Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on the microscopic level within solid tumors as well as on the macroscopic level across metastases may also contribute to acquired drug resistance. Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and the time to resistance. Specifically we address scenarios with sufficiently potent therapies that suppress growth of all preexisting genetic variants in the compartment with the highest possible drug concentration. To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance, we analyze a multi-type stochastic branching process describing growth of cancer cells in multiple compartments with different drug concentrations and limited migration between compartments. We show that resistance is likely to arise first in the sanctuary compartment with poor drug penetrations and from there populate non-sanctuary compartments with high drug concentrations. Moreover, we show that only below a threshold rate of cell migration does spatial heterogeneity accelerate resistance evolution, otherwise deterring drug resistance with excessively high migration rates. Our results provide new insights into understanding why cancers tend to quickly become resistant, and that cell migration and the presence of sanctuary sites with little drug exposure are essential to this end. Failure of cancer therapy is commonly attributed to the outgrowth of pre-existing resistant mutants already present prior to treatment, yet there is increasing evidence that the tumor microenvironment influences cell sensitivity to drugs and thus mediates the evolution of resistance during treatment. Here, we take into consideration important aspects of the tumor microenvironment, including spatial drug gradients and differential rates of cell proliferation. We show that the dependence of fitness on space together with cell migration facilitates the emergence of acquired resistance. Our analysis indicates that resistant cells that are selected for in compartments with high concentrations are likely to disseminate from sanctuary sites where they first acquire resistance preceding migration. The results suggest that it would be helpful to improve clinical outcomes by combining targeted therapy with anti-metastatic treatment aimed at constraining cell motility as well as by enhancing drug transportation and distribution throughout all metastatic compartments.

In this paper, we analyze Twitter signals as a medium for user sentiment to predict the price fluctuations of a small-cap alternative cryptocurrency called ZClassic. We extracted tweets on an hourly basis for a period of 3.5 weeks, classifying each tweet as positive, neutral, or negative. We then compiled these tweets into an hourly sentiment index, creating an unweighted and weighted index, with the latter giving larger weight to retweets. These two indices, alongside the raw summations of positive, negative, and neutral sentiment were juxtaposed to ~400 data points of hourly pricing data to train an Extreme Gradient Boosting Regression Tree Model. Price predictions produced from this model were compared to historical price data, with the resulting predictions having a 0.81 correlation with the testing data. Our model's predictive data yielded statistical significance at the p < 0.0001 level. Our model is the first academic proof of concept that social media platforms such as Twitter can serve as powerful social signals for predicting price movements in the highly speculative alternative cryptocurrency, or “alt-coin,” market.

Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.

In recent years, social media has become an important platform for political discourse, being a site of both political conversations between voters and political advertisements from campaigns. While their individual influences on public discourse are well documented, the interplay between individual-level cognitive biases, social influence processes, dueling campaign efforts, and social media platforms remains unexamined. We introduce an agent-based model that integrates these dynamics and illustrates how their combination can lead to the formation of echo chambers. We find that the range of political viewpoints that individuals are willing to consider is a key determinant in the formation of polarized networks and the emergence of echo chambers and show that aggressive political campaigns can have counterproductive outcomes by radicalizing supporters and alienating moderates. Our model results demonstrate how certain elements of public discourse and political polarization can be understood as the result of an interactive process of shifting individual opinions, evolving social networks, and political campaigns. We also introduce a dynamic empirical case, retweet networks from the final stage of the 2016 U.S. presidential election, to show how our proposed model can be calibrated with real-world behavior.

Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interest in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological systems and psychological-economic systems, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective paper, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world.

Sequential portfolio selection has attracted increasing interest in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision-making under uncertainty, namely the exploration versus exploitation dilemma, and therefore provides a natural connection to portfolio selection. In this paper, we incorporate risk awareness into the classic multi-armed bandit setting and introduce an algorithm to construct portfolio. Through filtering assets based on the topological structure of the financial market and combining the optimal multi-armed bandit policy with the minimization of a coherent risk measure, we achieve a balance between risk and return.