K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.

Simple method for the rapid simultaneous screening of photocatalytic activity over multiple positions of self-cleaning films

An intelligent ink, previously shown to be capable of rapidly assessing photocatalytic activity, was simply applied via a felt-pen onto a commercially available piece of Activ (TM) self-cleaning glass. The ink, comprising of redox dye resazurin and the sacrificial electron donor glycerol within an aqueous hydroxy ethyl cellulose (HEC) polymer media, was photocatalytically degraded in a two-step process. The key initial stage was the photo-reductive conversion of resazurin to resorufin, whereby a colour change from blue to pink occurred. The latter stage was the subsequent photo-reduction of the resorufin, where a slower change from pink to colourless was seen. Red and green components of red-green-blue colour extracted from flat-bed scanner digital images of resazurin ink coated photocatalytic films at intervals during the photocatalysis reaction were inversely proportional to the changes seen via UV-visible absorption spectroscopy and indicative of reaction kinetics. A 3 x 3 grid of intelligent ink was drawn onto a piece of Activ (TM) and a glass blank. The photocatalysis reaction was monitored solely by flat-bed digital scanning. Red-green-blue values of respective positions on the grid were extracted using a custom-built program entitled RGB Extractor (c). The program was capable of extracting a number of 5 x 5 pixel averages of red-green-blue components simultaneously. Allocation of merely three coordinates allowed for the automatic generation of a grid, with scroll-bars controlling the number of positions to be extracted on the grid formed. No significant change in red and green components for any position on the glass blank was observed; however, the Activ (TM) film displayed a homogenous photo-reduction of the dye, reaching maxima in red and minima in green components in 23 +/- 3 and 14 +/- 2 min, respectively. A compositionally graded N-doped titania film synthesised in house via a combinatorial APCVD reaction was also photocatalytically tested by this method where 247 positions on a 13 x 19 grid were simultaneously analysed. The dramatic variation in photocatalysis observed was rapidly quantified for all positions (2-3 hours) allowing for correlations to be made between thicknesses and N : Ti% compositions attained from Swanepoel and WDX analysis, respectively. N incorporation within this system was found to be detrimental to film activity for the photocatalysis reaction of intelligent ink under 365 nm light.

TAZ Expression as a Prognostic Indicator in Colorectal Cancer

The Hippo pathway restricts the activity of transcriptional coactivators TAZ (WWTR1) and YAP. TAZ and YAP are reported to be overexpressed in various cancers, however, their prognostic significance in colorectal cancers remains unstudied. The expression levels of TAZ and YAP, and their downstream transcriptional targets, AXL and CTGF, were extracted from two independent colon cancer patient datasets available in the Gene Expression Omnibus database, totaling 522 patients. We found that mRNA expressions of both TAZ and YAP were positively correlated with those of AXL and CTGF (p<0.05). High level mRNA expression of TAZ, AXL or CTGF significantly correlated with shorter survival. Importantly, patients co-overexpressing all 3 genes had a significantly shorter survival time, and combinatorial expression of these 3 genes was an independent predictor for survival. The downstream target genes for TAZ-AXL-CTGF overexpression were identified by Java application MyStats. Interestingly, genes that are associated with colon cancer progression (ANTXR1, EFEMP2, SULF1, TAGLN, VCAN, ZEB1 and ZEB2) were upregulated in patients co-overexpressing TAZ-AXL-CTGF. This TAZ-AXL-CTGF gene expression signature (GES) was then applied to Connectivity Map to identify small molecules that could potentially be utilized to reverse this GES. Of the top 20 small molecules identified by connectivity map, amiloride (a potassium sparing diuretic,) and tretinoin (all-trans retinoic acid) have shown therapeutic promise in inhibition of colon cancer cell growth. Using MyStats, we found that low level expression of either ANO1 or SQLE were associated with a better prognosis in patients who co-overexpressed TAZ-AXL-CTGF, and that ANO1 was an independent predictor of survival together with TAZ-AXL-CTGF. Finally, we confirmed that TAZ regulates Axl, and plays an important role in clonogenicity and non-adherent growth in vitro and tumor formation in vivo. These data suggest that TAZ could be a therapeutic target for the treatment of colon cancer.

Zero-One Designs Produce Small Hard SAT Instances

Some basics of combinatorial block design are combined with certain constraint satisfaction problems of interest to the satisfiability community. The paper shows how such combinations lead to satisfiability problems, and shows empirically that these are some of the smallest very hard satisfiability problems ever constructed. Partially balanced (0,1) designs (PB01Ds) are introduced as an extension of balanced incomplete block designs (BIBDs) and (0,1) designs. Also, (0,1) difference sets are introduced as an extension of certain cyclical difference sets. Constructions based on (0,1) difference sets enable generation of PB01Ds over a much wider range of parameters than is possible for BIBDs. Building upon previous work of Spence, it is shown how PB01Ds lead to small, very hard, unsatisfiable formulas. A new three-dimensional form of combinatorial block design is introduced, and leads to small, very hard, satisfiable formulas. The methods are validated on solvers that performed well in the SAT 2009 and earlier competitions.

Nonlinear scattering by anisotropic dielectric periodic structures

The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures. © 2012 O. V. Shramkova and A. G. Schuchinsky.

Gaussian pulse mixing and scattering by finite nonlinear layered structures

Multiple Gaussian pulse interactions and scattering in the nonlinear layered dielectric structures have been examined. The Gaussian pulses with different centre frequencies and lengths are incident at oblique angles on the finite stack of nonlinear dielectric layers. The properties of the reflected and refracted waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed. It is shown that the efficiency of forward emission at the combinatorial frequency can be considerably increased when the wavelengths of interacting pulses are close to the edges of electromagnetic bandgap. © 2012 IEEE.

Three-wave Nonlinear Scattering by Quasiperiodic Dielectric Structure

The combinatorial frequency generation by a Fibonacci type quasi-periodic dielectric multilayered structure illuminated by two plane waves has been analysed. The effects of the layer parameters and Fibonacci sequence order on the properties of the combinatorial frequency waves emitted from the stacked nonlinear layers are discussed.

Gaussian pulse mixing by nonlinear photonic crystals

The properties of mixing and scattering of two non-collinear Gaussian pulses with different centre frequencies and lengths, incident on the finite nonlinear periodic layered dielectric structures, have been analysed. It is shown that at the backward emission grows with the number of layers and can reach the level of the forward emission in the direction of combinatorial frequency scattering.

Mechanisms and sources of passive intermodulation in printed circuits

Modern wireless systems are expected to operate in multiple frequency bands and support diverse communications standards to provide the high volume and speed of data transmission. Today's major limitations of their performance are imposed by interference, spurious emission and noise generated by high-power carriers in antennas and passive components of the RF front-end. Passive Intermodulation (PIM), which causes the combinatorial frequency generation in the operational bands, presents a primary challenge to signal integrity, system efficacy and data throughput. © 2013 IEEE.

Wave mixing by periodic nonlinear semiconductor multilayers

The properties of the combinatorial frequency generation and wave scattering by periodic stacks of nonlinear passive semiconductor layers are explored. It is demonstrated that the nonlinearity in passive weakly nonlinear semiconductor medium has the resistive nature associated with the dynamics of carriers. The features of the combinatorial frequency generation and the effects of the pump wave scattering and parameters of the constituent semiconductor layers on the efficiency of the frequency mixing are discussed and illustrated by the examples. © 2013 IEICE.

Enrichment of low-abundance proteins from bovine and porcine serum samples for proteomic studies

One of the main applications of serum proteomics is the identification of new biomarkers for animal disease or animal production. However, potential obstacles to these studies are the poor performance of affinity serum depletion methods based on human antigens when using animal samples, and loss of minor serum components bound to albumin and other proteins. In the present study, we have analyzed the efficiency and reproducibility of the ProteoMiner® beads with bovine and porcine serum samples, and compared to a traditional immunoaffinity-based albumin and IgG depletion system specific for human samples. The ProteoMiner kit is based on the use of a combinatorial peptide binding library and intends to enrich low-abundance proteins.

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional ( classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing - highlighting the crucial differences between these two methods - by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems ( namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.

Nonreciprocal scattering by stacked nonlinear magneto-active semiconductor layers

The combinatorial frequency generation by the periodic stacks of magnetically biased semiconductor layers has been modelled in a self-consistent problem formulation, taking into account the nonlinear dynamics of carriers. It is shown that magnetic bias not only renders nonreciprocity of the three-wave mixing process but also significantly enhances the nonlinear interactions in the stacks, especially at the frequencies close to the intrinsic magneto-plasma resonances of the constituent layers. The main mechanisms and properties of the combinatorial frequency generation and emission from the stacks are illustrated by the simulation results, and the effects of the individual layer parameters and the structure arrangement on the stack nonlinear and nonreciprocal response are discussed. © 2014 Elsevier B.V. All rights reserved.

RNAi dynamics in Juvenile Fasciola spp. Liver flukes reveals the persistence of gene silencing in vitro

Background: Fasciola spp. liver fluke cause pernicious disease in humans and animals. Whilst current control is unsustainable due to anthelmintic resistance, gene silencing (RNA interference, RNAi) has the potential to contribute to functional validation of new therapeutic targets. The susceptibility of juvenile Fasciola hepatica to double stranded (ds)RNA-induced RNAi has been reported. To exploit this we probe RNAi dynamics, penetrance and persistence with the aim of building a robust platform for reverse genetics in liver fluke. We describe development of standardised RNAi protocols for a commercially-available liver fluke strain (the US Pacific North West Wild Strain), validated via robust transcriptional silencing of seven virulence genes, with in-depth experimental optimisation of three: cathepsin L (FheCatL) and B (FheCatB) cysteine proteases, and a σ-class glutathione transferase (FheσGST).

Methodology/Principal Findings: Robust transcriptional silencing of targets in both F. hepatica and Fasciola gigantica juveniles is achievable following exposure to long (200–320 nt) dsRNAs or 27 nt short interfering (si)RNAs. Although juveniles are highly RNAi-susceptible, they display slower transcript and protein knockdown dynamics than those reported previously. Knockdown was detectable following as little as 4h exposure to trigger (target-dependent) and in all cases silencing persisted for ≥25 days following long dsRNA exposure. Combinatorial silencing of three targets by mixing multiple long dsRNAs was similarly efficient. Despite profound transcriptional suppression, we found a significant time-lag before the occurrence of protein suppression; FheσGST and FheCatL protein suppression were only detectable after 9 and 21 days, respectively.

Conclusions/Significance: In spite of marked variation in knockdown dynamics, we find that a transient exposure to long dsRNA or siRNA triggers robust RNAi penetrance and persistence in liver fluke NEJs supporting the development of multiple-throughput phenotypic screens for control target validation. RNAi persistence in fluke encourages in vivo studies on gene function using worms exposed to RNAi-triggers prior to infection.