Perturbations of Functional Inequalities for L\'evy Type Dirichlet Forms

Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy type Dirichlet forms are studied. When the range of jumps is finite our results are natural extensions to the corresponding ones derived earlier for diffusion processes; and we show that the study for the situation with infinite range of jumps is essentially different. Some examples are presented to illustrate the optimality of our results

No More Discrimination: Cross City Adaptation of Road Scene Segmenters

Despite the recent success of deep-learning based semantic segmentation, deploying a pre-trained road scene segmenter to a city whose images are not presented in the training set would not achieve satisfactory performance due to dataset biases. Instead of collecting a large number of annotated images of each city of interest to train or refine the segmenter, we propose an unsupervised learning approach to adapt road scene segmenters across different cities. By utilizing Google Street View and its time-machine feature, we can collect unannotated images for each road scene at different times, so that the associated static-object priors can be extracted accordingly. By advancing a joint global and class-specific domain adversarial learning framework, adaptation of pre-trained segmenters to that city can be achieved without the need of any user annotation or interaction. We show that our method improves the performance of semantic segmentation in multiple cities across continents, while it performs favorably against state-of-the-art approaches requiring annotated training data.Comment: 13 pages, 10 figure

Quantum correlations in the collective spin systems

Quantum and classical pairwise correlations in two typical collective spin systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are discussed. These correlations in the thermodynamical limit are obtained analytically and in a finite-size system are calculated numerically. Large-size scaling behavior for the quantum discord itself is observed, which has never been reported in another critical system. A logarithmic diverging behavior for the first derivative of the quantum discord is also found in both models, which might be universal in the second-order quantum phase transition. It is suggested that the pronounced maximum or minimum of first derivative of quantum discord signifies the critical point. Comparisons between the quantum discord and the scaled concurrence are performed. It is shown that the quantum discord is very small in one phase and robust in the other phase, while the scaled concurrence shows maximum at the critical point and decays rapidly when away from the the critical point.Comment: 8 pages, 4 figure

New universal gates for topological quantum computation with Fibonacci-ε\boldsymbol{\varepsilon} composite Majorana edge modes on topological superconductor multilayers

We propose a new design of universal topological quantum computer device through a hybrid of the 1-, 2- and 7-layers of chiral topological superconductor ($\chi$TSC) thin films. Based on the $SO(7)_1/(G_2)_1$ coset construction, strongly correlated Majorana fermion edge modes on the 7-layers of $\chi$TSC are factorized into the composite of the Fibonacci $\tau$-anyon and $\varepsilon$-anyon modes in the tricritical Ising model. Furthermore, the deconfinement of $\tau$ and $\varepsilon$ via the interacting potential gives the braiding of either $\tau$ or $\varepsilon$. Topological phase gates are assembled by the braidings. With these topological phase gates, we find a set of fully topological universal gates for the $(\tau,\varepsilon)$ composite Majorana-Ising-type quantum computation. Because the Hilbert space still possesses a tensor product structure of quibts and is characterized by the fermion parities, encoding quantum information in this machine is more efficient and substantial than that with Fibonacci anyons. The computation results is easier to be read out by electric signals, so are the initial data inputted.Comment: 6 pages, 3 figues, revised versio