Distribution of interstitial stem cells in Hydra

The distribution of interstitial stem cells along the Hydra body column was determined using a simplified cloning assay. The assay measures stem cells as clone-forming units (CFU) in aggregates of nitrogen mustard inactivated Hydra tissue. The concentration of stem cells in the gastric region was uniform at about 0.02 CFU/epithelial cell. In both the hypostome and basal disk the concentration was 20-fold lower. A decrease in the ratio of stem cells to committed nerve and nematocyte precursors was correlated with the decrease in stem cell concentration in both hypostome and basal disk. The ratio of stem cells to committed precursors is a sensitive indicator of the rate of self-renewal in the stem cell population. From the ratio it can be estimated that <10% of stem cells self-renew in the hypostome and basal disk compared to 60% in the gastric region. Thus, the results provide an explanation for the observed depletion of stem cells in these regions. The results also suggest that differentiation and self-renewal compete for the same stem cell population

Memory effects can make the transmission capability of a communication channel uncomputable

Most communication channels are subjected to noise. One of the goals of Information Theory is to add redundancy in the transmission of information so that the information is transmitted reliably and the amount of information transmitted through the channel is as large as possible. The maximum rate at which reliable transmission is possible is called the capacity. If the channel does not keep memory of its past, the capacity is given by a simple optimization problem and can be efficiently computed. The situation of channels with memory is less clear. Here we show that for channels with memory the capacity cannot be computed to within precision 1/5. Our result holds even if we consider one of the simplest families of such channels -information-stable finite state machine channels-, restrict the input and output of the channel to 4 and 1 bit respectively and allow 6 bits of memory.Comment: Improved presentation and clarified claim

Upper and lower bounds on resonances for manifolds hyperbolic near infinity

For a conformally compact manifold that is hyperbolic near infinity and of dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we establish a Poisson formula expressing the regularized wave trace as a sum over scattering resonances. This leads to an $r^{n+1}$ lower bound on the counting function for scattering poles.Comment: 29 pages, minor corrections, added one figur

Correlation Decay in Random Decision Networks

We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the corresponding nodes. The goal is to construct a decision vector which maximizes the total reward. This decision problem encompasses a variety of models, including maximum-likelihood inference in graphical models (Markov Random Fields), combinatorial optimization on graphs, economic team theory and statistical physics. The network is endowed with a probabilistic structure in which costs are sampled from a distribution. Our aim is to identify sufficient conditions to guarantee average-case polynomiality of the underlying optimization problem. We construct a new decentralized algorithm called Cavity Expansion and establish its theoretical performance for a variety of models. Specifically, for certain classes of models we prove that our algorithm is able to find near optimal solutions with high probability in a decentralized way. The success of the algorithm is based on the network exhibiting a correlation decay (long-range independence) property. Our results have the following surprising implications in the area of average case complexity of algorithms. Finding the largest independent (stable) set of a graph is a well known NP-hard optimization problem for which no polynomial time approximation scheme is possible even for graphs with largest connectivity equal to three, unless P=NP. We show that the closely related maximum weighted independent set problem for the same class of graphs admits a PTAS when the weights are i.i.d. with the exponential distribution. Namely, randomization of the reward function turns an NP-hard problem into a tractable one

Challenges concerning the discriminatory optical force for chiral molecules

In response to arXiv:1506.07423v1 we discuss the authors work, and our own, on proposed schemes aiming to achieve a discriminatory optical force for chiral molecules

Optical control of excited-state lifetimes

Electronic excitation of particles in fluorescent materials can now be controlled using laser-assisted energy-transfer techniques