# Your search: "author:"Komarova, Natalia L""

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## Scholarly Works (29 results)

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur e.g. when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study we present a new interpretation of existing algorithms to model and investigate the process of a learner learning from an inconsistent source. Our model allows us to analyze and present a theoretical explanation of a frequency boosting property, whereby the learner surpasses the fluency of the source by increasing the frequency of the most common input. We then focus on two applications of our model. One is using our model to describe the ``Object-Label-Order" effect. The other is to describe the evolution of the first word.

Similar to tissue stem cells, primitive tumor cells in chronic myelogenous leukemia have been observed to undergo quiescence; that is, the cells can temporarily stop dividing. Using mathematical models, we investigate the effect of cellular quiescence on the outcome of therapy with targeted small molecule inhibitors.

Methods and ResultsAccording to the models, the initiation of treatment can result in different patterns of tumor cell decline: a biphasic decline, a one-phase decline, and a reverse biphasic decline. A biphasic decline involves a fast initial phase (which roughly corresponds to the eradication of cycling cells by the drug), followed by a second and slower phase of exponential decline (corresponding to awakening and death of quiescent cells), which helps explain clinical data. We define the time when the switch to the second phase occurs, and identify parameters that determine whether therapy can drive the tumor extinct in a reasonable period of time or not. We further ask how cellular quiescence affects the evolution of drug resistance. We find that it has no effect on the probability that resistant mutants exist before therapy if treatment occurs with a single drug, but that quiescence increases the probability of having resistant mutants if patients are treated with a combination of two or more drugs with different targets. Interestingly, while quiescence prolongs the time until therapy reduces the number of cells to low levels or extinction, the therapy phase is irrelevant for the evolution of drug resistant mutants. If treatment fails as a result of resistance, the mutants will have evolved during the tumor growth phase, before the start of therapy. Thus, prevention of resistance is not promoted by reducing the quiescent cell population during therapy (e.g., by a combination of cell activation and drug-mediated killing).

ConclusionsThe mathematical models provide insights into the effect of quiescence on the basic kinetics of the response to targeted treatment of CML. They identify determinants of success in the absence of drug resistant mutants, and elucidate how quiescence influences the emergence of drug resistant mutants.

Investigating the interactions between universal and culturally specific influences on color categorization across individuals and cultures has proven to be a challenge for human color categorization and naming research. The present article simulates the evolution of color lexicons to evaluate the role of two realistic constraints found in the human phenomenon: (i) heterogeneous observer populations and (ii) heterogeneous color stimuli. Such constraints, idealized and implemented as agent categorization and communication games, produce interesting and unexpected consequences for stable categorization solutions evolved and shared by agent populations. We find that the presence of a small fraction of color deficient agents in a population, or the presence of a "region of increased salience" in the color stimulus space, break rotational symmetry in population categorization solutions, and confine color category boundaries to a subset of available locations. Further, these heterogeneities, each in a different, predictable, way, might lead to a change of category number and size. In addition, the concurrent presence of both types of heterogeneity gives rise to novel constrained solutions which optimize the success rate of categorization and communication games. Implications of these agent-based results for psychological theories of color categorization and the evolution of color naming systems in human societies are discussed.

Cooperation in biology and diversification of species have been widely studied by both evolutionary biologists and mathematicians. In this work we examine both of these seemingly unrelated phenomena and propose that there could be a context where they are connected. We focus on a setting where individuals in a shared environment cooperate by sharing products of two distinct parts of a complex task. Different strategies can evolve: individuals can complete all parts of the complex task, choosing self-sufficiency over cooperation, or they may choose to split parts of the task and share the products for mutual benefit, such that distinct groups of the organisms specialize on a subset of elementary tasks. We first examine this possibility using a quasispecies system, and then by using the methodology of adaptive dynamics, both analytically and by stochastic agent-based simulations, to investigate the conditions where branching into distinct cooperating subgroups occurs. We show that if performing multiple tasks is associated with additional cost, branching occurs for a wide parameter range, and is stable against the invasion of non-cooperating non-producers (``cheaters''). We hypothesize that over time, this can lead to evolutionary speciation, providing a novel mechanism of speciation based on cooperation. In addition, we investigate whether microscopic assumptions of the interaction rules of the simulations may play a role in the resulting dynamics. To do this, we derive ordinary differential equations for the mean trait values for four models, which differ by (1) the number of interactions each individual engages in before the payoff is determined (interacting with the entire population vs interacting with one randomly chosen individual), and (2) the type of criterion (probabilistic vs deterministic) by which the winner of each competition is determined. We find that the mean trait dynamics are the same in all four cases when only one trait in a population of cooperators is evolving. However, when we include ``cheaters'' we find, surprisingly, that the rules do make a difference, and the steady state to which the system converges can depend both on the number of interactions and on the criterion for determining the winners.

In this dissertation two independent studies are presented in the field of ordinary differential equations. In the first part we introduce a novel model of viral dynamics to describe the phenomenon of multiple infection. An important parameter in determining the properties of the model is the viral output of multiply infected cells compared to that of singly infected cells. If multiply infected cells produce more virus during their life-span than singly infected cells, then the properties of the viral dynamics can change fundamentally. The first part of this study presents a detailed mathematical analysis of this scenario.

In the second part we develop a class of mathematical models to study the evolutionary competition dynamics among different sub-populations in a heterogeneous tumor. We observe that despite the complexity of this system there are only a small number of scenarios expected in the context of the evolution of instability. Here we discuss these scenarios and their dependence on the subtle interplay among mutation rates and the death toll associated with instability. We also present possible patterns of instability for cancer lineages corresponding to different stages of progression and determine whether instability plays a causal role in tumor evolution.