Supersolvability and Freeness for ψ-Graphical Arrangements

Let G be a simple graph on the vertex set {v[subscript 1],…,v[subscript n]} with edge set E. Let K be a field. The graphical arrangement A[subscript G] in K[superscript n] is the arrangement x[subscript i]−x[subscript j]=0,v[subscript i]v[subscript j] ∈ E. An arrangement A is supersolvable if the intersection lattice L(c(A)) of the cone c(A) contains a maximal chain of modular elements. The second author has shown that a graphical arrangement A[subscript G] is supersolvable if and only if G is a chordal graph. He later considered a generalization of graphical arrangements which are called ψ-graphical arrangements. He conjectured a characterization of the supersolvability and freeness (in the sense of Terao) of a ψ-graphical arrangement. We provide a proof of the first conjecture and state some conditions on free ψ-graphical arrangements.China Scholarship CouncilNational Science Foundation (U.S.) (Grant DMS-1068625

BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy

Recently, the BTZ black hole in the presence of the gravitational Chern-Simons (GCS) term has been studied and it has been found that the usual thermodynamical quantities, like as the black hole mass, angular momentum, and black hole entropy, are modified. But, for large values of the GCS coupling, where the modification terms dominate the original terms, some exotic behaviors occur, like as the roles of the mass and angular momentum are interchanged and the black hole entropy depends more on the $inner$-horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking (BH) entropy. Moreover, this entropy does $not$ agree with the statistical entropy, in contrast to a good agreement for small values of the GCS coupling. Here I find that there is another entropy formula where the usual BH form dominates the inner-horizon term again, as in the small GCS coupling, such as the second law of thermodynamics can be guaranteed. I compare the result of the holographic approach with the classical- symmetry-algebra-based approach and I find exact agreements even with the higher-derivative term of GCS. This provides a non-trivial check of the AdS/CFT-correspondence in the presence of higher-derivative terms in the gravity action.Comment: Accepted in Phys. Rev. D; Shortened version, Raised a new question of the validity of the first law (No. 5 in Sec.5), Clarified the relation with the Euclidean action approach for $1/\hbar$ factor (below (3.2)

Efficient distributed information fusion using value of information based censoring

In many distributed sensing applications, not all agents have valuable information at all times. Therefore, requiring all agents to communicate at all times can be resource intensive. In this work, the notion of Value of Information (VoI) is used to improve the efficiency of distributed sensing algorithms. Particularly, only agents with high VoI broadcast their measurements to the network, while others censor their measurements. New VoI realized data fusion algorithms are introduced, and an in depth analysis of the costs incurred by these algorithms and conventional distributed data fusion algorithms is presented. Numerical simulations are used to compare the performance of the VoI realized algorithms with traditional data fusion algorithms. A VoI based algorithm that adaptively adjusts the criterion for being informative is presented and shown to strike a good balance between reduced communication cost and increased accuracy.United States. Army Research Office (MURI grant W911NF-11-1-0391

Superconductivity in half-Heusler compound TbPdBi

We have studied the half-Heusler compound TbPdBi through resistivity, magnetization, Hall effect and heat capacity measurements. A semimetal behavior is observed in its normal state transport properties, which is characterized by a large negative magnetoresistance below 100 K. Notably, we find the coexistence of superconductivity and antiferromagnetism in this compound. The superconducting transition appears at 1.7 K, while the antiferromagnetic phase transition takes place at 5.5 K. The upper critical field $H_{c2}$ shows an unusual linear temperature dependence, implying unconventional superconductivity. Moreover, when the superconductivity is suppressed by magnetic field, its resistivity shows plateau behavior, a signature often seen in topological insulators/semimetals. These findings establish TbPdBi as a platform for study of the interplay between superconductivity, magnetism and non-trivial band topology.Comment: 5 pages, 4 figure

Signals of Unparticles in Low Energy Parity Violation and NuTeV Experiment

We have studied the possible signals of unparticle in atomic parity violation(APV) along an isotope chain and in the NuTeV experiment. The effects of unparticle physics could be observed in APV, if the uncertainty in relative neutron/proton radius shift $\delta(\Delta\frac{R_N}{R_P})$ is less than a few times $10^{-4}$ by measuring the parity violating electron scattering. The constraints imposed by NuTeV experiment on unparticle physics are discussed in detail. If the NuTeV results are confirmed by future experiments, we suggest that unparticle could account for a part of NuTeV anomaly. There exist certain regions for the unparticle parameters ($\Lambda_{\cal U}$, $d_{\cal U}$, $c_{V{\cal U}}$ and $c_{A{\cal U}}$), where the NuTeV discrepancy could be completely explained by unparticle effects and the strange quark asymmetry, even with or without the contributions from the isoscalarity violation etc. It is remarkable that these parameter regions are consistent with the constraints from $b\to s\gamma$Comment: 19 pages, 7 figure

Self-assembly of Nanometer-scale Magnetic Dots with Narrow Size Distributions on an Insulating Substrate

The self-assembly of iron dots on the insulating surface of NaCl(001) is investigated experimentally and theoretically. Under proper growth conditions, nanometer-scale magnetic iron dots with remarkably narrow size distributions can be achieved in the absence of a wetting layer Furthermore, both the vertical and lateral sizes of the dots can be tuned with the iron dosage without introducing apparent size broadening, even though the clustering is clearly in the strong coarsening regime. These observations are interpreted using a phenomenological mean-field theory, in which a coverage-dependent optimal dot size is selected by strain-mediated dot-dot interactions.Comment: 5 pages, 4 figure

Electromagnetic mass splittings of π,a1,K,K1(1400)\pi, a_1, K, K_1(1400) and K∗(892)K^*(892)

To one-loop order and $O(\alpha_{em})$, the electromagnetic mass splittings of $\pi$, $a_1$, $K$, $K_1(1400)$, and $K^*(892)$ are calculated in the framework of $U(3)_L\times U(3)_R$ chiral field theory. The logarithmic divergences emerging in the Feynman integrations of the mesonic loops are factorized by using an intrinsic parameter $g$ of this theory. No other additional parameters or counterterms are introduced to absorb the mesonic loop divergences. When $f_\pi$,$m_\rho$ and $m_a$ are taken as inputs, the parameter $g$ will be determined and all the physical results are finite and fixed. Dashen's theorem is satisfied in the chiral SU(3) limit of this theory, and a rather large violation of the theorem is revealed at the order of $m_s$ or $m_K^2$. Mass ratios of light quarks have been determined. A relation for electromagnetic corrections to masses of axial-vector mesons is obtained. It could be regarded as a generalization of Dashen's theorem. Comparing with data, it is found that the non-electromagnetic mass difference of $K^*$ is in agreement with the estimation of Schechter, Subbaraman, Weigel.Comment: LateX, 40 pages and five PS files. Final version will appear in Phys. Rev. D5