Resistor-network anomalies in the heat transport of random harmonic chains.

We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance G on the length L of the sample. This is required by nanotechnology implementations because for such networks Fourier's law G∝1/L^{α} with α=1 is violated. In particular we consider "glassy" disorder in the coupling constants and find an anomaly which is related by duality to the Lifshitz-tail regime in the standard Anderson model.

CEL-Seq2: sensitive highly-multiplexed single-cell RNA-Seq.

Single-cell transcriptomics requires a method that is sensitive, accurate, and reproducible. Here, we present CEL-Seq2, a modified version of our CEL-Seq method, with threefold higher sensitivity, lower costs, and less hands-on time. We implemented CEL-Seq2 on Fluidigm's C1 system, providing its first single-cell, on-chip barcoding method, and we detected gene expression changes accompanying the progression through the cell cycle in mouse fibroblast cells. We also compare with Smart-Seq to demonstrate CEL-Seq2's increased sensitivity relative to other available methods. Collectively, the improvements make CEL-Seq2 uniquely suited to single-cell RNA-Seq analysis in terms of economics, resolution, and ease of use.

Diffusion in sparse networks: linear to semilinear crossover.

We consider random networks whose dynamics is described by a rate equation, with transition rates w(nm) that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient D. In one dimension it is well known that D can display an abrupt percolation-like transition from diffusion (D>0) to subdiffusion (D = 0). A question arises whether such a transition happens in higher dimensions. Numerically D can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a recent expectation that is based on a renormalization-group analysis, we deduce that D is finite, suggest an "effective-range-hopping" procedure to evaluate it, and contrast the results with the linear estimate. The same approach is useful in the analysis of networks that are described by quasi-one-dimensional sparse banded matrices.