Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size

Limit Synchronization in Markov Decision Processes

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing if the probability mass accumulates in a single state, possibly in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a probability distribution in the sequence assigns probability at least p to some state, and we distinguish three synchronization modes: (i) sure winning if there exists a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there exists a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there exists a strategy that produces a (1-epsilon)-synchronizing sequence. We consider the problem of deciding whether an MDP is sure, almost-sure, limit-sure winning, and we establish the decidability and optimal complexity for all modes, as well as the memory requirements for winning strategies. Our main contributions are as follows: (a) for each winning modes we present characterizations that give a PSPACE complexity for the decision problems, and we establish matching PSPACE lower bounds; (b) we show that for sure winning strategies, exponential memory is sufficient and may be necessary, and that in general infinite memory is necessary for almost-sure winning, and unbounded memory is necessary for limit-sure winning; (c) along with our results, we establish new complexity results for alternating finite automata over a one-letter alphabet

Experimental observation of second-harmonic generation and diffusion inside random media

We have experimentally measured the distribution of the second-harmonic intensity that is generated inside a highly-scattering slab of porous gallium phosphide. Two complementary techniques for determining the distribution are used. First, the spatial distribution of second-harmonic light intensity at the side of a cleaved slab has been recorded. Second, the total second-harmonic radiation at each side of the slab has been measured for several samples at various wavelengths. By combining these measurements with a diffusion model for second-harmonic generation that incorporates extrapolated boundary conditions, we present a consistent picture of the distribution of the second-harmonic intensity inside the slab. We find that the ratio $\ell_{2\omega}/L_c$ of the mean free path at the second-harmonic frequency to the coherence length, which was suggested by some earlier calculations, cannot describe the second-harmonic yield in our samples. For describing the total second-harmonic yield, our experiments show that the scattering parameter at the fundamental frequency \k_{1\omega}\ell_{1\omega} is the most relevant parameter in our type of samples.Comment: 10 pages, 7 figure

Impedance model for the polarization-dependent optical absorption of superconducting single-photon detectors

We measured the single-photon detection efficiency of NbN superconducting single photon detectors as a function of the polarization state of the incident light for different wavelengths in the range from 488 nm to 1550 nm. The polarization contrast varies from ~5% at 488 nm to ~30% at 1550 nm, in good agreement with numerical calculations. We use an optical-impedance model to describe the absorption for polarization parallel to the wires of the detector. For lossy NbN films, the absorption can be kept constant by keeping the product of layer thickness and filling factor constant. As a consequence, we find that the maximum possible absorption is independent of filling factor. By illuminating the detector through the substrate, an absorption efficiency of ~70% can be reached for a detector on Si or GaAs, without the need for an optical cavity.Comment: 15 pages, 5 figures, submitted to Journal of Applied Physic

Observation of nano-indent induced strain fields and dislocation generation in silicon wafers using micro-raman spectroscopy and white beam x-ray topography

In the semiconductor manufacturing industry, wafer handling introduces micro-cracks at the wafer edge. During heat treatment these can produce larger, long-range cracks in the wafer which can cause wafer breakage during manufacture. Two complimentary techniques, micro-Raman spectroscopy (μRS) and White Beam Synchrotron X-ray Topography (WBSXRT) were employed to study both the micro-cracks and the associated strain fields produced by nano-indentations in Si wafers, which were used as a means of introducing controlled strain in the wafers. It is shown that both the spatial lateral and depth distribution of these long range strain fields are relatively isotropic in nature. The Raman spectra suggest the presence of a region under tensile strain beneath the indents, which can indicate a crack beneath the indent and the data strongly suggests that there exists a minimum critical applied load below which cracking will not initiate

Modelling of the radiative properties of an opaque porous ceramic layer

Solid Oxide Fuel Cells (SOFCs) operate at temperatures above 1,100 K where radiation effects can be significant. Therefore, an accurate thermal model of an SOFC requires the inclusion of the contribution of thermal radiation. This implies that the thermal radiative properties of the oxide ceramics used in the design of SOFCs must be known. However, little information can be found in the literature concerning their operating temperatures. On the other hand, several types of ceramics with different chemical compositions and microstructures for designing efficient cells are now being tested. This is a situation where the use of a numerical tool making possible the prediction of the thermal radiative properties of SOFC materials, whatever their chemical composition and microstructure are, may be a decisive help. Using this method, first attempts to predict the radiative properties of a lanthanum nickelate porous layer deposited onto an yttria stabilized zirconium substrate can be reported

Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide

Nonlinear propagation experiments in GaAs photonic crystal waveguides (PCW) were performed, which exhibit a large enhancement of third order nonlinearities, due to light propagation in a slow mode regime, such as two-photon absorption (TPA), optical Kerr effect and refractive index changes due to TPA generated free-carriers. A theoretical model has been established that shows very good quantitative agreement with experimental data and demonstrates the important role that group velocity plays. These observations give a strong insight into the use of PCWs for optical switching devices.Comment: 6 page

Spectroscopic determination of hole density in the ferromagnetic semiconductor Ga1−x_{1-x}Mnx_{x}As

The measurement of the hole density in the ferromagnetic semiconductor Ga$_{1-x}$Mn$_{x}$As is notoriously difficult using standard transport techniques due to the dominance of the anomalous Hall effect. Here, we report the first spectroscopic measurement of the hole density in four Ga$_{1-x}$Mn$_{x}$As samples ($x=0, 0.038, 0.061, 0.083$) at room temperature using Raman scattering intensity analysis of the coupled plasmon-LO-phonon mode and the unscreened LO phonon. The unscreened LO phonon frequency linearly decreases as the Mn concentration increases up to 8.3%. The hole density determined from the Raman scattering shows a monotonic increase with increasing $x$ for $x\leq0.083$, exhibiting a direct correlation to the observed $T_c$. The optical technique reported here provides an unambiguous means of determining the hole density in this important new class of ``spintronic'' semiconductor materials.Comment: two-column format 5 pages, 4 figures, to appear in Physical Review

Avalanche amplification of a single exciton in a semiconductor nanowire

Interfacing single photons and electrons is a crucial ingredient for sharing quantum information between remote solid-state qubits. Semiconductor nanowires offer the unique possibility to combine optical quantum dots with avalanche photodiodes, thus enabling the conversion of an incoming single photon into a macroscopic current for efficient electrical detection. Currently, millions of excitation events are required to perform electrical read-out of an exciton qubit state. Here we demonstrate multiplication of carriers from only a single exciton generated in a quantum dot after tunneling into a nanowire avalanche photodiode. Due to the large amplification of both electrons and holes (> 10^4), we reduce by four orders of magnitude the number of excitation events required to electrically detect a single exciton generated in a quantum dot. This work represents a significant step towards single-shot electrical read-out and offers a new functionality for on-chip quantum information circuits