Hardness results for computing optimal locally Gabriel graphs

Delaunay and Gabriel graphs are widely studied geo-metric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as Locally Delaunay Graphs (LDGs) and Lo-cally Gabriel Graphs (LGGs) have been proposed. We propose another generalization of LGGs called Gener-alized Locally Gabriel Graphs (GLGGs) in the context when certain edges are forbidden in the graph. Unlike a Gabriel Graph, there is no unique LGG or GLGG for a given point set because no edge is necessarily in-cluded or excluded. This property allows us to choose an LGG/GLGG that optimizes a parameter of interest in the graph. We show that computing an edge max-imum GLGG for a given problem instance is NP-hard and also APX-hard. We also show that computing an LGG on a given point set with dilation ≤k is NP-hard. Finally, we give an algorithm to verify whether a given geometric graph G= (V, E) is a valid LGG.

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Ultrasonic attenuation in strongly disordered electronic systems

The attenuation of long-wavelength phonons due to their interaction with electronic excitations in disordered systems is investigated here. Lattice strain couples to electronic stress, and thus ultrasonic attenuation measures electronic viscosity. The enhancement and critical divergence of electronic viscosity due to localization effects is calculated for the first time. Experimental consequences for the anomalous increase of ultrasonic attenuation in disordered metals close to the metal-insulator transition are discussed. In the localized regime, the appropriate model is one of electronic two-level systems (TLS’s) coupled to phonons. The TLS consists of a pair of states with one localized state occupied and the other unoccupied. The density of such low-excitation-energy TLS’s is nonzero due to long-range Coulomb interactions. The question of whether these could be significant low-energy excitations in glasses is touched upon.

Covariant differentials lead to the design of a novel self-tuning power system stabilizer

Application of differential geometry to study the dynamics of electrical machines by Gabriel Kron evoked only theoretical interest among the power system engineers and was considered hardly suitable for any practical use. Extension of Kron's work led to a physical understanding of the processes governing the small oscillation instability in power system. This in turn has made it possible to design a self-tuning Power System Stabilizer to contain the oscillatory instability over arm extended range of system and operating conditions. This paper briefly recounts the history of this development and touches upon the essential design features of the stabilizer. It presents some results from simulation studies, laboratory experiments and recently conducted field trials at actual plants-all of which help to establish the efficacy of the proposed stabilizer and corroborate the theoretical findings.

A novel adeno-associated virus serotype (AAV)-8 capsid mutant improves human coagulation factor IX expression in vivo

Recombinant AAV-8 vectors have shown significant promise for hepatic gene therapy of hemophilia B. However, the theme of AAV vector dose dependent immunotoxicity seen with AAV2 vectors earlier seem to re-emerge with AAV8 vectors as well. It is therefore important to develop novel AAV8 vectors that provide enhanced gene expression at significantly less vector doses. We hypothesized that AAV8 during its intracellular trafficking, are targeted for destruction in the cytoplasm by the host-cellular kinase/ubiquitination/proteasomal degradation machinery and modification of specific serine/threonine kinase or ubiquitination targets on AAV8 capsid (Fig.1A) may improve its transduction efficiency. To test this, point mutations at specific serine (S)/threonine (T) > alanine (A) or lysine (K)>arginine (R) residues were generated on AAV8 capsid. scAAV8-EGFP vectors containing the wild-type (WT) and each one of the 5 S/T/K-mutant(S276A, S501A, S671A, T251A and K137R) capsids were evaluated for their liver transduction efficiency at a dose of 5 X 1010 vgs/ animal in C57BL/6 mice in vivo. The best performing mutant was found to be the K137R vector in terms of either the gene expression (46-fold) or the vector copy numbers in the hepatocytes (22-fold) compared to WT-AAV8 (Fig.1B). The K137R-AAV8 vector that showed significantly decreased ubiquitination of the viral capsid had reduced activation of markers of innate immune response [IL-6, IL-12, tumor necrosis factor α, Kupffer cells and TLR-9]. In addition, animals injected with the K137R mutant also demonstrated decreased (2-fold) levels of cross-neutralizing antibodies when compared to animals that received the WT-AAV8 vector. To study further the utility of the novel AAV8-K137R mutant in a therapeutic setting, we delivered human coagulation factor IX (h.FIX) under the control of liver specific promoters (LP1 or hAAT) at two different doses (2.5x10^10 and 1x10^11 vgs per mouse) in 8-12 weeks old male C57BL/6 mice. As can be seen in Fig.1C/D, the circulating levels of h.FIX were higher in all the K137R-AAV8 treated groups as compared to the WT-AAV8 treated groups either at 2 weeks (62% vs 37% for hAAT constructs and 47% vs 21% for LP1 constructs) or 4 weeks (78% vs 56% for hAAT constructs and 64% vs 30% for LP1 constructs) post hepatic gene transfer. These studies demonstrate the feasibility of the use of this novel vector for potential gene therapy of hemophilia B.

Surface Freshwater Storage Variations in the Orinoco Floodplains Using Multi-Satellite Observations

Variations in surface water extent and storage are poorly characterized from regional to global scales. In this study, a multi-satellite approach is proposed to estimate the water stored in the floodplains of the Orinoco Basin at a monthly time-scale using remotely-sensed observations of surface water from the Global Inundation Extent Multi-Satellite (GIEMS) and stages from Envisat radar altimetry. Surface water storage variations over 2003-2007 exhibit large interannual variability and a strong seasonal signal, peaking during summer, and associated with the flood pulse. The volume of surface water storage in the Orinoco Basin was highly correlated with the river discharge at Ciudad Bolivar (R = 0.95), the closest station to the mouth where discharge was estimated, although discharge lagged one month behind storage. The correlation remained high (R = 0.73) after removing seasonal effects. Mean annual variations in surface water volume represented similar to 170 km(3), contributing to similar to 45% of the Gravity Recovery and Climate Experiment (GRACE)-derived total water storage variations and representing similar to 13% of the total volume of water that flowed out of the Orinoco Basin to the Atlantic Ocean.

Interphase anisotropy effects on lamellar eutectics: A numerical study

In directional solidification of binary eutectics, it is often observed that two-phase lamellar growth patterns grow tilted with respect to the direction z of the imposed temperature gradient. This crystallographic effect depends on the orientation of the two crystal phases alpha and beta with respect to z. Recently, an approximate theory was formulated that predicts the lamellar tilt angle as a function of the anisotropy of the free energy of the solid(alpha)-solid(beta) interphase boundary. We use two different numerical methods-phase field (PF) and dynamic boundary integral (BI)-to simulate the growth of steady periodic patterns in two dimensions as a function of the angle theta(R) between z and a reference crystallographic axis for a fixed relative orientation of alpha and beta crystals, that is, for a given anisotropy function (Wulff plot) of the interphase boundary. For Wulff plots without unstable interphase-boundary orientations, the two simulation methods are in excellent agreement with each other and confirm the general validity of the previously proposed theory. In addition, a crystallographic ``locking'' of the lamellae onto a facet plane is well reproduced in the simulations. When unstable orientations are present in the Wulff plot, it is expected that two distinct values of the tilt angle can appear for the same crystal orientation over a finite theta(R) range. This bistable behavior, which has been observed experimentally, is well reproduced by BI simulations but not by the PF model. Possible reasons for this discrepancy are discussed.

Bioengineering of AAV2 Capsid at Specific Serine, Threonine, or Lysine Residues Improves Its Transduction Efficiency in Vitro and in Vivo

We hypothesized that the AAV2 vector is targeted for destruction in the cytoplasm by the host cellular kinase/ubiquitination/proteasomal machinery and that modification of their targets on AAV2 capsid may improve its transduction efficiency. In vitro analysis with pharmacological inhibitors of cellular serine/threonine kinases (protein kinase A, protein kinase C, casein kinase II) showed an increase (20-90%) on AAV2-mediated gene expression. The three-dimensional structure of AAV2 capsid was then analyzed to predict the sites of ubiquitination and phosphorylation. Three phosphodegrons, which are the phosphorylation sites recognized as degradation signals by ubiquitin ligases, were identified. Mutation targets comprising eight serine (S) or seven threonine (T) or nine lysine (K) residues were selected in and around phosphodegrons on the basis of their solvent accessibility, overlap with the receptor binding regions, overlap with interaction interfaces of capsid proteins, and their evolutionary conservation across AAV serotypes. AAV2-EGFP vectors with the wild-type (WT) capsid or mutant capsids (15 S/T -> alanine A] or 9 K -> arginine R] single mutant or 2 double K -> R mutants) were then evaluated in vitro. The transduction efficiencies of 11 S/T -> A and 7 K -> R vectors were significantly higher (similar to 63-90%) than the AAV2-WT vectors (similar to 30-40%). Further, hepatic gene transfer of these mutant vectors in vivo resulted in higher vector copy numbers (up to 4.9-fold) and transgene expression (up to 14-fold) than observed from the AAV2-WT vector. One of the mutant vectors, S489A, generated similar to 8-fold fewer antibodies that could be cross-neutralized by AAV2-WT. This study thus demonstrates the feasibility of the use of these novel AAV2 capsid mutant vectors in hepatic gene therapy.

Targeted Modifications in Adeno-Associated Virus Serotype 8 Capsid Improves Its Hepatic Gene Transfer Efficiency In Vivo

Recombinant adeno-associated virus vectors based on serotype 8 (AAV8) have shown significant promise for liver-directed gene therapy. However, to overcome the vector dose dependent immunotoxicity seen with AAV8 vectors, it is important to develop better AAV8 vectors that provide enhanced gene expression at significantly low vector doses. Since it is known that AAV vectors during intracellular trafficking are targeted for destruction in the cytoplasm by the host-cellular kinase/ubiquitination/proteasomal machinery, we modified specific serine/threonine kinase or ubiquitination targets on the AAV8 capsid to augment its transduction efficiency. Point mutations at specific serine (S)/threonine (T)/lysine (K) residues were introduced in the AAV8 capsid at the positions equivalent to that of the effective AAV2 mutants, generated successfully earlier. Extensive structure analysis was carried out subsequently to evaluate the structural equivalence between the two serotypes. scAAV8 vectors with the wild-type (WT) and each one of the S/T -> Alanine (A) or K-Arginine (R) mutant capsids were evaluated for their liver transduction efficiency in C57BL/6 mice in vivo. Two of the AAV8-S -> A mutants (S279A and S671A), and a K137R mutant vector, demonstrated significantly higher enhanced green fluorescent protein (EGFP) transcript levels (similar to 9- to 46-fold) in the liver compared to animals that received WT-AAV8 vectors alone. The best performing AAV8 mutant (K137R) vector also had significantly reduced ubiquitination of the viral capsid, reduced activation of markers of innate immune response, and a concomitant two-fold reduction in the levels of neutralizing antibody formation in comparison to WT-AAV8 vectors. Vector bio-distribution studies revealed that the K137R mutant had a significantly higher and preferential transduction of the liver (106 vs. 7.7 vector copies/mouse diploid genome) when compared to WT-AAV8 vectors. To further study the utility of the K137R-AAV8 mutant in therapeutic gene transfer, we delivered human coagulation factor IX (h. FIX) under the control of liver-specific promoters (LP1 or hAAT) into C57BL/6 mice. The circulating levels of h. FIX: Ag were higher in all the K137R-AAV8 treated groups up to 8 weeks post-hepatic gene transfer. These studies demonstrate the feasibility of the use of this novel AAV8 vectors for potential gene therapy of hemophilia B.

A Variant of the Hadwiger-Debrunner (p, q)-Problem in the Plane

Let X be a convex curve in the plane (say, the unit circle), and let be a family of planar convex bodies such that every two of them meet at a point of X. Then has a transversal of size at most . Suppose instead that only satisfies the following ``(p, 2)-condition'': Among every p elements of , there are two that meet at a common point of X. Then has a transversal of size . For comparison, the best known bound for the Hadwiger-Debrunner (p, q)-problem in the plane, with , is . Our result generalizes appropriately for if is, for example, the moment curve.