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

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

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

Student understanding of rotational and rolling motion concepts

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level mechanics course. Interviews were conducted with six physics juniors and ten introductory students using demonstration-based tasks. We also administered free-response and multiple-choice questions to a large number of students enrolled in introductory physics courses, and interviewed six additional introductory students on the test questions (during the test design phase). All students showed similar difficulties regardless of their background, and higher mathematical sophistication did not seem to help acquire a deeper understanding. We found that some difficulties were due to related difficulties with linear motion, while others were tied specifically to the more intricate nature of rotational and rolling motion.Comment: 23 pages, 3 figures, 2 tables; it includes a multiple-choice test (in Appendix B

Direct strain and elastic energy evaluation in rolled-up semiconductor tubes by x-ray micro-diffraction

We depict the use of x-ray diffraction as a tool to directly probe the strain status in rolled-up semiconductor tubes. By employing continuum elasticity theory and a simple model we are able to simulate quantitatively the strain relaxation in perfect crystalline III-V semiconductor bi- and multilayers as well as in rolled-up layers with dislocations. The reduction in the local elastic energy is evaluated for each case. Limitations of the technique and theoretical model are discussed in detail.Comment: 32 pages (single column), 9 figures, 39 reference

Quantum key distribution with delayed privacy amplification and its application to security proof of a two-way deterministic protocol

Privacy amplification (PA) is an essential post-processing step in quantum key distribution (QKD) for removing any information an eavesdropper may have on the final secret key. In this paper, we consider delaying PA of the final key after its use in one-time pad encryption and prove its security. We prove that the security and the key generation rate are not affected by delaying PA. Delaying PA has two applications: it serves as a tool for significantly simplifying the security proof of QKD with a two-way quantum channel, and also it is useful in QKD networks with trusted relays. To illustrate the power of the delayed PA idea, we use it to prove the security of a qubit-based two-way deterministic QKD protocol which uses four states and four encoding operations.Comment: 11 pages, 3 figure

Robust pinning of magnetic moments in pyrochlore iridates

Pyrochlore iridates A2Ir2O7 (A = rare earth elements, Y or Bi) hold great promise for realizing novel electronic and magnetic states owing to the interplay of spin-orbit coupling, electron correlation and geometrical frustration. A prominent example is the formation of all-in/all-out (AIAO)antiferromagnetic order in the Ir4+ sublattice that comprises of corner-sharing tetrahedra. Here we report on an unusual magnetic phenomenon, namely a cooling-field induced shift of magnetic hysteresis loop along magnetization axis, and its possible origin in pyrochlore iridates with non-magnetic Ir defects (e.g. Ir3+). In a simple model, we attribute the magnetic hysteresis loop to the formation of ferromagnetic droplets in the AIAO antiferromagnetic background. The weak ferromagnetism originates from canted antiferromagnetic order of the Ir4+ moments surrounding each non-magnetic Ir defect. The shift of hysteresis loop can be understood quantitatively based on an exchange-bias like effect in which the moments at the shell of the FM droplets are pinned by the AIAO AFM background via mainly the Heisenberg (J) and Dzyaloshinsky-Moriya (D) interactions. The magnetic pinning is stable and robust against the sweeping cycle and sweeping field up to 35 T, which is possibly related to the magnetic octupolar nature of the AIAO order.Comment: 16 pages, 4 figure