Which Are You In A Photo?

Automatic image tagging has been a long standing problem, it mainly relies on image recognition techniques of which the accuracy is still not satisfying. This paper attempts to explore out-of-band sensing base on the mobile phone to sense the people in a picture while the picture is being taken and create name tags on-the-fly. The major challenges pertain to two aspects - "Who" and "Which". (1) "Who": discriminating people who are in the picture from those that are not; (2) "Which": correlating each name tag with its corresponding people in the picture. We propose an accurate acoustic scheme applying on the mobile phones, which leverages the Doppler effect of sound wave to address these two challenges. As a proof of concept, we implement the scheme on 7 android phones and take pictures in various real-life scenarios with people positioning in different ways. Extensive experiments show that the accuracy of tag correlation is above 85% within 3m for picturing

Topological non-symmorphic crystalline insulators

In this work, we identify a new class of Z2 topological insulator protected by non-symmorphic crystalline symmetry, dubbed a "topological non-symmorphic crystalline insulator". We construct a concrete tight-binding model with the non-symmorphic space group pmg and confirm the topological nature of this model by calculating topological surface states and defining a Z2 topological invariant. Based on the projective representation theory, we extend our discussion to other non-symmorphic space groups that allows to host topological non-symmorphic crystalline insulators.Comment: 7 pages, 5 figure

Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires

One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into a 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.Comment: 32 pages, 6 figure

Topological invariants for three dimensional Dirac semimetals and four dimensional topological rotational insulators

Dirac semimetal is a class of semi-metallic phase protected by certain types of crystalline symmetries, and its low-energy effective Hamiltonian is described by Dirac equations in three dimensions (3D). Despite of various theoretical studies, theories that describe the topological nature of Dirac semimetals have not been well established. In this work, we define a topological invariant for 3D Dirac semimetals by establishing a mapping between a 3D Dirac semimetal and a topological crystalline insulator in four dimension (4D). We demonstrate this scheme by constructing a tight-binding model for 4D topological crystalline insulators that are protected by rotational symmetry. A new type of topological invariant, "rotational Chern number", is shown to characterize the topology of this system. As a consequence of the rotational Chern number, gapless Dirac points are found on the 3D surface of this 4D system. For a slab with two surfaces, we find that the corresponding low-energy effective theory of two surface states can be directly mapped to that of a 3D Dirac semimetal, suggesting that topological nature of 3D Dirac semimetals can be characterized by rotational Chern number which is defined in 4D. Our scheme provides a new systematic approach to extract topological nature for topological semimetal phases.Comment: 12 pages, 3 figure

Interacting topological phases in thin films of topological mirror Kondo insulators

We study the interaction effects on thin films of topological mirror Kondo insulators (TMKI), where the strong interaction is expected to play an important role. Our study has led to the following results: (1) We identify a rich phase diagram of non-interacting TMKI with different mirror Chern numbers in the monolayer and bilayer thin films; (2) We obtain the phase diagram with interaction and identify the regimes of interaction parameters to mimic bosonic symmetry protected topological phases with either gapless bosonic modes or spontaneous mirror symmetry breaking at the boundary; (3) For the spontaneous mirror symmetry breaking boundary, we also study various domain-wall defects between different mirror symmetry breaking order parameters at the boundary. Our results reveal that the thin film TMKI serves as an intriguing platform for the experimental studies of interacting topological phases.Comment: 11 pages, 4 figure

Structures, optical properties, and electrical transport processes of SnO2_2 films with oxygen deficiencies

The structures, optical and electrical transport properties of SnO$_2$ films, fabricated by rf sputtering method at different oxygen partial pressures, were systematically investigated. It has been found that preferred growth orientation of SnO$_2$ film is strongly related to the oxygen partial pressure during deposition, which provides an effective way to tune the surface texture of SnO$_2$ film. All films reveal relatively high transparency in the visible range, and both the transmittance and optical band gap increase with increasing oxygen partial pressure. The temperature dependence of resisitivities was measured from 380 K down to liquid helium temperatures. At temperature above $\sim 80$ K, besides the nearest-neighbor-hopping process, thermal activation processes related to two donor levels ($\sim 30$ and $\sim 100$ meV below the conduction band minimum) of oxygen vacancies are responsible for the charge transport properties. Below $\sim 80$ K, Mott variable-range-hopping conduction process governs the charge transport properties at higher temperatures, while Efros-Shklovskii variable-range-hopping conduction process dominates the transport properties at lower temperatures. Distinct crossover from Mott type to Efros-Shklovskii type variable-range-hopping conduction process at several to a few tens kelvin are observed for all SnO$_2$ films.Comment: 6 pages and 7 figure

Averaging algebras, rewriting systems and Gro¨\"obner-Shirshov bases

In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain a sufficient and necessary condition for the confluence. We supply the relationship between rewriting systems and Grobner-Shirshov bases based on bracketed polynomials. As an application, we give a basis of the free unitary averaging algebra on a non-empty set.Comment: 24 page

Weighted infinitesimal bialgebras

As a uniform of two versions of infinitesimal bialgebras introduced respectively by Joni-Rota and Loday-Ronco, weighted infinitesimal bialgebras play an important role in mathematics and mathematical physics. In this paper, we introduce the concept of weighted infinitesimal Hopf modules and show that any module carries a natural structure of weighted infinitesimal unitary Hopf module over a weighted quasitriangular infinitesimal unitary bialgebra. We decorate planar rooted forests $H_{\mathrm{RT}}(X, \Omega)$ in a new way, and prove that the $H_{\mathrm{RT}}(X, \Omega)$, together with a coproduct $\Delta_{\epsilon}$ and grafting operations $\{ B^+_\omega \mid \omega\in \Omega\}$, is the free $\Omega$-cocycle infinitesimal unitary bialgebra (resp. Hopf algebra) of weight zero on a set $X$. A combinatorial description of $\Delta_{\epsilon}$ is given. As applications, we obtain the initial object in the category of cocycle infinitesimal unitary bialgebras (resp. Hopf algebras) on undecorated planar rooted forests, which is the object studied in the (noncommutative) Connes-Kreimer Hopf algebra. Finally, we derive two pre-Lie algebras from an arbitrary weighted infinitesimal bialgebra and weighted commutative infinitesimal bialgebra, respectively. The second construction generalizes the Gelfand-Dorfman Theorem on Novikov algebras.Comment: 44 pages; give the right reference

Sharp endpoint estimates for eigenfunctions restricted to submanifolds of codimension 2

Burq-G\'erard-Tzvetkov and Hu established $L^p$ estimates ($2\le p\le \infty$) for the restriction of eigenfunctions to submanifolds. The estimates are sharp, except for the log loss at the endpoint $L^2$ estimates for submanifolds of codimension 2. It has long been believed that the log loss at the endpoint can be removed in general, while the problem is still open. So this paper is devoted to the study of sharp endpoint restriction estimates for eigenfunctions in this case. Chen and Sogge removed the log loss for the geodesics on 3-dimensional manifolds. In this paper, we generalize their result to higher dimensions and prove that the log loss can be removed for totally geodesic submanifolds of codimension 2. Moreover, on 3-dimensional manifolds, we can remove the log loss for curves with nonvanishing geodesic curvatures, and more general finite type curves. The problem in 3D is essentially related to Hilbert transforms along curves in the plane and a class of singular oscillatory integrals studied by Phong-Stein, Ricci-Stein, Pan, Seeger, Carbery-P\'erez.Comment: 17 page

Free operated monoids and Rewriting systems

The construction of bases for quotients is an important problem. In this paper, applying the method of rewriting systems, we give a unified approach to construct sections---an alternative name for bases in semigroup theory---for quotients of free operated monoids. As applications, we capture sections of free $\ast$-monoids and free groups, respectively.Comment: 17 page