General formula for the four-quark condensate and vacuum factorization assumption

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):|{\tilde 0}>$. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):| {\tilde 0}>$ holds only when the dressed vertex is taken to be the bare one. This property also holds for all other type of four-quark condensate.Comment: Revtex4, 11 pages, no figure

Rainbow tensor model with two tensors of rank three

We give the keystone operators and construct a graded ring with tree and loop operators. In terms of the keystones operators, connected tree and loop operators in the ring, we construct the rainbow tensor model with two tensors of rank-3 and present its $W$-representation. Moreover we derive the compact expressions of correlators from the $W$-representation and analyze the free energy in large $N$ limit. In addition, we establish the correspondence between two colored Dyck walks in the Fredkin spin chain and tree operators in the ring. Based on the classification Dyck walks, we give the number of tree operators with the given level. Furthermore, for the entanglement entropy of the Fredkin spin chain, we show the entanglement scaling beyond logarithmic scaling in the ordinary critical systems from the viewpoint of tensor model.Comment: 27 pages, 15 figures, 1 tabl

Analysis of interspecies adherence of oral bacteria using a membrane binding assay coupled with polymerase chain reaction-denaturing gradient gel electrophoresis profiling.

Information on co-adherence of different oral bacterial species is important for understanding interspecies interactions within oral microbial community. Current knowledge on this topic is heavily based on pariwise coaggregation of known, cultivable species. In this study, we employed a membrane binding assay coupled with polymerase chain reaction-denaturing gradient gel electrophoresis (PCR-DGGE) to systematically analyze the co-adherence profiles of oral bacterial species, and achieved a more profound knowledge beyond pairwise coaggregation. Two oral bacterial species were selected to serve as "bait": Fusobacterium nucleatum (F. nucleatum) whose ability to adhere to a multitude of oral bacterial species has been extensively studied for pairwise interactions and Streptococcus mutans (S. mutans) whose interacting partners are largely unknown. To enable screening of interacting partner species within bacterial mixtures, cells of the "bait" oral bacterium were immobilized on nitrocellulose membranes which were washed and blocked to prevent unspecific binding. The "prey" bacterial mixtures (including known species or natural saliva samples) were added, unbound cells were washed off after the incubation period and the remaining cells were eluted using 0.2 mol x L(-1) glycine. Genomic DNA was extracted, subjected to 16S rRNA PCR amplification and separation of the resulting PCR products by DGGE. Selected bands were recovered from the gel, sequenced and identified via Nucleotide BLAST searches against different databases. While few bacterial species bound to S. mutans, consistent with previous findings F. nucleatum adhered to a variety of bacterial species including uncultivable and uncharacterized ones. This new approach can more effectively analyze the co-adherence profiles of oral bacteria, and could facilitate the systematic study of interbacterial binding of oral microbial species

Structure-Exploiting Delay-Dependent Stability Analysis Applied to Power System Load Frequency Control

Linear matrix inequality (LMI) based delay-dependent stability analysis/synthesis methods have been applied to power system load frequency control (LFC) which has communication networks in its loops. However, the computational burden of solving large-scale LMIs poses a great challenge to the application of those methods to real-world power systems. This paper investigates the computational aspect of delay-dependent stability analysis (DDSA) of LFC. The basic idea is to improve the numerical tractability of DDSA by exploiting the chordal sparsity and symmetry of the graph related to LFC loops. The graph-theoretic analysis yields the structure restrictions of weighting matrices needed for the LMIs to inherit the chordal sparsity of the control loops. By enforcing those structure restrictions on weighting matrices, the positive semidefinite constraints in the LMIs can be decomposed into smaller ones, and the number of decision variables can be greatly reduced. Symmetry in LFC control loops is also exploited to reduce the number of decision variables. Numerical studies show the proposed structure-exploiting techniques significantly improves the numerical tractability of DDSA at the cost of the introduction of acceptable minor conservatism

Deep learning assisted jet tomography for the study of Mach cones in QGP

Mach cones are expected to form in the expanding quark-gluon plasma (QGP) when energetic quarks and gluons (called jets) traverse the hot medium at a velocity faster than the speed of sound in high-energy heavy-ion collisions. The shape of the Mach cone and the associated diffusion wake are sensitive to the initial jet production location and the jet propagation direction relative to the radial flow because of the distortion by the collective expansion of the QGP and large density gradient. The shape of jet-induced Mach cones and their distortions in heavy-ion collisions provide a unique and direct probe of the dynamical evolution and the equation of state of QGP. However, it is difficult to identify the Mach cone and the diffusion wake in current experimental measurements of final hadron distributions because they are averaged over all possible initial jet production locations and propagation directions. To overcome this difficulty, we develop a deep learning assisted jet tomography which uses the full information of the final hadrons from jets to localize the initial jet production positions. This method can help to constrain the initial regions of jet production in heavy-ion collisions and enable a differential study of Mach-cones with different jet path length and orientation relative to the radial flow of the QGP in heavy-ion collisions