Knapsack Problems in Groups

We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time decidable in hyperbolic groups and give various examples of finitely presented groups where the subset sum problem is NP-complete.Comment: 28 pages, 12 figure

Bragg diffraction of microcavity polaritons by a surface acoustic wave

Bragg scattering of polaritons by a coherent acoustic wave is mediated and strongly enhanced by the exciton states resonant with the acoustic and optic fields in the intraband and interband transitions, respectively. In this case, in contrast with conventional acousto-optics, the resonantly enhanced Bragg spectra reveal the multiple orders of diffracted light. For polaritons in GaAs microcavities driven by a surface acoustic wave of νSAW=1 GHz and Iac≲100 W/cm2 the main acoustically induced band gap can be as large as ΔMCac≃0.6 meV and the Bragg replicas up to n=3 can be observed

Di-chromatic InGaN based color tuneable monolithic LED with high color rendering index

We demonstrate a phosphor free, dichromatic GaN-based monolithic white LED with vertically stacked green and blue emitting multiple quantum wells. The optimal thickness of GaN barrier layer between green and blue quantum wells used is 8 nm. This device can be tuned over a wide range of correlated color temperature (CCT) to achieve warm white (CCT = 3600 K) to cool white (CCT = 13,000 K) emission by current modulation from 2.3 A/cm2 to 12.9 A/cm2. It is also demonstrated for the first time that a color rendering index (CRI) as high as 67 can be achieved with such a dichromatic source. The observed CCT and CRI tunability is associated with the spectral power evolution due to the pumping-induced carrier redistribution

Nuclear shadowing in Glauber-Gribov theory with Q2-evolution

We consider deep inelastic scattering off nuclei in the Regge limit within the Glauber-Gribov model. Using unitarized parton distribution functions for the proton, we find sizeable shadowing effects on the nuclear total and longitudinal structure functions, $F_2^A$ and $F_L^A$, in the low-x limit. Extending a fan-diagram analysis for the large-mass region of coherent diffraction off nuclei to high Q2, we also find significant shadowing effects in this kinematical regime. Finally, we discuss shortcomings of our approach and possible extensions of the model to other kinematical regimes.Comment: 16 pages, 9 figure

Verbal subgroups of hyperbolic groups have infinite width

Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subgroup $w(G)=$ is infinite. That is, there is no such $l\in\mathbb Z$ that any $g\in w(G)$ can be represented as a product of $\le l$ values of $w$ and their inverses.Comment: To appear in Journal of the London Mathematical Society. 22 pages, 8 figure

Epithelial NEMO links innate immunity to chronic intestinal inflammation

Deregulation of intestinal immune responses seems to have a principal function in the pathogenesis of inflammatory bowel disease(1-4). The gut epithelium is critically involved in the maintenance of intestinal immune homeostasis-acting as a physical barrier separating luminal bacteria and immune cells, and also expressing antimicrobial peptides(3,5,6). However, the molecular mechanisms that control this function of gut epithelial cells are poorly understood. Here we show that the transcription factor NF kappa B, a master regulator of pro-inflammatory responses(7,8), functions in gut epithelial cells to control epithelial integrity and the interaction between the mucosal immune system and gut microflora. Intestinal epithelial-cell-specific inhibition of NF-kappa B through conditional ablation of NEMO ( also called I kappa B kinase-gamma ( IKK gamma)) or both IKK1 ( IKK alpha) and IKK2 ( IKK beta)-IKK subunits essential for NF-kappa B activation(7-9)-spontaneously caused severe chronic intestinal inflammation in mice. NF-kappa B deficiency led to apoptosis of colonic epithelial cells, impaired expression of antimicrobial peptides and translocation of bacteria into the mucosa. Concurrently, this epithelial defect triggered a chronic inflammatory response in the colon, initially dominated by innate immune cells but later also involving T lymphocytes. Deficiency of the gene encoding the adaptor protein MyD88 prevented the development of intestinal inflammation, demonstrating that Toll-like receptor activation by intestinal bacteria is essential for disease pathogenesis in this mouse model. Furthermore, NEMO deficiency sensitized epithelial cells to tumour-necrosis factor ( TNF)-induced apoptosis, whereas TNF receptor-1 inactivation inhibited intestinal inflammation, demonstrating that TNF receptor-1 signalling is crucial for disease induction. These findings demonstrate that a primary NF-kappa B signalling defect in intestinal epithelial cells disrupts immune homeostasis in the gastrointestinal tract, causing an inflammatory-bowel-disease-like phenotype. Our results identify NF-kappa B signalling in the gut epithelium as a critical regulator of epithelial integrity and intestinal immune homeostasis, and have important implications for understanding the mechanisms controlling the pathogenesis of human inflammatory bowel disease.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62858/1/nature05698.pd