Succinct Representations of Permutations and Functions

We investigate the problem of succinctly representing an arbitrary permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in constant time, for any positive constant \epsilon <= 1. A representation taking the optimal \ceil{\lg n!} + o(n) bits can be used to compute arbitrary powers in O(lg n / lg lg n) time. We then consider the more general problem of succinctly representing an arbitrary function, f: [n] \rightarrow [n] so that f^k(i) can be computed quickly for any i and any integer power k. We give a representation that takes (1+\epsilon) n lg n + O(1) bits, for any positive constant \epsilon <= 1, and computes arbitrary positive powers in constant time. It can also be used to compute f^k(i), for any negative integer k, in optimal O(1+|f^k(i)|) time. We place emphasis on the redundancy, or the space beyond the information-theoretic lower bound that the data structure uses in order to support operations efficiently. A number of lower bounds have recently been shown on the redundancy of data structures. These lower bounds confirm the space-time optimality of some of our solutions. Furthermore, the redundancy of one of our structures "surpasses" a recent lower bound by Golynski [Golynski, SODA 2009], thus demonstrating the limitations of this lower bound.Comment: Preliminary versions of these results have appeared in the Proceedings of ICALP 2003 and 2004. However, all results in this version are improved over the earlier conference versio

Gravitational Lorentz Violation and Superluminality via AdS/CFT Duality

A weak quantum mechanical coupling is constructed permitting superluminal communication within a preferred region of a gravitating AdS_5 spacetime. This is achieved by adding a spatially non-local perturbation of a special kind to the Hamiltonian of a four-dimensional conformal field theory with a weakly-coupled AdS dual, such as maximally supersymmetric Yang-Mills theory. In particular, two issues are given careful treatment: (1) the UV-completeness of our deformed CFT, guaranteeing the existence of a ``deformed string theory'' AdS dual, and (2) the demonstration that superluminal effects can take place in AdS, both on its boundary as well as in the bulk. Exotic Lorentz-violating properties such as these may have implications for tests of General Relativity, addressing the cosmological constant problem, or probing "behind'' horizons. Our construction may give insight into the interpretation of wormhole solutions in Euclidean AdS gravity.Comment: 23 pages LaTex. Typo in Eq. (37) corrected. References adde

An Optically Plugged Quadrupole Trap for Bose-Einstein Condensates

We created sodium Bose-Einstein condensates in an optically plugged quadrupole magnetic trap (OPT). A focused, 532nm laser beam repelled atoms from the coil center where Majorana loss is significant. We produced condensates of up to $3 \times 10^7$ atoms, a factor of 60 improvement over previous work [1], a number comparable to the best all-magnetic traps, and transferred up to $9 \times 10^6$ atoms into a purely optical trap. Due to the tight axial confinement and azimuthal symmetry of the quadrupole coils, the OPT shows promise for creating Bose-Einstein condensates in a ring geometry

RLZAP: Relative Lempel-Ziv with Adaptive Pointers

Relative Lempel-Ziv (RLZ) is a popular algorithm for compressing databases of genomes from individuals of the same species when fast random access is desired. With Kuruppu et al.'s (SPIRE 2010) original implementation, a reference genome is selected and then the other genomes are greedily parsed into phrases exactly matching substrings of the reference. Deorowicz and Grabowski (Bioinformatics, 2011) pointed out that letting each phrase end with a mismatch character usually gives better compression because many of the differences between individuals' genomes are single-nucleotide substitutions. Ferrada et al. (SPIRE 2014) then pointed out that also using relative pointers and run-length compressing them usually gives even better compression. In this paper we generalize Ferrada et al.'s idea to handle well also short insertions, deletions and multi-character substitutions. We show experimentally that our generalization achieves better compression than Ferrada et al.'s implementation with comparable random-access times

Bragg Spectroscopy of Vortex Lattices in Bose-Einstein condensates

We have measured the velocity field of a vortex lattice within a sodium Bose-Einstein condensate using Bragg scattering. The phase gradient of the macroscopic wavefunction was mapped into the spatial structure of the diffracted atom cloud, allowing for single shot measurement of the rotation parameters. A combination of spectral and spatial information yields a complete description of the superfluid flow, coarse-grained over the lattice structure, including direct and independent measurements of the rate and sense of rotation. Signatures of the microscopic quantum rotation have also been observed.Comment: 5 pages, 5 Figures, A movie built from the CM data is available in our Webpage: http://www.physics.gatech.edu/chandra/index.htm; added Fig.5 presents new data, showing signatures of the microscopic vortex structure in the diffracted clou

Lifetime Measurements in 120Xe

Lifetimes for the lowest three transitions in the nucleus $^{120}$Xe have been measured using the Recoil Distance Technique. Our data indicate that the lifetime for the $2_{1}^{+} \to 0_{1}^{+}$ transition is more than a factor of two lower than the previously adopted value and is in keeping with more recent measurements performed on this nucleus. The theoretical implications of this discrepancy and the possible reason for the erroneous earlier results are discussed. All measured lifetimes in $^{120}$Xe, as well as the systematics of the lifetimes of the 2$_{1}^{+}$ states in Xe isotopes, are compared with predictions of various models. The available data are best described by the Fermion Dynamic Symmetry Model (FDSM).Comment: 9 pages, RevTeX, 3 figures with Postscript file available on request at [email protected], [email protected]. Submitted to Phys. Rev.

Subset feedback vertex set is fixed parameter tractable

The classical Feedback Vertex Set problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. Feedback Vertex Set has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fixed-parameter algorithms have been a rich source of ideas in the field. In this paper we consider a more general and difficult version of the problem, named Subset Feedback Vertex Set (SUBSET-FVS in short) where an instance comes additionally with a set S ? V of vertices, and we ask for a set of at most k vertices that hits all simple cycles passing through S. Because of its applications in circuit testing and genetic linkage analysis SUBSET-FVS was studied from the approximation algorithms perspective by Even et al. [SICOMP'00, SIDMA'00]. The question whether the SUBSET-FVS problem is fixed-parameter tractable was posed independently by Kawarabayashi and Saurabh in 2009. We answer this question affirmatively. We begin by showing that this problem is fixed-parameter tractable when parametrized by |S|. Next we present an algorithm which reduces the given instance to 2^k n^O(1) instances with the size of S bounded by O(k^3), using kernelization techniques such as the 2-Expansion Lemma, Menger's theorem and Gallai's theorem. These two facts allow us to give a 2^O(k log k) n^O(1) time algorithm solving the Subset Feedback Vertex Set problem, proving that it is indeed fixed-parameter tractable.Comment: full version of a paper presented at ICALP'1

Upper and Lower Bounds for Weak Backdoor Set Detection

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6^k. We also prove a 2^k lower bound for these problems, subject to the Strong Exponential Time Hypothesis.Comment: A short version will appear in the proceedings of the 16th International Conference on Theory and Applications of Satisfiability Testin

Optimized coupling of cold atoms into a fiber using a blue-detuned hollow-beam funnel

We theoretically investigate the process of coupling cold atoms into the core of a hollow-core photonic-crystal optical fiber using a blue-detuned Laguerre-Gaussian beam. In contrast to the use of a red-detuned Gaussian beam to couple the atoms, the blue-detuned hollow-beam can confine cold atoms to the darkest regions of the beam thereby minimizing shifts in the internal states and making the guide highly robust to heating effects. This single optical beam is used as both a funnel and guide to maximize the number of atoms into the fiber. In the proposed experiment, Rb atoms are loaded into a magneto-optical trap (MOT) above a vertically-oriented optical fiber. We observe a gravito-optical trapping effect for atoms with high orbital momentum around the trap axis, which prevents atoms from coupling to the fiber: these atoms lack the kinetic energy to escape the potential and are thus trapped in the laser funnel indefinitely. We find that by reducing the dipolar force to the point at which the trapping effect just vanishes, it is possible to optimize the coupling of atoms into the fiber. Our simulations predict that by using a low-power (2.5 mW) and far-detuned (300 GHz) Laguerre-Gaussian beam with a 20-{\mu}m radius core hollow-fiber it is possible to couple 11% of the atoms from a MOT 9 mm away from the fiber. When MOT is positioned further away, coupling efficiencies over 50% can be achieved with larger core fibers.Comment: 11 pages, 12 figures, 1 tabl