Symplectic Geometry on Quantum Plane

A study of symplectic forms associated with two dimensional quantum planes and the quantum sphere in a three dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit.Comment: 12 pages, Late

Point Interactions: PT-Hermiticity and Reality of the Spectrum

General point interactions for the second derivative operator in one dimension are studied. In particular, ${\mathcal P \mathcal T}$-self-adjoint point interactions with the support at the origin and at points $\pm l$ are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.Comment: 17 page

BRST Structures and Symplectic Geometry on a Class of Supermanifolds

By investigating the symplectic geometry and geometric quantization on a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed and q-deformed cases in the classical as well as in the quantum cases.Comment: 14 pages, Late

A Note on Invariants and Entanglements

The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential applications in studying separability and calculating entanglement of formation for high dimensional mixed quantum states.Comment: Latex, 11 page

Some New Exact Ground States for Generalize Hubbard Models

A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum systems.Comment: 9 pages, Late

An explicitly solvable model of the spontaneous PT-symmetry breaking

We contemplate the pair of the purely imaginary delta-function potentials on a finite interval with Dirichlet boundary conditions. The two parameter model exhibits nicely the expected quantitative features of the unavoided level crossing and of a "phase-transition" complexification of the energies. Combining analytic and numerical techniques we investigate strength- and position-dependence of its spectrum.Comment: presented in the int. conference "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (Instanbul, Koc University, June 20 - 22, 2005). accepted in Czechoslovak J. Phy

Plasmonic Hot Spots in Triangular Tapered Graphene Microcrystals

Recently, plasmons in graphene have been observed experimentally using scattering scanning near-field optical microscopy. In this paper, we develop a simplified analytical approach to describe the behavior in triangular samples. Replacing Coulomb interaction by a short-range one reduces the problem to a Helmholtz equation, amenable to analytical treatment. We demonstrate that even with our simplifications, the system still exhibits the key features seen in the experiment.Comment: 4 pages, 3 figure

Detecting Singleton Review Spammers Using Semantic Similarity

Online reviews have increasingly become a very important resource for consumers when making purchases. Though it is becoming more and more difficult for people to make well-informed buying decisions without being deceived by fake reviews. Prior works on the opinion spam problem mostly considered classifying fake reviews using behavioral user patterns. They focused on prolific users who write more than a couple of reviews, discarding one-time reviewers. The number of singleton reviewers however is expected to be high for many review websites. While behavioral patterns are effective when dealing with elite users, for one-time reviewers, the review text needs to be exploited. In this paper we tackle the problem of detecting fake reviews written by the same person using multiple names, posting each review under a different name. We propose two methods to detect similar reviews and show the results generally outperform the vectorial similarity measures used in prior works. The first method extends the semantic similarity between words to the reviews level. The second method is based on topic modeling and exploits the similarity of the reviews topic distributions using two models: bag-of-words and bag-of-opinion-phrases. The experiments were conducted on reviews from three different datasets: Yelp (57K reviews), Trustpilot (9K reviews) and Ott dataset (800 reviews).Comment: 6 pages, WWW 201

Zero-shot keyword spotting for visual speech recognition in-the-wild

Visual keyword spotting (KWS) is the problem of estimating whether a text query occurs in a given recording using only video information. This paper focuses on visual KWS for words unseen during training, a real-world, practical setting which so far has received no attention by the community. To this end, we devise an end-to-end architecture comprising (a) a state-of-the-art visual feature extractor based on spatiotemporal Residual Networks, (b) a grapheme-to-phoneme model based on sequence-to-sequence neural networks, and (c) a stack of recurrent neural networks which learn how to correlate visual features with the keyword representation. Different to prior works on KWS, which try to learn word representations merely from sequences of graphemes (i.e. letters), we propose the use of a grapheme-to-phoneme encoder-decoder model which learns how to map words to their pronunciation. We demonstrate that our system obtains very promising visual-only KWS results on the challenging LRS2 database, for keywords unseen during training. We also show that our system outperforms a baseline which addresses KWS via automatic speech recognition (ASR), while it drastically improves over other recently proposed ASR-free KWS methods.Comment: Accepted at ECCV-201