The Random-Query Model and the Memory-Bounded Coupon Collector

We study a new model of space-bounded computation, the random-query model. The model is based on a branching-program over input variables x_1,…,x_n. In each time step, the branching program gets as an input a random index i ∈ {1,…,n}, together with the input variable x_i (rather than querying an input variable of its choice, as in the case of a standard (oblivious) branching program). We motivate the new model in various ways and study time-space tradeoff lower bounds in this model. Our main technical result is a quadratic time-space lower bound for zero-error computations in the random-query model, for XOR, Majority and many other functions. More precisely, a zero-error computation is a computation that stops with high probability and such that conditioning on the event that the computation stopped, the output is correct with probability 1. We prove that for any Boolean function f: {0,1}^n → {0,1}, with sensitivity k, any zero-error computation with time T and space S, satisfies T ⋅ (S+log n) ≥ Ω(n⋅k). We note that the best time-space lower bounds for standard oblivious branching programs are only slightly super linear and improving these bounds is an important long-standing open problem. To prove our results, we study a memory-bounded variant of the coupon-collector problem that seems to us of independent interest and to the best of our knowledge has not been studied before. We consider a zero-error version of the coupon-collector problem. In this problem, the coupon-collector could explicitly choose to stop when he/she is sure with zero-error that all coupons have already been collected. We prove that any zero-error coupon-collector that stops with high probability in time T, and uses space S, satisfies T⋅(S+log n) ≥ Ω(n^2), where n is the number of different coupons

Pseudoscalar Goldstone Bosons Scattering off Charmed Baryons with Chiral Perturbation Theory

We have systematically calculated the pseudoscalar Goldstone boson and charmed baryon scattering lengths to the third order with heavy baryon chiral perturbation theory. The scattering lengths can reveal the interaction of $K \Lambda_c$, $K \Sigma_c$, $\pi \Omega_c$ etc. For each channel, we take into account of the interaction between the external particle and every possible charmed baryon in the triplet, sextet, and excited sextet. We use dimensional regularization and modified minimal subtraction to get rid of the divergences in the loop-diagram corrections. We notice that the convergence of chiral expansion for most of the channels becomes better after we let the low energy constants absorb the analytic contributions of the loop-diagram corrections and keep the nonanalytic terms only.Comment: 4 pages, 1 figure. Proceeding of Eleventh International Conference on Hypernuclear and Strange Particle Physics - HYP2012, Barcelon

Automated approaches for band gap mapping in STEM-EELS

Band gap variations in thin film structures, across grain boundaries, and in embedded nanoparticles are of increasing interest in the materials science community. As many common experimental techniques for measuring band gaps do not have the spatial resolution needed to observe these variations directly, probe-corrected Scanning Transmission Electron Microscope (STEM) with monochromated Electron Energy-Loss Spectroscopy (EELS) is a promising method for studying band gaps of such features. However, extraction of band gaps from EELS data sets usually requires heavy user involvement, and makes the analysis of large data sets challenging. Here we develop and present methods for automated extraction of band gap maps from large STEM-EELS data sets with high spatial resolution while preserving high accuracy and precision