Maximum likelihood decoding of neuronal inputs from an interspike interval distribution

An expression for the probability distribution of the interspike interval of a leaky integrate-and-fire (LIF) model neuron is rigorously derived, based on recent theoretical developments in the theory of stochastic processes. This enables us to find for the first time a way of developing maximum likelihood estimates (MLE) of the input information (e.g., afferent rate and variance) for an LIF neuron from a set of recorded spike trains. Dynamic inputs to pools of LIF neurons both with and without interactions are efficiently and reliably decoded by applying the MLE, even within time windows as short as 25 msec

Reducing the Tension Between the BICEP2 and the Planck Measurements: A Complete Exploration of the Parameter Space

A large inflationary tensor-to-scalar ratio $r_\mathrm{0.002} = 0.20^{+0.07}_{-0.05}$ is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the $95\%$ confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which $\alpha_\mathrm{s}$, $n_\mathrm{t}$, $n_\mathrm{s}$ and the neutrino parameters $N_\mathrm{eff}$ and $\Sigma m_\mathrm{\nu}$ are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on $r_\mathrm{0.002}$ are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that $N_\mathrm{eff}$ probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO datasets all together, we obtain $r_{0.002} = 0.14_{-0.11}^{+0.05}$, $n_\mathrm{t} = 0.35_{-0.47}^{+0.28}$, $n_\mathrm{s}=0.98_{-0.02}^{+0.02}$, and $\alpha_\mathrm{s}=-0.0086_{-0.0189}^{+0.0148}$; if the consistency relation is adopted, we get $r_{0.002} = 0.22_{-0.06}^{+0.05}$.Comment: 8 pages, 4 figures, submitted to PL

Exotic phase diagram of a topological quantum system

We study the quantum phase transitions (QPTs) in the Kitaev spin model on a triangle-honeycomb lattice. In addition to the ordinary topological QPTs between Abelian and non-Abelian phases, we find new QPTs which can occur between two phases belonging to the same topological class, namely, either two non-Abelian phases with the same Chern number or two Abelian phases with the same Chern number. Such QPTs result from the singular behaviors of the nonlocal spin-spin correlation functions at the critical points.Comment: 10 pages, 5 figure

Flux Balance Analysis of Dynamic Metabolism in Shewanella oneidensis MR-1 Using a Static Optimization Approach

Shewanella bacteria are facultative anaerobes isolated from aquatic and sedimentary environments (Hau and Gralnick 2007) with a broad capacity for reduction of multiple electron receptors (Pinchuk et al. 2009; Serres and Riley 2006), including Fe(III), Mn(IV), sulfur, nitrate, and fumarate. With the accomplishment of complete genome sequencing of several Shewanella bacteria, the general pictures of the carbon metabolism have been revealed (Serres and Riley 2006). metabolism. One of the most physiological methods to decipher the time-variant metabolic regulation is to determine the dynamic distribution of intracellular metabolic fluxes since it reveals the final response of cellular metabolism to genomic, transcriptional and post-transcriptional regulations (Sauer 2006; Tang et al. 2009). In order to track the dynamic intracellular metabolic regulation, dynamic flux balance analysis (DFBA) was developed (Mahadevan et al. 2002), in which cell growth phase was divided into numerous stages, assuming that at each stage a new metabolic steady state was maintained. All the metabolic fluxes were then searched to satisfy the objective functions set for each stage. By solving this nonlinear optimization model using a cutting-edge nonlinear optimization solver (IPOPT), we confirmed the changing of carbon sources for the growth of Shewanella oneidensis MR-1 and deciphered the dynamic regulation of intracellular metabolism