Finding Subcube Heavy Hitters in Analytics Data Streams

Data streams typically have items of large number of dimensions. We study the fundamental heavy-hitters problem in this setting. Formally, the data stream consists of $d$-dimensional items $x_1,\ldots,x_m \in [n]^d$. A $k$-dimensional subcube $T$ is a subset of distinct coordinates $\{ T_1,\cdots,T_k \} \subseteq [d]$. A subcube heavy hitter query ${\rm Query}(T,v)$, $v \in [n]^k$, outputs YES if $f_T(v) \geq \gamma$ and NO if $f_T(v) < \gamma/4$, where $f_T$ is the ratio of number of stream items whose coordinates $T$ have joint values $v$. The all subcube heavy hitters query ${\rm AllQuery}(T)$ outputs all joint values $v$ that return YES to ${\rm Query}(T,v)$. The one dimensional version of this problem where $d=1$ was heavily studied in data stream theory, databases, networking and signal processing. The subcube heavy hitters problem is applicable in all these cases. We present a simple reservoir sampling based one-pass streaming algorithm to solve the subcube heavy hitters problem in $\tilde{O}(kd/\gamma)$ space. This is optimal up to poly-logarithmic factors given the established lower bound. In the worst case, this is $\Theta(d^2/\gamma)$ which is prohibitive for large $d$, and our goal is to circumvent this quadratic bottleneck. Our main contribution is a model-based approach to the subcube heavy hitters problem. In particular, we assume that the dimensions are related to each other via the Naive Bayes model, with or without a latent dimension. Under this assumption, we present a new two-pass, $\tilde{O}(d/\gamma)$-space algorithm for our problem, and a fast algorithm for answering ${\rm AllQuery}(T)$ in $O(k/\gamma^2)$ time. Our work develops the direction of model-based data stream analysis, with much that remains to be explored.Comment: To appear in WWW 201

Excited states of quantum many-body interacting systems: A variational coupled-cluster description

We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin $\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Anserson's spin-wave theory. Implications of these new collective modes are discussed.Comment: 17 pages, 4 figure

Germanene: a novel two-dimensional Germanium allotrope akin to Graphene and Silicene

Using a gold (111) surface as a substrate we have grown in situ by molecular beam epitaxy an atom-thin, ordered, two-dimensional multi-phase film. Its growth bears strong similarity with the formation of silicene layers on silver (111) templates. One of the phases, forming large domains, as observed in Scanning Tunneling Microscopy, shows a clear, nearly flat, honeycomb structure. Thanks to thorough synchrotron radiation core-level spectroscopy measurements and advanced Density Functional Theory calculations we can identify it to a $\sqrt{3}$x$\sqrt{3}$R(30{\deg}) germanene layer in coincidence with a $\sqrt{7}$x$\sqrt{7}$R(19.1{\deg}) Au(111) supercell, thence, presenting the first compelling evidence of the birth of a novel synthetic germanium-based cousin of graphene.Comment: 16 pages, 4 figures, 1 tabl

η\eta photoproduction on the quasi-free nucleons in the chiral quark model

A chiral quark-model approach is adopted to study the $\eta$ photoproduction off the quasi-free neutron and proton from a deuteron target. Good descriptions of the differential cross sections, total cross sections and beam asymmetries for these two processes are obtained in the low energy region. For $\gamma p\rightarrow \eta p$, the dominant resonances are $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, $D_{13}(1700)$ and $P_{13}(1720)$. While for the $\gamma n\rightarrow \eta n$ process, the dominant resonances are $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, $D_{15}(1675)$ and $P_{13}(1720)$. Furthermore, the $u$ channel backgrounds have significant contributions to the $\eta$ photoproduction processes. The configuration mixings in the $S_{11}(1535,1650)$ and $D_{13}(1520,1700)$ can be extracted, i.e. $\theta_S\simeq 26^\circ$ and $\theta_D\simeq 21^\circ$. It shows that the narrow bump-like structure around $W= 1.68$ GeV observed in $\gamma n\rightarrow \eta n$ can be naturally explained by the constructive interferences between $S_{11}(1535)$ and $S_{11}(1650)$. In contrast, the destructive interference between $S_{11}(1535)$ and $S_{11}(1650)$ produces the shallow dip around $W= 1.67$ GeV in $\gamma p\rightarrow \eta p$. The $S$ wave interfering behaviors in the proton and neutron reactions are correlated with each other in the quark model framework, and no new exotic nucleon resonances are needed in these two reactions.Comment: 12 pages, 11 figures, helicity amplitudes are added, to be published in PR

Electro-diffusion in a plasma with two ion species

Electric field is a thermodynamic force that can drive collisional inter-ion-species transport in a multicomponent plasma. In an inertial confinement fusion (ICF) capsule, such transport causes fuel ion separation even with a target initially prepared to have equal number densities for the two fuel ion species. Unlike the baro-diffusion driven by ion pressure gradient and the thermo-diffusion driven by ion and electron temperature gradients, electro-diffusion has a critical dependence on the charge-to-mass ratio of the ion species. Specifically, it is shown here that electro-diffusion vanishes if the ion species have the same charge-to-mass ratio. An explicit expression for the electro-diffusion ratio is obtained and used to investigate the relative importance of electro- and baro-diffusion mechanisms. In particular, it is found that electro-diffusion reinforces baro-diffusion in the deuterium and tritium mix, but tends to cancel it in the deuterium and helium-3 mix.Comment: Submitted to Phys. Plasmas on 2012-03-06 (revised version 05/13/2012

Universal slow plasmons and giant field enhancement in atomically thin quasi-two-dimensional metals

Plasmons depend strongly on dimensionality: while plasmons in three-dimensional systems start with finite energy at wavevector q = 0, plasmons in traditional two-dimensional (2D) electron gas disperse as ωp∼q√. However, besides graphene, plasmons in real, atomically thin quasi-2D materials were heretofore not well understood. Here we show that the plasmons in real quasi-2D metals are qualitatively different, being virtually dispersionless for wavevectors of typical experimental interest. This stems from a broken continuous translational symmetry which leads to interband screening; so, dispersionless plasmons are a universal intrinsic phenomenon in quasi-2D metals. Moreover, our ab initio calculations reveal that plasmons of monolayer metallic transition metal dichalcogenides are tunable, long lived, able to sustain field intensity enhancement exceeding 107, and localizable in real space (within ~20 nm) with little spreading over practical measurement time. This opens the possibility of tracking plasmon wave packets in real time for novel imaging techniques in atomically thin materials

GeV detection of HESS J0632+057

HESS J0632+057 is the only gamma-ray binary that has been detected at TeV energies, but not at GeV energies yet. Based on nearly nine years of Fermi Large Area Telescope (LAT) Pass 8 data, we report here on a deep search for the gamma-ray emission from HESS J0632+057 in the 0.1-300 GeV energy range. We find a previously unknown gamma-ray source, Fermi J0632.6+0548, spatially coincident with HESS J0632+057. The measured flux of Fermi J0632.6+0548 is consistent with the previous flux upper limit on HESS J0632+057 and shows variability that can be related to the HESS J0632+057 orbital phase. We propose that Fermi J0632.6+0548 is the GeV counterpart of HESS J0632+057. Considering the Very High Energy (VHE) spectrum of HESS J0632+057, a possible spectral turnover above 10 GeV may exist in Fermi J0632.6+0548, as appears to be common in other established gamma-ray binaries.Comment: 17 pages, 4 figures, 1 table; Accepted for publication in Ap

Fundamental Limits to Coherent Photon Generation with Solid-State Atomlike Transitions

Coherent generation of indistinguishable single photons is crucial for many quantum communication and processing protocols. Solid-state realizations of two-level atomic transitions or three-level spin-$\Lambda$ systems offer significant advantages over their atomic counterparts for this purpose, albeit decoherence can arise due to environmental couplings. One popular approach to mitigate dephasing is to operate in the weak excitation limit, where excited state population is minimal and coherently scattered photons dominate over incoherent emission. Here we probe the coherence of photons produced using two-level and spin-$\Lambda$ solid-state systems. We observe that the coupling of the atomic-like transitions to the vibronic transitions of the crystal lattice is independent of driving strength and detuning. We apply a polaron master equation to capture the non-Markovian dynamics of the ground state vibrational manifolds. These results provide insight into the fundamental limitations for photon coherence from solid-state quantum emitters, with the consequence that deterministic single-shot quantum protocols are impossible and inherently probabilistic approaches must be embraced.Comment: 16 pages [with supplementary information], 8 figure

Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogen-like ions

High precision multipole polarizabilities, $\alpha_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10$^{-6}$ up to $Z = 100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules $\sum_i f^{(\ell)}_{0i} = 0$ for all multipoles from $\ell = 1$ to $\ell = 4$. The dispersion coefficients for the long-range H-H and H-He$^+$ interactions are given.Comment: 8 figures, 8 table

Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy

By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.Comment: 9 page