We address a central issue of phononics: the search of properties or mechanisms to manage the heat flow in reliable materials. We analytically study standard and simple systems modeling the heat flow in solids, namely, the harmonic, self-consistent harmonic and also anharmonic chains of oscillators, and we show an interesting insulating effect: While in the homogeneous models the heat flow decays as the inverse of the particle mass, in the chain with alternate masses it decays as the inverse of the square of the mass difference, that is, it decays essentially as the mass ratio (between the smaller and the larger one) for a large mass difference. A similar effect holds if we alternate on-site potentials instead of particle masses. The existence of such behavior in these different systems, including anharmonic models, indicates that it is a ubiquitous phenomenon with applications in the heat flow control.

IntroductionMultiple myeloma (MM) is a heterogeneous disease where cancer-driver mutations and aberrant signaling may lead to disease progression and drug resistance. Drug responses vary greatly, and there is an unmet need for biomarkers that can guide precision cancer medicine in this disease.MethodsTo identify potential predictors of drug sensitivity, we applied integrated data from drug sensitivity screening, mutational analysis and functional signaling pathway profiling in 9 cell line models of MM. We studied the sensitivity to 33 targeted drugs and their association with the mutational status of cancer-driver genes and activity level of signaling proteins.ResultsWe found that sensitivity to mitogen-activated protein kinase kinase 1 (MEK1) and phosphatidylinositol-3 kinase (PI3K) inhibitors correlated with mutations in NRAS/KRAS, and PI3K family genes, respectively. Phosphorylation status of MEK1 and protein kinase B (AKT) correlated with sensitivity to MEK and PI3K inhibition, respectively. In addition, we found that enhanced phosphorylation of proteins, including Tank-binding kinase 1 (TBK1), as well as high expression of B cell lymphoma 2 (Bcl-2), correlated with low sensitivity to MEK inhibitors.DiscussionTaken together, this study shows that mutational status and signaling protein profiling might be used in further studies to predict drug sensitivities and identify resistance markers in MM.

A major cause of chemoresistance and recurrence in tumors is the presence of dormant tumor foci that survive chemotherapy and can eventually transition to active growth to regenerate the cancer. In this paper, we propose a Quasi Birth-and-Death (QBD) model for the dynamics of tumor growth and recurrence/remission of the cancer. Starting from a discrete-state master equation that describes the timedependent transition probabilities between states with different numbers of dormant and active tumor foci, we develop a framework based on a continuum-limit approach to determine the time-dependent probability that an undetectable residual tumor will become large enough to be detectable. We derive an exact formula for the probability of recurrence at large times and show that it displays a phase transition as a function of the ratio of the death rate µ A of an active tumor focus to its doubling rate λ. We also derive forward and backward Kolmogorov equations for the transition probability density in the continuum limit and, using a first-passage time formalism, we obtain a drift-diffusion equation for the mean recurrence time and solve it analytically to leading order for a large detectable tumor size N . We show that simulations of the discretestate model agree with the analytical results, except for O(1/N ) corrections. Finally, we describe a scheme to fit the model to recurrence-free survival (Kaplan-Meier) curves from clinical cancer data, using ovarian cancer data as an example. Our model has potential applications in predicting how changing chemotherapy schedules may affect disease recurrence rates, especially in cancer types for which no targeted therapy is available.model is formulated in terms of a continuous-time master equation in the discrete state space that represents the numbers of dormant and active tumor foci. In Section 4, it is shown that an expansion of the master equation for a large detectable-tumor size N leads to a simplified approach by mapping the original discretestate model to a stochastic process in a continuous two-dimensional state space. In Section 5, we find the large-time probability of recurrence in closed analytic form and calculate the mean recurrence time (MRT) 70 analytically to leading order in N . In Section 5, we compare these analytical results to simulations and describe a scheme to fit the model to recurrence-free survival (Kaplan-Meier) curves from clinical cancer data, using ovarian cancer data as an example. Finally, in Section (6) we present our concluding remarks. Overview of the discrete-state modelThe precise discrete model for tumor recurrence that will be described in this section was inspired by 75 previous work on the effect of quiescence (i.e., the presence of dormant tumor foci) on treatment success, such as the work of Komarova and Wodarz [8], which inspired the stochastic model described below, or to deterministic versions of their model, proposed in [9], [10], or [11]. However, in contrast to these earlier studies, the focus of our paper is on finding a relatio...