Local Markov Property for Models Satisfying Composition Axiom

The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential number of conditional independencies. This paper shows that the number of conditional independence relations required may be reduced if the probability distributions satisfy the composition axiom. In certain types of graphs, only linear number of conditional independencies are required. The result has applications in testing linear structural equation models with correlated errors.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

Polynomial Constraints in Causal Bayesian Networks

We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce the complexity of the implicitization problem and make the problem tractable in certain causal Bayesian networks. We also show some preliminary results on the algebraic structure of polynomial constraints. The results have applications in distinguishing between causal models and in testing causal models with combined observational and experimental data.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007

Riemann-Hilbert approach and N-soliton formula for the N-component Fokas-Lenells equations

In this work, the generalized $N$-component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for $N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main purpose of this is to study the soliton solutions of the coupled Fokas-Lenells(FL) equations for any positive integer $N$, which have more complex linear relationship than the analogues reported before. We first analyze the spectral analysis of the Lax pair associated with a $(N+1)\times (N+1)$ matrix spectral problem for the $N$-component FL equations. Then, a kind of RH problem is successfully formulated. By introducing the special conditions of irregularity and reflectionless case, the $N$-soliton solution formula of the equations are derived through solving the corresponding RH problem. Furthermore, take $N=2,3$ and $4$ for examples, the localized structures and dynamic propagation behavior of their soliton solutions and their interactions are discussed by some graphical analysis.Comment: 29 pages, 10 figure

The normalized Laplacian spectra of the double corona based on RR-graph

For simple graphs $G$, $G_1$ and $G_2$, we denote their double corona based on $R$-graph by $G^{(R)}\otimes{\{G_1,G_2\}}$. This paper determines the normalized Laplacian spectrum of $G^{(R)}\otimes{\{G_1,G_2\}}$ in terms of these of $G$, $G_1$ and $G_2$ whenever $G$, $G_1$ and $G_2$ are regular. The obtained result reduces to the normalized Laplacian spectra of the $R$-vertex corona $G^{(R)}\odot{G_1}$ and $R$-edge corona $G^{(R)}\circleddash{G_2}$ by choosing $G_2$ or $G_1$ as a null-graph, respectively. Finally, applying the results of the paper, we construct infinitely many pairs of normalized Laplacian cospectral graphs.Comment: 9 pages, 19 conferenc

Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation

In this work, a generalized nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation is introduced, and its integrability as an infinite dimensional Hamilton dynamic system is established. Motivated by the ideas of Ablowitz and Musslimani (2016 Nonlinearity 29 915), we successfully derive the inverse scattering transform (IST) of the nonlocal LPD equation. The direct scattering problem of the equation is first constructed, and some important symmetries of the eigenfunctions and the scattering data are discussed. By using a novel Left-Right Riemann-Hilbert (RH) problem, the inverse scattering problem is analyzed, and the potential function is recovered. By introducing the special conditions of reflectionless case, the time-periodic soliton solutions formula of the equation is derived successfully. Take $J=\overline{J}=1,2,3$ and $4$ for example, we obtain some interesting phenomenon such as breather-type solitons, arc solitons, three soliton and four soliton. Furthermore, the influence of parameter $\delta$ on these solutions is further considered via the graphical analysis. Finally, the eigenvalues and conserved quantities are investigated under a few special initial conditions.Comment: 33 pages, 8 figure

78 Pairs of Possible PSR-SNR Associations

We discuss the criteria to associate PSRs with SNRs, and summary 78 pairs of possible PSR-SNR associations which is the most complete sample so far. We refine them into three categories according to degree of reliability. Statistic study on PSR-SNR associations helps us understand massive star evolution and constrain pulsar's theory models.Comment: Accepted for publication in NARIT Conference Series (NCS), 2 pages, 1 tabl

Deformation of a soft boundary induced and enhanced by enclosed active particles

We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two typical stages in the variation of the morphology with the increase of active force. One is at small force characterized by radially inhomogeneous redistribution of particles and suppression of local fluctuations of the boundary. The other is at large force featured by angularly redistribution of particles and global shape deformation of the boundary. The last two processes are strongly cooperative. We also find different mechanisms in the particle redistribution and opposite force-dependences of the rate of the shape variation at low and high particle concentrations.Comment: 11 pages, 6 figure

Itinerant metamagnetism in manganites caused by the field-induced electronic nematic order

Itinerant metamagnetism transition is observed and studied in perovskite La1-xCaxMn0.90Cu0.10O3 system for x = 0.30. At a constant low temperature, 10 K < T < 150 K, there is a continuous second-order metamagnetism jump from a low magnetic state to a high one with the magnetic field H increasing. However, at an exceeding low temperature, T = 2.5 K, the metamagnetism jump at H = 3.5 T becomes to be a robust first-order transition, and another metamagnetism transition occurs at a higher field H = 7.0 T. Since there is no charge ordering sign in the present system, it can not be understood by using the phase separation model or the prior martensite/austenitic phase transition scenario. A theoretical electronic nematic order phase formation is evidenced to answer for the two consecutive metamagnetic transitions, which separate the nematic phase from the low-field (H 7.0 T) isotropic phases.Comment: 10 pages, 5 figure

Inequality Constraints in Causal Models with Hidden Variables

We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects that are not directly measured in randomized experiments. We derive instrumental inequality type of constraints on nonexperimental distributions. The results have applications in testing causal models with observational or experimental data.Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006

Spontaneous symmetry breaking induced unidirectional rotation of chain-grafted colloid in the active bath

Exploiting the energy of randomly moving active agents such as bacteria is a fascinating way to power a microdevice. Here we show, by simulations, that a chain-grafted disk-like colloid can rotate unidirectionally when immersed in a thin film of active particle suspension. The spontaneous symmetry breaking of chain configurations is the origin of the unidirectional rotation. Long persistence time, large propelling force and/or small rotating friction are keys to keeping the broken symmetry and realizing the rotation. In the rotating state, we find very simple linear relations, e.g. between mean angular speed and propelling force. The time-evolving asymmetry of chain configurations reveals that there are two types of non-rotating state. Our findings provide new insights into the phenomena of spontaneous symmetry breaking in active systems with flexible objects and also open the way to conceive new soft/deformable microdevices.Comment: 14 pages (single column, double spaced), 5 figure