Relation between directed polymers in random media and random bond dimer models

We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media. Further potential applications of the equivalence are briefly discussed.Comment: 6 pages, 3 figure

Deconfined quantum critical point in one dimension

We perform a numerical study of a spin-1/2 model with $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by Landau-Ginzburg-Wilson symmetry-breaking theory.Comment: 20 pages, 18 figure

Activation of phospholipase C beta4 by heterotrimeric GTP-binding proteins

Transient transfection assays were used to determine how the activity of phospholipase C beta 4, which is preferentially expressed in retina, was regulated. An expression vector carrying the full-length cDNA corresponding to phospholipase C beta 4 was constructed and co- transfected into COS-7 cells together with cDNA encoding the alpha subunits of the Gq class and various beta and gamma subunits corresponding to the heterotrimeric GTP-binding proteins. We found that all the alpha subunits of the Gq class, including G alpha q, G alpha 11, G alpha 14, G alpha 15, and G alpha 16 could activate PLC beta 4 and that none of the G beta gamma subunits that we tested including G beta 1 gamma 1, G beta 1 gamma 2, G beta 1 gamma 3, or G beta 2 gamma 2 activated phospholipase C beta 4. In control experiments, cotransfection with cDNA encoding the alpha subunit of transducin or Gi2 gave no activation of PLC beta 4. These results indicate that phospholipase C beta 4 is activated by G alpha subunits that are members of the Gq class, and, like the phospholipase C beta 1 isoform, it is refractory to activation in the transfection assay by many of the combinations of beta and gamma subunits found in the heterotrimeric G- proteins

Characterizing Human Mobility Patterns in a Large Street Network

Previous studies demonstrated empirically that human mobility exhibits Levy flight behaviour. However, our knowledge of the mechanisms governing this Levy flight behaviour remains limited. Here we analyze over 72 000 people's moving trajectories, obtained from 50 taxicabs during a six-month period in a large street network, and illustrate that the human mobility pattern, or the Levy flight behaviour, is mainly attributed to the underlying street network. In other words, the goal-directed nature of human movement has little effect on the overall traffic distribution. We further simulate the mobility of a large number of random walkers, and find that (1) the simulated random walkers can reproduce the same human mobility pattern, and (2) the simulated mobility rate of the random walkers correlates pretty well (an R square up to 0.87) with the observed human mobility rate.Comment: 13 figures, 17 page

Hartree-Fock calculations of a finite inhomogeneous quantum wire

We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We find that with the increase in the potential barrier, the low density electrons under it go from a non-magnetic state to an antiferromagnetic state, and then to a state with a well-localized spin-aligned region isolated by two antiferromagnetic regions from the high density leads. At this final stage, in response to a continuously increasing barrier potential, the system undergoes a series of abrupt density changes, corresponding to the successive expulsion of a single electron from the spin-aligned region under the barrier. Motivated by the recent momentum-resolved tunneling experiments in a parallel wire geometry, we also compute the momentum resolved tunneling matrix elements. Our calculations suggest that the eigenstates being expelled are spatially localized, consistent with the experimental observations. However, additional mechanisms are needed to account for the experimentally observed large spectral weight at near $k=0$ in the tunneling matrix elements.Comment: 10 pages, 14 figure

Trajectory and stability of Lagrangian point L2L_2 in the Sun-Earth system

This paper describes design of the trajectory and analysis of the stability of collinear point $L_2$ in the Sun-Earth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the model for the Sun-Earth system. The effect of radiation pressure of the Sun and oblate shape of the Earth are considered. The point $L_2$ is asymptotically stable upto a specific value of time $t$ correspond to each set of values of parameters and initial conditions. The results obtained from this study would be applicable to locate a satellite, a telescope or a space station around the point $L_2$.Comment: Accepted for publication in Astrophysics & Space Scienc

Analyzing Disproportionate Reaction via Comparative Multilingual Targeted Sentiment in Twitter

Global events such as terrorist attacks are commented upon in social media, such as Twitter, in different languages and from different parts of the world. Most prior studies have focused on monolingual sentiment analysis, and therefore excluded an extensive proportion of the Twitter userbase. In this paper, we perform a multilingual comparative sentiment analysis study on the terrorist attack in Paris, during November 2015. In particular, we look at targeted sentiment, investigating opinions on specific entities, not simply the general sentiment of each tweet. Given the potentially inflammatory and polarizing effect that these types of tweets may have on attitudes, we examine the sentiments expressed about different targets and explore whether disproportionate reaction was expressed about such targets across different languages. Specifically, we assess whether the sentiment for French speaking Twitter users during the Paris attack differs from English-speaking ones. We identify disproportionately negative attitudes in the English dataset over the French one towards some entities and, via a crowdsourcing experiment, illustrate that this also extends to forming an annotator bias