Likelihood inference for exponential-trawl processes

Integer-valued trawl processes are a class of serially correlated, stationary and infinitely divisible processes that Ole E. Barndorff-Nielsen has been working on in recent years. In this Chapter, we provide the first analysis of likelihood inference for trawl processes by focusing on the so-called exponential-trawl process, which is also a continuous time hidden Markov process with countable state space. The core ideas include prediction decomposition, filtering and smoothing, complete-data analysis and EM algorithm. These can be easily scaled up to adapt to more general trawl processes but with increasing computation efforts.Comment: 29 pages, 6 figures, forthcoming in: "A Fascinating Journey through Probability, Statistics and Applications: In Honour of Ole E. Barndorff-Nielsen's 80th Birthday", Springer, New Yor

Mixed-State Entanglement and Quantum Teleportation through Noisy Channels

The quantum teleportation with noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when $\bar{F} \leq 2/3$, where $\bar{F}$ is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues on the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the three-qubit mixed states are discussed by adopting a teleportation with W-stateComment: 18 pages, 4 figure

Tripartite Entanglement in Noninertial Frame

The tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As Unruh effect indicates, the tripartite entanglement exhibits a decreasing behavior with increasing the acceleration. Unlike the bipartite entanglement, however, the tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or W-state initially, the corresponding $\pi$-tangle, one of the measures for tripartite entanglement, is shown to be $\pi/6 \sim 0.524$ or 0.176 in this limit, respectively. This fact indicates that the tripartite quantum information processing may be possible even if one of the parties approaches to the Rindler horizon. The physical implications of this striking result are discussed in the context of black hole physics.Comment: 19 pages, 5 figure

Conformally rescaled spacetimes and Hawking radiation

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transformation factor is unity at their location.Comment: 22 pages, version submitted to journa

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population Histories

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure -- the history of multiple subpopulations that merge, split and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.Comment: 38 pages, Appeared in RECOMB 201

Near-complete genome sequencing of swine vesicular disease virus using the Roche GS FLX sequencing platform

Swine vesicular disease virus (SVDV) is an enterovirus that is both genetically and antigenically closely related to human coxsackievirus B5 within the Picornaviridae family. SVDV is the causative agent of a highly contagious (though rarely fatal) vesicular disease in pigs. We report a rapid method that is suitable for sequencing the complete protein-encoding sequences of SVDV isolates in which the RNA is relatively intact. The approach couples a single PCR amplification reaction, using only a single PCR primer set to amplify the near-complete SVDV genome, with deep-sequencing using a small fraction of the capacity of a Roche GS FLX sequencing platform. Sequences were initially verified through one of two criteria; either a match between a de novo assembly and a reference mapping, or a match between all of five different reference mappings performed against a fixed set of starting reference genomes with significant genetic distances within the same species of viruses. All reference mappings used an iterative method to avoid bias. Further verification was achieved through phylogenetic analysis against published SVDV genomes and additional Enterovirus B sequences. This approach allows high confidence in the obtained consensus sequences, as well as provides sufficiently high and evenly dispersed sequence coverage to allow future studies of intra-host variation

Visual, Motor and Attentional Influences on Proprioceptive Contributions to Perception of Hand Path Rectilinearity during Reaching

We examined how proprioceptive contributions to perception of hand path straightness are influenced by visual, motor and attentional sources of performance variability during horizontal planar reaching. Subjects held the handle of a robot that constrained goal-directed movements of the hand to the paths of controlled curvature. Subjects attempted to detect the presence of hand path curvature during both active (subject driven) and passive (robot driven) movements that either required active muscle force production or not. Subjects were less able to discriminate curved from straight paths when actively reaching for a target versus when the robot moved their hand through the same curved paths. This effect was especially evident during robot-driven movements requiring concurrent activation of lengthening but not shortening muscles. Subjects were less likely to report curvature and were more variable in reporting when movements appeared straight in a novel “visual channel” condition previously shown to block adaptive updating of motor commands in response to deviations from a straight-line hand path. Similarly, compromised performance was obtained when subjects simultaneously performed a distracting secondary task (key pressing with the contralateral hand). The effects compounded when these last two treatments were combined. It is concluded that environmental, intrinsic and attentional factors all impact the ability to detect deviations from a rectilinear hand path during goal-directed movement by decreasing proprioceptive contributions to limb state estimation. In contrast, response variability increased only in experimental conditions thought to impose additional attentional demands on the observer. Implications of these results for perception and other sensorimotor behaviors are discussed

Attack of Many Eavesdroppers via Optimal Strategy in Quantum Cryptography

We examine a situation that $n$ eavesdroppers attack the Bennett-Brassard cryptographic protocol via their own optimal and symmetric strategies. Information gain and mutual information with sender for each eavesdropper are explicitly derived. The receiver's error rate for the case of arbitrary $n$ eavesdroppers can be derived using a recursive relation. Although first eavesdropper can get mutual information without disturbance arising due to other eavesdroppers, subsequent eavesdropping generally increases the receiver's error rate. Other eavesdroppers cannot gain information on the input signal sufficiently. As a result, the information each eavesdropper gains becomes less than optimal one.Comment: 17 pages, 8 figure

Amplitude Damping for single-qubit System with single-qubit mixed-state Environment

We study a generalized amplitude damping channel when environment is initially in the single-qubit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.Comment: 13 pages, 2 figures incluided V2: homepage address is included in reference V3: version to appear in J. Phys. A: Mathematical and Theoretica