Further results on the nullity of signed graphs

The nullity of a graph is the multiplicity of the eigenvalues zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we obtain the coefficient theorem of the characteristic polynomial of a signed graph, give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graph $\Gamma(\infty(p,q,l))$, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.Comment: 17 pages. arXiv admin note: text overlap with arXiv:1207.6765, arXiv:1107.0400 by other author

Amphoteric Soy Protein-Rich Fibers for Rapid and Selective Adsorption and Desorption of Ionic Dyes.

Uniquely amphoteric soy protein (SP)-rich ultra-fine fibers (231 nm average diameter) have been facilely electrospun from aq. colloids and rendered water-insoluble by heating (150 °C, 12 h) to be highly stable over 14 d (pH 7) as well as under extremely acidic to basic (pH 0-10, 2 d) or at boil (2 h) conditions. The SP-rich fibrous membranes are easily tuned to be charged either negatively by deprotonation above or positively by protonation below the 4.5 PI of SPs. This pH-responsive amphoterism has been demonstrated for rapid adsorption of either cationic or anionic dyes, selective adsorption of either dye from their mixtures, and repetitive adsorption/desorption to recover and reuse both dyes and membranes. Chemisorption and heterogeneous adsorption of ionic dyes was confirmed by close fitting to the pseudo-second-order kinetic model (R 2 = 0.9977-0.9999) and Freundlich adsorption isotherm (R 2 = 0.9879). This is the first report of water-resilient and pH-robust ultrafine fibrous membranes fabricated from aqueous colloids of neat globular SPs, the major byproducts of under-utilized edible oil and biodiesel. The natural polyampholyte origin, amphoterism, and green processing make these fibrous materials unique and versatile for many potential applications involving both anionic and cationic species

Relating Weight Constraint and Aggregate Programs: Semantics and Representation

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint programs and the answer set semantics based on conditional satisfaction for aggregate programs. Both classes of programs are instances of logic programs with constraints, and in particular, the answer set semantics for aggregate programs can be applied to weight constraint programs. We show that the two semantics are closely related. First, we show that for a broad class of weight constraint programs, called strongly satisfiable programs, the two semantics coincide. When they disagree, a stable model admitted by the stable model semantics may be circularly justified. We show that the gap between the two semantics can be closed by transforming a weight constraint program to a strongly satisfiable one, so that no circular models may be generated under the current implementation of the stable model semantics. We further demonstrate the close relationship between the two semantics by formulating a transformation from weight constraint programs to logic programs with nested expressions which preserves the answer set semantics. Our study on the semantics leads to an investigation of a methodological issue, namely the possibility of compact representation of aggregate programs by weight constraint programs. We show that almost all standard aggregates can be encoded by weight constraints compactly. This makes it possible to compute the answer sets of aggregate programs using the ASP solvers for weight constraint programs. This approach is compared experimentally with the ones where aggregates are handled more explicitly, which show that the weight constraint encoding of aggregates enables a competitive approach to answer set computation for aggregate programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP), 2011. 30 page

Block Belief Propagation for Parameter Learning in Markov Random Fields

Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose \emph{block belief propagation learning} (BBPL), which uses block-coordinate updates of approximate marginals to compute approximate gradients, removing the need to compute inference on the entire graphical model. Thus, the iteration complexity of BBPL does not scale with the size of the graphs. We prove that the method converges to the same solution as that obtained by using full inference per iteration, despite these approximations, and we empirically demonstrate its scalability improvements over standard training methods.Comment: Accepted to AAAI 201

Quantifying Fluid Shear Stress in a Rocking Culture Dish

Fluid shear stress (FSS) is an important stimulus for cell functions. Compared with the well established parallel-plate and cone-and-plate systems, a rocking “see-saw” system offers some advantages such as easy operation, low cost, and high throughput. However, the FSS spatiotemporal pattern in the system has not been quantified. In the present study, we developed a lubrication-based model to analyze the FSS distributions in a rocking rectangular culture dish. We identified an important parameter (the critical flip angle) that dictates the overall FSS behaviors and suggested the right conditions to achieving temporally oscillating and spatially relatively uniform FSS. If the maximal rocking angle is kept smaller than the critical flip angle, which is defined as the angle when the fluid free surface intersects the outer edge of the dish bottom, the dish bottom remains covered with a thin layer of culture medium. The spatial variations of the peak FSS within the central 84% and 50% dish bottom are limited to 41% and 17%, respectively. The magnitude of FSS was found to be proportional to the fluid viscosity and the maximal rocking angle, and inversely proportional to the square of the fluid depth-to-length ratio and the rocking period. For a commercial rectangular dish (length of 37.6 mm) filled with ∼2 mL culture medium, the FSS at the center of the dish bottom is expected to be on the order of 0.9 dyn/cm2 when the dish is rocked +5° at 1 cycle/s. Our analysis suggests that a rocking “see-saw” system, if controlled well, can be used as an alternative method to provide low-magnitude, dynamic FSS to cultured cells