Faster Existential FO Model Checking on Posets

We prove that the model checking problem for the existential fragment of first-order (FO) logic on partially ordered sets is fixed-parameter tractable (FPT) with respect to the formula and the width of a poset (the maximum size of an antichain). While there is a long line of research into FO model checking on graphs, the study of this problem on posets has been initiated just recently by Bova, Ganian and Szeider (CSL-LICS 2014), who proved that the existential fragment of FO has an FPT algorithm for a poset of fixed width. We improve upon their result in two ways: (1) the runtime of our algorithm is O(f(|{\phi}|,w).n^2) on n-element posets of width w, compared to O(g(|{\phi}|). n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow. We complement this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.Comment: Paper as accepted to the LMCS journal. An extended abstract of an earlier version of this paper has appeared at ISAAC'14. Main changes to the previous version are improvements in the Multicoloured Clique part (Section 4

Parameterized Algorithms for Graph Partitioning Problems

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at least) $p$, where $\alpha_1,\alpha_2\in\mathbb{R}$ are constants defining the problem, and $m_1, m_2$ are the cardinalities of the edge sets having both endpoints, and exactly one endpoint, in $U$, respectively. This class of fixed cardinality graph partitioning problems (FGPP) encompasses Max $(k,n-k)$-Cut, Min $k$-Vertex Cover, $k$-Densest Subgraph, and $k$-Sparsest Subgraph. Our main result is an $O^*(4^{k+o(k)}\Delta^k)$ algorithm for any problem in this class, where $\Delta \geq 1$ is the maximum degree in the input graph. This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain faster algorithms for certain subclasses of FGPPs, parameterized by $p$, or by $(k+p)$. In particular, we give an $O^*(4^{p+o(p)})$ time algorithm for Max $(k,n-k)$-Cut, thus improving significantly the best known $O^*(p^p)$ time algorithm

Fast Quasi-Threshold Editing

We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the quasi-threshold (also called trivially perfect) graph editing problem with edge insertion and deletion. Given a graph it computes a quasi-threshold graph which is close in terms of edit count. This edit problem is NP-hard. We present an extensive experimental study, in which we show that QTM is the first algorithm that is able to scale to large real-world graphs in practice. As a side result we further present a simple linear-time algorithm for the quasi-threshold recognition problem.Comment: 26 pages, 4 figures, submitted to ESA 201

Interaction of a Nanomagnet with a Weak Superconducting Link

We study electromagnetic interaction of a nanomagnet with a weak superconducting link. Equations that govern coupled dynamics of the two systems are derived and investigated numerically. We show that the presence of a small magnet in the proximity of a weak link may be detected through Shapiro-like steps caused by the precession of the magnetic moment. Despite very weak magnetic field generated by the weak link, a time-dependent bias voltage applied to the link can initiate a non-linear dynamics of the nanomagnet that leads to the reversal of its magnetic moment. We also consider quantum problem in which a nanomagnet interacting with a weak link is treated as a two-state spin system due to quantum tunneling between spin-up and spin-down states.Comment: 7 pages, 4 figure

Invariant information and complementarity in high-dimensional states

Using a generalization of the invariant information introduced by Brukner and Zeilinger [Phys. Rev. Lett. \textbf{83}, 3354 (1999)] to high-dimensional systems, we introduce a complementarity relation between the local and nonlocal information for $d\times d$ systems under the isolated environment, where $d$ is prime or the power of prime. We also analyze the dynamics of the local information in the decoherence process.Comment: 4 pages, 2 figure

Cyclic Universe with Quintom matter in Loop Quantum Cosmology

In this paper, we study the possibility of model building of cyclic universe with Quintom matter in the framework of Loop Quantum Cosmology. After a general demonstration, we provide two examples, one with double-fluid and another double-scalar field, to show how such a scenario is obtained. Analytical and numerical calculations are both presented in the paper.Comment: 11 pages, 2 figure

Drinfel'd Realization of Quantum Affine Superalgebra Uq(gl(1∣1))^U_q\hat{(gl(1|1))}

We obtain Drinfel'd's realization of quantum affine superalgebra $U_q\hat{(gl(1|1))}$ based on the super version of RS construction method and Gauss decomposition

Nonorthogonal decoy-state Quantum Key Distribution

In practical quantum key distribution (QKD), weak coherent states as the photon sources have a limit in secure key rate and transmission distance because of the existence of multiphoton pulses and heavy loss in transmission line. Decoy states method and nonorthogonal encoding protocol are two important weapons to combat these effects. Here, we combine these two methods and propose a efficient method that can substantially improve the performance of QKD. We find a 79 km increase in transmission distance over the prior record using decoy states method.Comment: 4 pages, 1 figure; Revtex4, submitted to PR

A Metamaterial-Inspired Model for Electron Waves in Bulk Semiconductors

Based on an analogy with electromagnetic metamaterials, we develop an effective medium description for the propagation of electron matter waves in bulk semiconductors with a zincblende structure. It is formally demonstrated that even though departing from a different starting point, our theory gives results for the energy stationary states consistent with Bastard's envelope function approximation in the long-wavelength limit. Using the proposed approach, we discuss the time evolution of a wave packet in a bulk semiconductor with a zero-gap and linear energy-momentum dispersion.Comment: 43 pages, 4 figure

Linearly and Circularly Polarized Emission in Sagittarius A*

We perform general relativistic ray-tracing calculations of the transfer of polarized synchrotron radiation through the relativistic accretion flow in Sagittarius (Sgr) A*. Based on a two-temperature magneto-rotational-instability (MRI) induced accretion mode, the birefringence effects are treated self-consistently. By fitting the spectrum and polarization of Sgr A* from millimeter to near-infrared bands, we are able to not only constrain the basic parameters related to the MRI and the electron heating rate, but also limit the orientation of the accretion torus. These constraints lead to unique polarimetric images, which may be compared with future millimeter and sub-millimeter VLBI observations. In combination with general relativistic MHD simulations, the model has the potential to test the MRI with observations of Sgr A*.Comment: 12 pages, 2 figures, ApJL accepte