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.

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.

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.

According 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).

The 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.