose by secreting pulses of insulin that parallel oscillations in β-cell metabolism, intracellular Ca(2+) concentration, and bursting electrical activity. The mechanisms that maintain an oscillatory response are not fully understood, yet several models have been proposed. Only some can account for experiments supporting that metabolism is intrinsically oscillatory in β-cells. The dual oscillator model (DOM) implicates glycolysis as the source of...
Show morePancreatic islets respond to elevated blood glucose by secreting pulses of insulin that parallel oscillations in β-cell metabolism, intracellular Ca(2+) concentration, and bursting electrical activity. The mechanisms that maintain an oscillatory response are not fully understood, yet several models have been proposed. Only some can account for experiments supporting that metabolism is intrinsically oscillatory in β-cells. The dual oscillator model (DOM) implicates glycolysis as the source of oscillatory metabolism. In the companion article, we use recently developed biosensors to confirm that glycolysis is oscillatory and further elucidate the coordination of metabolic and electrical signals in the insulin secretory pathway. In this report, we modify the DOM by incorporating an established link between metabolism and intracellular Ca(2+) to reconcile model predictions with experimental observations from the companion article. With modification, we maintain the distinguishing feature of the DOM, oscillatory glycolysis, but introduce the ability of Ca(2+) influx to reshape glycolytic oscillations by promoting glycolytic efflux. We use the modified model to explain measurements from the companion article and from previously published experiments with islets.
Show less - Date Issued
- 2016-02-02
- Identifier
- FSU_pmch_26840737, 10.1016/j.bpj.2015.11.3526, PMC4744176, 26840737, 26840737, S0006-3495(15)04814-6
- Format
- Citation
- Title
- CAM Stochastic Volatility Model for Option Pricing.
- Creator
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Huang, Wanwan, Ewald, Brian, Oekten, Giray
- Abstract/Description
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The coupled additive and multiplicative (CAM) noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional...
Show moreThe coupled additive and multiplicative (CAM) noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks) of the model. We also derive an approximation for the characteristic function of the model.
Show less - Date Issued
- 2016
- Identifier
- FSU_libsubv1_wos_000376329800001, 10.1155/2016/5496945
- Format
- Citation
- Title
- A Confidence Building Exercise In Data And Identifiability: Modeling Cancer Chemotherapy As A Case Study.
- Creator
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Eisenberg, Marisa C., Jain, Harsh V.
- Abstract/Description
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Mathematical modeling has a long history in the field of cancer therapeutics, and there is increasing recognition that it can help uncover the mechanisms that underlie tumor response to treatment. However, making quantitative predictions with such models often requires parameter estimation from data, raising questions of parameter identifiability and estimability. Even in the case of structural (theoretical) identifiability, imperfect data and the resulting practical unidentifiability of...
Show moreMathematical modeling has a long history in the field of cancer therapeutics, and there is increasing recognition that it can help uncover the mechanisms that underlie tumor response to treatment. However, making quantitative predictions with such models often requires parameter estimation from data, raising questions of parameter identifiability and estimability. Even in the case of structural (theoretical) identifiability, imperfect data and the resulting practical unidentifiability of model parameters can make it difficult to infer the desired information, and in some cases, to yield biologically correct inferences and predictions. Here, we examine parameter identifiability and estimability using a case study of two compartmental, ordinary differential equation models of cancer treatment with drugs that are cell cycle-specific (taxol) as well as non-specific (oxaliplatin). We proceed through model building, structural identifiability analysis, parameter estimation, practical identifiability analysis and its biological implications, as well as alternative data collection protocols and experimental designs that render the model identifiable. We use the differential algebra/input-output relationship approach for structural identifiability, and primarily the profile likelihood approach for practical identifiability. Despite the models being structurally identifiable, we show that without consideration of practical identifiability, incorrect cell cycle distributions can be inferred, that would result in suboptimal therapeutic choices. We illustrate the usefulness of estimating practically identifiable combinations (in addition to the more typically considered structurally identifiable combinations) in generating biologically meaningful insights. We also use simulated data to evaluate how the practical identifiability of the model would change under alternative experimental designs. These results highlight the importance of understanding the underlying mechanisms rather than purely using parsimony or information criteria/goodness-of-fit to decide model selection questions. The overall roadmap for identifiability testing laid out here can be used to help provide mechanistic insight into complex biological phenomena, reduce experimental costs, and optimize model-driven experimentation. (C) 2017 Published by Elsevier Ltd.
Show less - Date Issued
- 10/27/2017
- Identifier
- FSU_libsubv1_wos_000410463600007, 10.1016/j.jtbi.2017.07.018
- Format
- Citation
- Title
- Effects Of Nonuniform Viscosity On Ciliary Locomotion.
- Creator
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Shoele, Kourosh, Eastham, Patrick S.
- Abstract/Description
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The effect of nonuniform viscosity on the swimming velocity of a free swimmer at zero Reynolds number is examined. Using the generalized reciprocal relation for Stokes flow with nonuniform viscosity, we formulate the locomotion problem in a fluid medium with spatially varying viscosity. Assuming the limit of small variation in the viscosity of the fluid as a result of nonuniform distribution of nutrients around a swimmer, we derive a perturbation model to calculate the changes in the swimming...
Show moreThe effect of nonuniform viscosity on the swimming velocity of a free swimmer at zero Reynolds number is examined. Using the generalized reciprocal relation for Stokes flow with nonuniform viscosity, we formulate the locomotion problem in a fluid medium with spatially varying viscosity. Assuming the limit of small variation in the viscosity of the fluid as a result of nonuniform distribution of nutrients around a swimmer, we derive a perturbation model to calculate the changes in the swimming performance of a spherical swimmer as a result of position-dependent viscosity. The swimmer is chosen to be a spherical squirmer with a steady tangential motion on its surface modeling ciliary motion. The nutrient concentration around the body is described by an advection-diffusion equation. The roles of the surface stroke pattern, the specific relationship between the nutrient and viscosity, and the Peclet number of the nutrient in the locomotion velocity of the squirmer are investigated. Our results show that for a pure treadmill stroke, the velocity change is maximum at the limit of zero Peclet number and monotonically decreases toward zero at very high Peclet number. When higher surface stroke modes are present, larger modification in swimming velocity is captured at high Peclet number where two mechanisms of thinning the nutrient boundary layer and appearance of new stagnation points along the surface of squirmer are found to be the primary reasons behind the swimming velocity modifications. It is observed that the presence of nonuniform viscosity allows for optimal swimming speed to be achieved with stroke combinations other than pure treadmill.
Show less - Date Issued
- 2018-04-24
- Identifier
- FSU_libsubv1_wos_000430691900001, 10.1103/PhysRevFluids.3.043101
- Format
- Citation
- Title
- Generalized Mahalanobis Depth In Point Process And Its Application In Neural Coding.
- Creator
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Liu, Shuyi, Wu, Wei
- Abstract/Description
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In this paper, we propose to generalize the notion of depth in temporal point process observations. The new depth is defined as a weighted product of two probability terms: (1) the number of events in each process, and (2) the center-outward ranking on the event times conditioned on the number of events. In this study, we adopt the Poisson distribution for the first term and the Mahalanobis depth for the second term. We propose an efficient boot-strapping approach to estimate parameters in...
Show moreIn this paper, we propose to generalize the notion of depth in temporal point process observations. The new depth is defined as a weighted product of two probability terms: (1) the number of events in each process, and (2) the center-outward ranking on the event times conditioned on the number of events. In this study, we adopt the Poisson distribution for the first term and the Mahalanobis depth for the second term. We propose an efficient boot-strapping approach to estimate parameters in the defined depth. In the case of Poisson process, the observed events are order statistics where the parameters can be estimated robustly with respect to sample size. We demonstrate the use of the new depth by ranking realizations from a Poisson process. We also test the new method in classification problems using simulations as well as real neural spike train data. It is found that the new framework provides more accurate and robust classifications as compared to commonly used likelihood methods.
Show less - Date Issued
- 2017-06
- Identifier
- FSU_libsubv1_wos_000408732000021, 10.1214/17-AOAS1030
- Format
- Citation
- Title
- Genome-wide Association Study Reveals Multiple Loci Influencing Normal Human Facial Morphology.
- Creator
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Shaffer, John R., Orlova, Ekaterina, Lee, Myoung Keun, Leslie, Elizabeth J., Raffensperger, Zachary D., Heike, Carrie L., Cunningham, Michael L., Hecht, Jacqueline T., Kau,...
Show moreShaffer, John R., Orlova, Ekaterina, Lee, Myoung Keun, Leslie, Elizabeth J., Raffensperger, Zachary D., Heike, Carrie L., Cunningham, Michael L., Hecht, Jacqueline T., Kau, Chung How, Nidey, Nichole L., Moreno, Lina M., Wehby, George L., Murray, Jeffrey C., Laurie, Cecelia A., Laurie, Cathy C., Cole, Joanne, Ferrara, Tracey, Santorico, Stephanie, Klein, Ophir, Mio, Washington, Feingold, Eleanor, Hallgrimsson, Benedikt, Spritz, Richard A., Marazita, Mary L., Weinberg, Seth M.
Show less - Abstract/Description
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Numerous lines of evidence point to a genetic basis for facial morphology in humans, yet little is known about how specific genetic variants relate to the phenotypic expression of many common facial features. We conducted genome-wide association meta-analyses of 20 quantitative facial measurements derived from the 3D surface images of 3118 healthy individuals of European ancestry belonging to two US cohorts. Analyses were performed on just under one million genotyped SNPs (Illumina...
Show moreNumerous lines of evidence point to a genetic basis for facial morphology in humans, yet little is known about how specific genetic variants relate to the phenotypic expression of many common facial features. We conducted genome-wide association meta-analyses of 20 quantitative facial measurements derived from the 3D surface images of 3118 healthy individuals of European ancestry belonging to two US cohorts. Analyses were performed on just under one million genotyped SNPs (Illumina OmniExpress+Exome v1.2 array) imputed to the 1000 Genomes reference panel (Phase 3). We observed genome-wide significant associations (p < 5 x 10(-8)) for cranial base width at 14q21.1 and 20q12, intercanthal width at 21p13.3 and Xq13.2, nasal width at 20p11.22, nasal ala length at 14q11.2, and upper facial depth at 11q22.1. Several genes in the associated regions are known to play roles in craniofacial development or in syndromes affecting the face: MAFB, PAX9, MIPOL1, ALX3, HDAC8, and PAX1. We also tested genotype-phenotype associations reported in two previous genome-wide studies and found evidence of replication for nasal ala length and SNPs in CACNA2D3 and PRDM16. These results provide further evidence that common variants in regions harboring genes of known craniofacial function contribute to normal variation in human facial features. Improved understanding of the genes associated with facial morphology in healthy individuals can provide insights into the pathways and mechanisms controlling normal and abnormal facial morphogenesis.
Show less - Date Issued
- 2016-08
- Identifier
- FSU_libsubv1_wos_000382394500007, 10.1371/journal.pgen.1006149
- Format
- Citation
- Title
- Genomewide Association Study of African Children Identifies Association of SCHIP1 and PDE8A with Facial Size and Shape.
- Creator
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Cole, Joanne B., Manyama, Mange, Kimwaga, Emmanuel, Mathayo, Joshua, Larson, Jacinda R., Liberton, Denise K., Lukowiak, Ken, Ferrara, Tracey M., Riccardi, Sheri L., Li, Mao, Mio...
Show moreCole, Joanne B., Manyama, Mange, Kimwaga, Emmanuel, Mathayo, Joshua, Larson, Jacinda R., Liberton, Denise K., Lukowiak, Ken, Ferrara, Tracey M., Riccardi, Sheri L., Li, Mao, Mio, Washington, Prochazkova, Michaela, Williams, Trevor, Li, Hong, Jones, Kenneth L., Klein, Ophir D., Santorico, Stephanie A., Hallgrimsson, Benedikt, Spritz, Richard A.
Show less - Abstract/Description
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The human face is a complex assemblage of highly variable yet clearly heritable anatomic structures that together make each of us unique, distinguishable, and recognizable. Relatively little is known about the genetic underpinnings of normal human facial variation. To address this, we carried out a large genomewide association study and two independent replication studies of Bantu African children and adolescents from Mwanza, Tanzania, a region that is both genetically and environmentally...
Show moreThe human face is a complex assemblage of highly variable yet clearly heritable anatomic structures that together make each of us unique, distinguishable, and recognizable. Relatively little is known about the genetic underpinnings of normal human facial variation. To address this, we carried out a large genomewide association study and two independent replication studies of Bantu African children and adolescents from Mwanza, Tanzania, a region that is both genetically and environmentally relatively homogeneous. We tested for genetic association of facial shape and size phenotypes derived from 3D imaging and automated landmarking of standard facial morphometric points. SNPs within genes SCHIP1 and PDE8A were associated with measures of facial size in both the GWAS and replication cohorts and passed a stringent genomewide significance threshold adjusted for multiple testing of 34 correlated traits. For both SCHIP1 and PDE8A, we demonstrated clear expression in the developing mouse face by both whole-mount in situ hybridization and RNA-seq, supporting their involvement in facial morphogenesis. Ten additional loci demonstrated suggestive association with various measures of facial shape. Our findings, which differ from those in previous studies of European-derived whites, augment understanding of the genetic basis of normal facial development, and provide insights relevant to both human disease and forensics.
Show less - Date Issued
- 2016-08
- Identifier
- FSU_libsubv1_wos_000382394500010, 10.1371/journal.pgen.1006174
- Format
- Citation
- Title
- Inverse Scattering Transform For The Nonlocal Nonlinear Schrodinger Equation With Nonzero Boundary Conditions.
- Creator
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Ablowitz, Mark J., Luo, Xu-Dan, Musslimani, Ziad H.
- Abstract/Description
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In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrodinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of...
Show moreIn 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrodinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons. Published by AIP Publishing.
Show less - Date Issued
- 2018-01
- Identifier
- FSU_libsubv1_wos_000424017000001, 10.1063/1.5018294
- Format
- Citation
- Title
- Investigation of drop impact on dry and wet surfaces with consideration of surrounding air.
- Creator
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Guo, Yisen, Lian, Yongsheng, Sussman, Mark
- Abstract/Description
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Numerical simulations were conducted to investigate drop impingement and splashing on both dry and wet surfaces at impact velocities greater than 50 m/s with the consideration of the effect of surrounding air. The Navier-Stokes equations were solved using the variable density pressure projection method on a dynamic block structured adaptive grid. The moment of fluid method was used to reconstruct interfaces separating different phases. A dynamic contact angle model was used to define the...
Show moreNumerical simulations were conducted to investigate drop impingement and splashing on both dry and wet surfaces at impact velocities greater than 50 m/s with the consideration of the effect of surrounding air. The Navier-Stokes equations were solved using the variable density pressure projection method on a dynamic block structured adaptive grid. The moment of fluid method was used to reconstruct interfaces separating different phases. A dynamic contact angle model was used to define the boundary condition at the moving contact line. Simulations showed that lowering the ambient gas density can suppress dry surface splashing, which is in agreement with the experiments. A recirculation zone was observed inside the drop after contact: a larger recirculation zone was formed earlier in the higher gas density case than in the lower gas density case. Increasing gas density also enhances the creation of secondary droplets from the lamella breakup. For high speed impact on a dry surface, lowering ambient gas density attenuates splashing. However, ambient air does not significantly affect splashing on a wet surface. Simulations showed that the splashed droplets are primarily from the exiting liquid film. Published by AIP Publishing.
Show less - Date Issued
- 2016-07
- Identifier
- FSU_libsubv1_wos_000382446200015, 10.1063/1.4958694
- Format
- Citation
- Title
- Iterated Elliptic And Hypergeometric Integrals For Feynman Diagrams.
- Creator
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Ablinger, J., Bluemlein, J., De Freitas, A., van Hoeij, M., Imamoglu, E., Raab, C. G., Radu, C.-S., Schneider, C.
- Abstract/Description
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We calculate 3-loop master integrals for heavy quark correlators and the 3-loop quantum chromodynamics corrections to the rho-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of F-2(1) Gau beta hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic...
Show moreWe calculate 3-loop master integrals for heavy quark correlators and the 3-loop quantum chromodynamics corrections to the rho-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of F-2(1) Gau beta hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's nu(i) functions and Dedekind's eta-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/eta(k) (tau), logarithms, and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented. Published by AIP Publishing.
Show less - Date Issued
- 2018-06-01
- Identifier
- FSU_libsubv1_wos_000437094100030, 10.1063/1.4986417
- Format
- Citation
- Title
- Large Deviations And Applications For Markovian Hawkes Processes With A Large Initial Intensity.
- Creator
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Gao, Xuefeng, Zhu, Lingjiong
- Abstract/Description
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Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study linear Hawkes process with an exponential kernel in the asymptotic regime where the initial intensity of the Hawkes process is large. We establish large deviations for...
Show moreHawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study linear Hawkes process with an exponential kernel in the asymptotic regime where the initial intensity of the Hawkes process is large. We establish large deviations for Hawkes processes in this regime as well as the regime when both the initial intensity and the time are large. We illustrate the strength of our results by discussing the applications to insurance and queueing systems.
Show less - Date Issued
- 2018-11-01
- Identifier
- FSU_libsubv1_wos_000429696200015, 10.3150/17-BEJ948
- Format
- Citation
- Title
- On The Evolution Of Partial Respect For Ownership.
- Creator
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Mesterton-Gibbons, Mike, Karabiyik, Tugba, Sherratt, Tom N.
- Abstract/Description
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An early prediction of game theory was that respect for ownership-"Bourgeois" or behavior-can arise as an arbitrary convention to avoid costly disputes. However, its mirror image-the dispute-avoiding "anti-Bourgeois" or behavior through which owners concede their property to intruders-also corresponds to an evolutionarily stable strategy (ESS) under the same conditions. It has since been found repeatedly that first finders of valuable resources are frequently left unchallenged in nature,...
Show moreAn early prediction of game theory was that respect for ownership-"Bourgeois" or behavior-can arise as an arbitrary convention to avoid costly disputes. However, its mirror image-the dispute-avoiding "anti-Bourgeois" or behavior through which owners concede their property to intruders-also corresponds to an evolutionarily stable strategy (ESS) under the same conditions. It has since been found repeatedly that first finders of valuable resources are frequently left unchallenged in nature, while evidence for ceding property to intruders without a contest is rare at best. An early verbal rationale for the observed rarity of was that two individuals employing such behavior over repeated rounds would be interchanging roles repeatedly, a potentially inefficient outcome known as "infinite regress." This argument was formalized only recently, through a Hawk-Dove model with ownership asymmetry and a fixed probability that two individuals meet again. The analysis showed that if and the cost of fighting exceed thresholds determined by the costs of assuming and relinquishing ownership, then becomes the only stable convention. However, contrary to expectation, and despite the inefficiency of the equilibrium, the analysis also showed that "infinite regress" does not invariably render unviable. Nevertheless, this model dealt only with ESSs at which respect for ownership is either absolute or entirely absent. Here, we extend the model to allow for polymorphic evolutionarily stable states, and we use it to explore the conditions that favor partial respect for ownership. In this way, we produce an analytic model that predicts a range of degrees of partial respect for ownership, dependent on model parameters. In particular, we identify a pathway through which any degree of respect for ownership can evolve from absolute disrespect under increasing with increasing costs of fighting.
Show less - Date Issued
- 2016-09
- Identifier
- FSU_libsubv1_wos_000381210600006, 10.1007/s13235-015-0152-4
- Format
- Citation
- Title
- OPTIMAL MODEL MANAGEMENT FOR MULTIFIDELITY MONTE CARLO ESTIMATION.
- Creator
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Peherstorfer, Benjamin, Willcox, Karen, Gunzburger, Max
- Abstract/Description
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This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector...
Show moreThis work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only.
Show less - Date Issued
- 2016
- Identifier
- FSU_libsubv1_wos_000387347700070, 10.1137/15M1046472
- Format
- Citation
- Title
- OPTIMAL MODEL MANAGEMENT FOR MULTIFIDELITY MONTE CARLO ESTIMATION.
- Creator
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Peherstorfer, Benjamin, Willcox, Karen, Gunzburger, Max
- Abstract/Description
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This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector...
Show moreThis work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only.
Show less - Date Issued
- 2016
- Identifier
- FSU_libsubv1_wos_000387347700070, 10.1137/15M1046472
- Format
- Citation
- Title
- Phase Analysis of Metabolic Oscillations and Membrane Potential in Pancreatic Islet β-Cells.
- Creator
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Merrins, Matthew J, Poudel, Chetan, McKenna, Joseph P, Ha, Joon, Sherman, Arthur, Bertram, Richard, Satin, Leslie S
- Abstract/Description
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Metabolism in islet β-cells displays oscillations that can trigger pulses of electrical activity and insulin secretion. There has been a decades-long debate among islet biologists about whether metabolic oscillations are intrinsic or occur in response to oscillations in intracellular Ca(2+) that result from bursting electrical activity. In this article, the dynamics of oscillatory metabolism were investigated using five different optical reporters. Reporter activity was measured...
Show moreMetabolism in islet β-cells displays oscillations that can trigger pulses of electrical activity and insulin secretion. There has been a decades-long debate among islet biologists about whether metabolic oscillations are intrinsic or occur in response to oscillations in intracellular Ca(2+) that result from bursting electrical activity. In this article, the dynamics of oscillatory metabolism were investigated using five different optical reporters. Reporter activity was measured simultaneously with membrane potential bursting to determine the phase relationships between the metabolic oscillations and electrical activity. Our experimental findings suggest that Ca(2+) entry into β-cells stimulates the rate of mitochondrial metabolism, accounting for the depletion of glycolytic intermediates during each oscillatory burst. We also performed Ca(2+) clamp tests in which we clamped membrane potential with the KATP channel-opener diazoxide and KCl to fix Ca(2+) at an elevated level. These tests confirm that metabolic oscillations do not require Ca(2+) oscillations, but show that Ca(2+) plays a larger role in shaping metabolic oscillations than previously suspected. A dynamical picture of the mechanisms of oscillations emerged that requires the restructuring of contemporary mathematical β-cell models, including our own dual oscillator model. In the companion article, we modified our model to account for these new data.
Show less - Date Issued
- 2016-02-02
- Identifier
- FSU_pmch_26840733, 10.1016/j.bpj.2015.12.029, PMC4744170, 26840733, 26840733, S0006-3495(15)04813-4
- Format
- Citation
- Title
- Predictive Computer Models for Biofilm Detachment Properties in Pseudomonas aeruginosa.
- Creator
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Cogan, Nick G., Harro, Janette M., Stoodley, Paul, Shirtliff, Mark E.
- Abstract/Description
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Microbial biofilm communities are protected against environmental extremes or clearance by antimicrobial agents or the host immune response. They also serve as a site from which microbial populations search for new niches by dispersion via single planktonic cells or by detachment by protected biofilm aggregates that, until recently, were thought to become single cells ready for attachment. Mathematically modeling these events has provided investigators with testable hypotheses for further...
Show moreMicrobial biofilm communities are protected against environmental extremes or clearance by antimicrobial agents or the host immune response. They also serve as a site from which microbial populations search for new niches by dispersion via single planktonic cells or by detachment by protected biofilm aggregates that, until recently, were thought to become single cells ready for attachment. Mathematically modeling these events has provided investigators with testable hypotheses for further study. Such was the case in the recent article by Kragh et al. (K. N. Kragh, J. B. Hutchison, G. Melaugh, C. Rodesney, A. E. Roberts, Y. Irie, P. O. Jensen, S. P. Diggle, R. J. Allen, V. Gordon, and T. Bjarnsholt, mBio 7: e00237-16, 2016, http://dx.doi.org/10.1128/mBio.00237-16), in which investigators were able to identify the differential competitive advantage of biofilm aggregates to directly attach to surfaces compared to the single-celled planktonic populations. Therefore, as we delve deeper into the properties of the biofilm mode of growth, not only do we need to understand the complexity of biofilms, but we must also account for the properties of the dispersed and detached populations and their effect on reseeding.
Show less - Date Issued
- 2016-06
- Identifier
- FSU_libsubv1_wos_000383440300066, 10.1128/mBio.00815-16
- Format
- Citation
- Title
- Predictive Computer Models for Biofilm Detachment Properties in Pseudomonas aeruginosa.
- Creator
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Cogan, Nick G, Harro, Janette M, Stoodley, Paul, Shirtliff, Mark E
- Abstract/Description
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Microbial biofilm communities are protected against environmental extremes or clearance by antimicrobial agents or the host immune response. They also serve as a site from which microbial populations search for new niches by dispersion via single planktonic cells or by detachment by protected biofilm aggregates that, until recently, were thought to become single cells ready for attachment. Mathematically modeling these events has provided investigators with testable hypotheses for further...
Show moreMicrobial biofilm communities are protected against environmental extremes or clearance by antimicrobial agents or the host immune response. They also serve as a site from which microbial populations search for new niches by dispersion via single planktonic cells or by detachment by protected biofilm aggregates that, until recently, were thought to become single cells ready for attachment. Mathematically modeling these events has provided investigators with testable hypotheses for further study. Such was the case in the recent article by Kragh et al. (K. N. Kragh, J. B. Hutchison, G. Melaugh, C. Rodesney, A. E. Roberts, Y. Irie, P. Ø. Jensen, S. P. Diggle, R. J. Allen, V. Gordon, and T. Bjarnsholt, mBio 7:e00237-16, 2016, http://dx.doi.org/10.1128/mBio.00237-16), in which investigators were able to identify the differential competitive advantage of biofilm aggregates to directly attach to surfaces compared to the single-celled planktonic populations. Therefore, as we delve deeper into the properties of the biofilm mode of growth, not only do we need to understand the complexity of biofilms, but we must also account for the properties of the dispersed and detached populations and their effect on reseeding.
Show less - Date Issued
- 2016-06-14
- Identifier
- FSU_pmch_27302761, 10.1128/mBio.00815-16, PMC4916383, 27302761, 27302761, mBio.00815-16
- Format
- Citation
- Title
- Quantifying the Relative Contributions of Divisive and Subtractive Feedback to Rhythm Generation.
- Creator
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Tabak-Sznajder, Joel, Rinzel, John, Bertram, R. (Richard)
- Abstract/Description
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Biological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes:...
Show moreBiological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes: divisive (decreases the gain of the positive feedback loop) and subtractive (increases the input threshold) that both contribute to slowly move the system between the high- and low-activity states. Can we determine the relative contribution of each type of negative feedback process to the rhythmic activity? Does one dominate? Do they control the active and silent phase equally? To answer these questions we use a neural network model with excitatory coupling, regulated by synaptic depression (divisive) and cellular adaptation (subtractive feedback). We first attempt to apply standard experimental methodologies: either passive observation to correlate the variations of a variable of interest to system behavior, or deletion of a component to establish whether a component is critical for the system. We find that these two strategies can lead to contradictory conclusions, and at best their interpretive power is limited. We instead develop a computational measure of the contribution of a process, by evaluating the sensitivity of the active (high activity) and silent (low activity) phase durations to the time constant of the process. The measure shows that both processes control the active phase, in proportion to their speed and relative weight. However, only the subtractive process plays a major role in setting the duration of the silent phase. This computational method can be used to analyze the role of negative feedback processes in a wide range of biological rhythms.
Show less - Date Issued
- 2011
- Identifier
- FSU_migr_math_faculty_publications-0003, 10.1371/journal.pcbi.1001124
- Format
- Citation
- Title
- Statistical Shape Analysis Of Simplified Neuronal Trees.
- Creator
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Duncan, Adam, Klassen, Eric, Srivastava, Anuj
- Abstract/Description
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Neuron morphology plays a central role in characterizing cognitive health and functionality of brain structures. The problem of quantifying neuron shapes and capturing statistical variability of shapes is difficult because neurons differ both in geometry and in topology. This paper develops a mathematical representation of neuronal trees, restricting to the trees that consist of: (1) a main branch viewed as a parameterized curve in R-3, and (2) some number of secondary branches-also...
Show moreNeuron morphology plays a central role in characterizing cognitive health and functionality of brain structures. The problem of quantifying neuron shapes and capturing statistical variability of shapes is difficult because neurons differ both in geometry and in topology. This paper develops a mathematical representation of neuronal trees, restricting to the trees that consist of: (1) a main branch viewed as a parameterized curve in R-3, and (2) some number of secondary branches-also parameterized curves in R-3-which emanate from the main branch at arbitrary points. It imposes a metric on the representation space, in order to compare neuronal shapes, and to obtain optimal deformations (geodesics) across arbitrary trees. The key idea is to impose certain equivalence relations that allow trees with different geometries and topologies to be compared efficiently. The combinatorial problem of matching side branches across trees is reduced to a linear assignment with well-known efficient solutions. This framework is then applied to comparing, clustering, and classifying neurons using fully automated algorithms. The framework is illustrated on three datasets of neuron reconstructions, specifically showing geodesics paths and cross-validated classification between experimental groups.
Show less - Date Issued
- 2018-09-01
- Identifier
- FSU_libsubv1_wos_000444259500002, 10.1214/17-AOAS1107
- Format
- Citation
- Title
- Twofold PT symmetry in doubly exponential optical lattices.
- Creator
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Cole, J. T., Makris, K. G., Musslimani, Z. H., Christodoulides, D. N., Rotter, S.
- Abstract/Description
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We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of PT symmetry is not around zero and the potential satisfies a shifted PT-symmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics,...
Show moreWe introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of PT symmetry is not around zero and the potential satisfies a shifted PT-symmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted PT-symmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.
Show less - Date Issued
- 2016-01-04
- Identifier
- FSU_libsubv1_wos_000367658200014, 10.1103/PhysRevA.93.013803
- Format
- Citation
- Title
- Vortices In Bose-einstein Condensates With Pt-symmetric Gain And Loss.
- Creator
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Schwarz, Lukas, Cartarius, Holger, Musslimani, Ziad H., Main, Joerg, Wunner, Guenter
- Abstract/Description
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We investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex PT symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to nonvortex states. In addition, we study...
Show moreWe investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex PT symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to nonvortex states. In addition, we study the influences of PT symmetry on the dynamics of nonstationary vortex states placed at off-center positions.
Show less - Date Issued
- 2017-05-12
- Identifier
- FSU_libsubv1_wos_000401189500012, 10.1103/PhysRevA.95.053613
- Format
- Citation
