arXiv subjects

Tom Chou

Publications and source records attributed to Tom Chou.

At least 55 records · Page 3Linked to original sources

arXiv2020

Efficient Scaling and Moving Techniques for Spectral Methods in Unbounded Domains

When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or translated to safely capture the unknown solution. Simply increasing the number of collocation points cannot ensure a fast convergence to spectral accuracy. In this paper, we propose a scaling technique and a moving technique to adaptively cluster enough collocation points in a region of interest in order to achieve a fast spectral convergence. Our scaling algorithm employs an indicator in the frequency domain that is used to determine when scaling is needed and informs the tuning of a scaling factor to redistribute collocation points to adapt to the diffusive behavior of the solution. Our moving technique adopts an exterior-error indicator and moves the collocation points to capture the translation. Both frequency and exterior-error indicators are defined using only the numerical solutions. We apply our methods to a number of different models, including diffusive and moving Fermi-Dirac distributions and nonlinear Dirac solitary waves, and demonstrate recovery of spectral convergence for time-dependent simulations. Performance comparison in solving a linear parabolic problem shows that our frequency scaling algorithm outperforms the existing scaling approaches. We also show our frequency scaling technique is able to track the blowup of average cell sizes in a model for cell proliferation.

math.NA↗

arXiv2020

Stochastic model of randomly end-linked polymer network micro-regions

Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue engineering. While considerable research has been devoted to the modeling of polymer networks to determine averaged, mean-field, global properties, there are fewer studies that specifically examine the variance of the composition across "micro-regions" (composed of a large, but finite, number of polymer network strands) within the larger polymer network.Here, we mathematically model the stochastic formation of polymer networks comprised of linear homobifunctional network strands that undergo an end-linking gelation process. We introduce a master equation that describes the evolution of the probabilities of possible network micro-region configurations as a function of time and extent of reaction. We specifically focus on the dynamics of network formation and the statistical variability of the gel micro-regions, particularly at intermediate extents of reaction. We also consider possible annealing effects and study how cooperative binding between the two end-groups on a single network-strand affects network formation. Our results allow for a more detailed and thorough understanding of polymer network dynamics and variability of network properties.

cond-mat.soft↗

arXiv2020

A machine learning approach to using Quality-of-Life patient scores in guiding prostate radiation therapy dosing

Thanks to advancements in diagnosis and treatment, prostate cancer patients have high long-term survival rates. Currently, an important goal is to preserve quality-of-life during and after treatment. The relationship between the radiation a patient receives and the subsequent side effects he experiences is complex and difficult to model or predict. Here, we use machine learning algorithms and statistical models to explore the connection between radiation treatment and post-treatment gastro-urinary function. Since only a limited number of patient datasets are currently available, we used image flipping and curvature-based interpolation methods to generate more data in order to leverage transfer learning. Using interpolated and augmented data, we trained a convolutional autoencoder network to obtain near-optimal starting points for the weights. A convolutional neural network then analyzed the relationship between patient-reported quality-of-life and radiation. We also used analysis of variance and logistic regression to explore organ sensitivity to radiation and develop dosage thresholds for each organ region. Our findings show no connection between the bladder and quality-of-life scores. However, we found a connection between radiation applied to posterior and anterior rectal regions to changes in quality-of-life. Finally, we estimated radiation therapy dosage thresholds for each organ. Our analysis connects machine learning methods with organ sensitivity, thus providing a framework for informing cancer patient care using patient reported quality-of-life metrics.

q-bio.QM↗

arXiv2020

Why case fatality ratios can be misleading: individual- and population-based mortality estimates and factors influencing them

Different ways of calculating mortality ratios during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. We formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality ratios. The key parameters that affect the dynamics of the different mortality estimates are the incubation period and the time individuals were infected before confirmation of infection. We stress that none of these ratios are accurately represented by the often misinterpreted case fatality ratio (CFR), the number of deaths to date divided by the total number of confirmed infected cases to date. Using data on the recent SARS-CoV-2 outbreaks, we estimate and compare the different dynamic mortality ratios and highlight their differences. Informed by our modeling, we propose more systematic methods to determine mortality ratios during epidemic outbreaks and discuss sensitivity to confounding effects and uncertainties in the data.

q-bio.PE↗

arXiv2020

PDE models of adder mechanisms in cellular proliferation

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth -- the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.

q-bio.CB↗

arXiv2020

Uniformly accurate effective equations for disease transmission mediated by pair formation dynamics

We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptibles and infecteds are distinguished from the population of three types of pairs of individuals; both susceptible, one susceptible and one infected, and both infected. Disease transmission can occur only within a pair consisting of one susceptible individual and one infected individual. By considering the fast pair formation and fast pair dissociation limits, we use a perturbation expansion to formally derive a uniformly valid approximation for the dynamics of the total infected and susceptible populations. Under different parameter regimes, we derive uniformly valid effective equations for the total infected population and compare their results to those of the full mass-action model. Our results are derived from the fundamental mass-action system without implicitly imposing transmission mechanisms such as that used in frequency-dependent models. They provide a new formulation for effective pairing models and are compared with previous models.

q-bio.PE↗

arXiv2020

How heterogeneous thymic output and homeostatic proliferation shape naive T cell receptor clone abundance distributions

The set of T cells that express the same T cell receptor (TCR) sequence represents a T cell clone. The number of different naive T cell clones in an organism reflects the number of different T cell receptors (TCRs) arising from recombination of the V(D)J gene segments during T cell development in the thymus. TCR diversity and more specifically, the clone abundance distribution is an important factor in immune function. Specific recombination patterns occur more frequently than others while subsequent interactions between TCRs and self-antigens are known to trigger proliferation and sustain naive T cell survival. These processes are TCR-dependent, leading to clone-dependent thymic export and naive T cell proliferation rates. Using a mean-field approximation to the solution of a regulated birth-death-immigration model and a modification arising from sampling, we systematically quantify how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells, or "clone counts"). By comparing predicted clone counts derived from our heterogeneous birth-death-immigration model with experimentally sampled clone abundances, we show that although heterogeneity in immigration rates causes very little change to predicted clone-counts, significant heterogeneity in proliferation rates is necessary to generate the observed abundances with reasonable physiological parameter values. Our analysis provides constraints among physiological parameters that are necessary to yield predictions that qualitatively match the data. Assumptions of the model and potentially other important mechanistic factors are discussed.

q-bio.PE↗

arXiv2020

Diversity in Biology: definitions, quantification, and models

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population before outlining the various definitions of `diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.

q-bio.PE↗

arXiv2019

Dynamics of T Cell Receptor Distributions Following Acute Thymic Atrophy and Resumption

Naive human T cells are produced in the thymus, which atrophies abruptly and severely in response to physical or psychological stress. To understand how an instance of stress affects the size and "diversity" of the peripheral naive T cell pool, we derive a mean-field autonomous ODE model of T cell replenishment that allows us to track the clone abundance distribution (the mean number of different TCRs each represented by a specific number of cells). We identify equilibrium solutions that arise at different rates of T cell production, and derive analytic approximations to the dominant eigenvalues and eigenvectors of the problem linearized about these equilibria. From the forms of the eigenvalues and eigenvectors, we estimate rates at which counts of clones of different sizes converge to and depart from equilibrium values--that is, how the number of clones of different sizes "adjust" to the changing rate of T cell production. Under most physiologically realistic realizations of our model, the dominant eigenvalue (representing the slowest dynamics of the clone abundance distribution) scales as a power law in the thymic output for low output levels, but saturates at higher T cell production rates. Our analysis provides a framework for quantitatively understanding how the clone abundance distributions evolve under small changes in the overall T cell production rate by the thymus.

q-bio.PE↗

arXiv2019

A network model of immigration: Enclave formation vs. cultural integration

Successfully integrating newcomers into native communities has become a key issue for policy makers, as the growing number of migrants has brought cultural diversity, new skills, and at times, societal tensions to receiving countries. We develop an agent-based network model to study interacting "hosts" and "guests" and identify the conditions under which cooperative/integrated or uncooperative/segregated societies arise. Players are assumed to seek socioeconomic prosperity through game theoretic rules that shift network links, and cultural acceptance through opinion dynamics. We find that the main predictor of integration under given initial conditions is the timescale associated with cultural adjustment relative to social link remodeling, for both guests and hosts. Fast cultural adjustment results in cooperation and the establishment of host-guest connections that are sustained over long times. Conversely, fast social link remodeling leads to the irreversible formation of isolated enclaves, as migrants and natives optimize their socioeconomic gains through in-group connections. We discuss how migrant population sizes and increasing socioeconomic rewards for host-guest interactions, through governmental incentives or by admitting migrants with highly desirable skills, may affect the overall immigrant experience.

physics.soc-ph↗

arXiv2019

A mathematical model of the effects of aging on naive T-cell population and diversity

The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T-cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T-cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T-cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T-cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T-cells and the resulting overall loss of small immunoclones.

q-bio.PE↗

arXiv2018

Stochastic Evolution of Coagulation-Fragmentation processes using the Accurate Chemical Master Equation approach

Coagulation and fragmentation (CF) is a fundamental process by which particles attach to each other to form clusters while existing clusters break up into smaller ones. It is a ubiquitous process that plays a key role in many physical and biological phenomena. CF is typically a stochastic process that often occurs in confined spaces with a limited number of available particles. In this study, we use the discrete Chemical Master Equation (dCME) to describe the CF process. Using the newly developed Accurate Chemical Master Equation (ACME) method, we calculate the time-dependent behavior of the CF system. We investigate the effects of a number important factors that influence the overall behavior of the system, including the dimensionality, the ratio of attachment to detachment rates among clusters, and the initial conditions. By comparing CF in one and three dimensions we conclude that systems in higher dimensions are more likely to form large clusters. We also demonstrate how the ratio of the attachment to detachment rates affect the dynamics and the steady-state of the system. Finally, we demonstrate the relationship between the formation of large clusters and the initial condition.

cond-mat.stat-mech↗

arXiv2018

Immigration-induced phase transition in a regulated multispecies birth-death process

Power-law-distributed species counts or clone counts arise in many biological settings such as multispecies cell populations, population genetics, and ecology. This empirical observation that the number of species $c_{k}$ represented by $k$ individuals scales as negative powers of $k$ is also supported by a series of theoretical birth-death-immigration (BDI) models that consistently predict many low-population species, a few intermediate-population species, and very high-population species. However, we show how a simple global population-dependent regulation in a neutral BDI model destroys the power law distributions. Simulation of the regulated BDI model shows a high probability of observing a high-population species that dominates the total population. Further analysis reveals that the origin of this breakdown is associated with the failure of a mean-field approximation for the expected species abundance distribution. We find an accurate estimate for the expected distribution $\langle c_k \rangle$ by mapping the problem to a lower-dimensional Moran process, allowing us to also straightforwardly calculate the covariances $\langle c_k c_\ell \rangle$. Finally, we exploit the concepts associated with energy landscapes to explain the failure of the mean-field assumption by identifying a phase transition in the quasi-steady-state species counts triggered by a decreasing immigration rate.

q-bio.PE↗

arXiv2018

Exact steady-state distributions of multispecies birth-death-immigration processes: effects of mutations and carrying capacity on diversity

Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing gene family sizes, modeling lymphocyte evolution in the body, and modeling the evolution of firm sizes. Many of these applications involve the immigration of new species into the system. We develop the full high-dimensional stochastic process associated with multispecies birth-death-immigration processes and present a number of exact and asymptotic results for the steady-state solutions to these types of processes. We considered models that include carrying capacity and random mutations and find analytic and approximate results for the statistics of the total number of individuals, the total number of species, the species size distribution, and various diversity indices. Our results include a rigorous analysis of the behavior of these systems in the fast immigration limit which shows that of the different diversity indices, the species richness is best able to distinguish different types of birth-death-immigration models. Surprisingly, we also find that detailed balance is preserved in all of our neutral birth-death-immigration models, except for those that incorporate carrying capacity through the birth rate.

q-bio.PE↗

arXiv2018

Age-structured social interactions enhance radicalization

Disaffected youth are among the most susceptible in espousing and acting on extremist ideals, as confirmed by demographic studies. To study age-dependent radicalization we introduce a three-stage model where individuals progress through non-radical, activist, and radical states, while also aging. Transitions between stages are modeled as age-dependent interactions that are maximized for individuals of the same age and that are enhanced at early adulthood. For comparison, we also derive the age-independent formulation corresponding to the full age-dependent model. We find that age-dependence leads to more complex dynamics, enhancing radicalization in certain parameter regimes. We also observe waves of radical behavior ebbing and flowing over generational cycles, realizing well known paradigms in political science. While government intervention is most effective when the appropriate ages are targeted, deciding whether preventive or corrective action is preferable depends on the aggressiveness of the radicalization process.

physics.soc-ph↗

arXiv2018

A bistable belief dynamics model for radicalization within sectarian conflict

We introduce a two-variable model to describe spatial polarization, radicalization, and conflict. Individuals in the model harbor a continuous belief variable as well as a discrete radicalization level expressing their tolerance to neighbors with different beliefs. A novel feature of our model is that it incorporates a bistable radicalization process to address memory-dependent social behavior. We demonstrate how bistable radicalization may explain contradicting observations regarding whether social segregation exacerbates or alleviates conflicts. We also extend our model by introducing a mechanism to include institutional influence, such as propaganda or education, and examine its effectiveness. In some parameter regimes, institutional influence may suppress the progression of radicalization and allow a population to achieve social conformity over time. In other cases, institutional intervention may exacerbate the spread of radicalization through a population of mixed beliefs. In such instances, our analysis implies that social segregation may be a viable option against sectarian conflict.

physics.soc-ph↗

arXiv2018

The Effects of Statistical Multiplicity of Infection on Virus Quantification and Infectivity Assays

Many biological assays are employed in virology to quantify parameters of interest. Two such classes of assays, virus quantification assays (VQA) and infectivity assays (IA), aim to estimate the number of viruses present in a solution, and the ability of a viral strain to successfully infect a host cell, respectively. VQAs operate at extremely dilute concentrations and results can be subject to stochastic variability in virus-cell interactions. At the other extreme, high viral particle concentrations are used in IAs, resulting in large numbers of viruses infecting each cell, enough for measurable change in total transcription activity. Furthermore, host cells can be infected at any concentration regime by multiple particles, resulting in a statistical multiplicity of infection (SMOI) and yielding potentially significant variability in the assay signal and parameter estimates. We develop probabilistic models for SMOI at low and high viral particle concentration limits and apply them to the plaque (VQA), endpoint dilution (VQA), and luciferase reporter (IA) assays. A web-based tool implementing our models and analysis is also developed and presented. We test our proposed new methods for inferring experimental parameters from data using numerical simulations and show improvement on existing procedures in all limits.

q-bio.QM↗

arXiv2018

Quantifying the Sensitivity of HIV-1 Viral Entry to Receptor and Coreceptor Expression

Infection by many viruses begins with fusion of viral and cellular lipid membranes, followed by entry of viral contents into the target cell and ultimately, after many biochemical steps, integration of viral DNA into that of the host cell. The early steps of membrane fusion and viral capsid entry are mediated by adsorption to the cell surface, and receptor and coreceptor binding. HIV-1 specifically targets CD4+ helper T-cells of the human immune system and binds to the receptor CD4 and coreceptor CCR5 before fusion is initiated. Previous experiments have been performed using a cell line (293-Affinofile) in which the expression of CD4 and CCR5 concentration were independently controlled. After exposure to HIV-1 of various strains, the resulting infectivity was measured through the fraction of infected cells. To design and evaluate the effectiveness of drug therapies that target the inhibition of the entry processes, an accurate functional relationship between the CD4/CCR5 concentrations and infectivity is desired in order to more quantitatively analyze experimental data. We propose three kinetic models describing the possible mechanistic processes involved in HIV entry and fit their predictions to infectivity measurements, contrasting and comparing different outcomes. Our approach allows interpretation of the clustering of infectivity of different strains of HIV-1 in the space of mechanistic kinetic parameters. Our model fitting also allows inference of nontrivial stoichiometries of receptor and coreceptor binding and provides a framework through which to quantitatively investigate the effectiveness of fusion inhibitors and neutralizing antibodies.

q-bio.QM↗