The effect of temperature evolution on the interior structure of H2{}_{2}O-rich planets

For most planets in the range of radii from 1 to 4 R$_{\oplus}$, water is a major component of the interior composition. At high pressure H${}_{2}$O can be solid, but for larger planets, like Neptune, the temperature can be too high for this. Mass and age play a role in determining the transition between solid and fluid (and mixed) water-rich super-Earth. We use the latest high-pressure and ultra-high-pressure phase diagrams of H${}_{2}$O, and by comparing them with the interior adiabats of various planet models, the temperature evolution of the planet interior is shown, especially for the state of H${}_{2}$O. It turns out that the bulk of H${}_{2}$O in a planet's interior may exist in various states such as plasma, superionic, ionic, Ice VII, Ice X, etc., depending on the size, age and cooling rate of the planet. Different regions of the mass-radius phase space are also identified to correspond to different planet structures. In general, super-Earth-size planets (isolated or without significant parent star irradiation effects) older than about 3 Gyr would be mostly solid.Comment: Accepted by ApJ, in print for March 2014 (14 pages, 3 colored figures, 1 table

Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems

On the performance of two protocols: SARG04 and BB84

We compare the performance of BB84 and SARG04, the later of which was proposed by V. Scarani et al., in Phys. Rev. Lett. 92, 057901 (2004). Specifically, in this paper, we investigate SARG04 with two-way classical communications and SARG04 with decoy states. In the first part of the paper, we show that SARG04 with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than SARG04 with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for SARG04 with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in SARG04 to obtain unconditional security even when realistic devices are used. We compare the performance of SARG04 with decoy states and BB84 with decoy states. We find that the optimal mean-photon number for SARG04 is higher than that of BB84 when the bit error rate is small. Also, we observe that SARG04 does not achieve a longer secure distance and a higher key generation rate than BB84, assuming a typical experimental parameter set.Comment: 48 pages, 10 figures, 1 column, changed Figs. 7 and

Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene

The Dirac mass-vortex at the surface of a topological insulator or in graphene is considered. Within the linear approximation for the vortex amplitude's radial dependence, the spectrum is a series of degenerate bound states, which can be classified by a set of accidental SU(2) and supersymmetry generators (I. F. Herbut and C.-K. Lu, Phys. Rev. B 83 125412 (2011)). Here we discuss further the properties and manifestations of the supersymmetry of the vortex Hamiltonian, and point out some interesting analogies to the Runge-Lenz-Pauli vector in the non-relativistic hydrogen atom. Symmetry breaking effects due to a finite chemical potential, and the Zeeman field are also analyzed. We find that a residual accidental degeneracy remains only in the special case of equal magnitudes of both terms, whereas otherwise it becomes removed entirely.Comment: revised version with added reference and a new paragraph on interpretation of two-velocity Weyl fermions realized in 2D optical lattice; to appear in J Phys

A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution

We discuss excess noise contributions of a practical balanced homodyne detector in Gaussian-modulated coherent-state (GMCS) quantum key distribution (QKD). We point out the key generated from the original realistic model of GMCS QKD may not be secure. In our refined realistic model, we take into account excess noise due to the finite bandwidth of the homodyne detector and the fluctuation of the local oscillator. A high speed balanced homodyne detector suitable for GMCS QKD in the telecommunication wavelength region is built and experimentally tested. The 3dB bandwidth of the balanced homodyne detector is found to be 104MHz and its electronic noise level is 13dB below the shot noise at a local oscillator level of 8.5*10^8 photon per pulse. The secure key rate of a GMCS QKD experiment with this homodyne detector is expected to reach Mbits/s over a few kilometers.Comment: 22 pages, 11 figure

Models of Social Groups in Blogosphere Based on Information about Comment Addressees and Sentiments

This work concerns the analysis of number, sizes and other characteristics of groups identified in the blogosphere using a set of models identifying social relations. These models differ regarding identification of social relations, influenced by methods of classifying the addressee of the comments (they are either the post author or the author of a comment on which this comment is directly addressing) and by a sentiment calculated for comments considering the statistics of words present and connotation. The state of a selected blog portal was analyzed in sequential, partly overlapping time intervals. Groups in each interval were identified using a version of the CPM algorithm, on the basis of them, stable groups, existing for at least a minimal assumed duration of time, were identified.Comment: Gliwa B., Ko\'zlak J., Zygmunt A., Models of Social Groups in Blogosphere Based on Information about Comment Addressees and Sentiments, in the K. Aberer et al. (Eds.): SocInfo 2012, LNCS 7710, pp. 475-488, Best Paper Awar

Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain

We analysis the symmetries of the reflection equation for open $XYZ$ model and find their solutions $K^{\pm}$ case by case. In the general open boundary conditions, the Lax pair for open one-dimensional $XYZ$ spin-chain is given.Comment: LaTeX, 17 pages, errors in references correcte

Security proof of a three-state quantum key distribution protocol without rotational symmetry

Standard security proofs of quantum key distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states, |0_z> and |1_z>, can contribute to key generation and the third state, |+>=(|0_z>+|1_z>)/\sqrt{2}, is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result on the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the BB84 protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol; while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.Comment: 10 pages, 3 figures, 2 column

Charge-density Waves Survive the Pauli Paramagnetic Limit

Measurements of the resistance of single crystals of (Per)$_2$Au(mnt)$_2$ have been made at magnetic fields $B$ of up to 45 T, exceeding the Pauli paramagnetic limit of $B_{\rm P}\approx 37$ T. The continued presence of non-linear charge-density wave electrodynamics at $B \geq 37$ T unambiguously establishes the survival of the charge-density wave state above the Pauli paramagnetic limit, and the likely emergence of an inhomogeneous phase analogous to that anticipated to occur in superconductors.Comment: 4 pages, three figure