Polynomial evaluation over finite fields: new algorithms and complexity bounds

An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation in the decoding of Reed-Solomon codes are highlighted.Comment: accepted for publication in Applicable Algebra in Engineering, Communication and Computing. The final publication will be available at springerlink.com. DOI: 10.1007/s00200-011-0160-

Natural Little Hierarchy from a Partially Goldstone Twin Higgs

We construct a simple theory in which the fine-tuning of the standard model is significantly reduced. Radiative corrections to the quadratic part of the scalar potential are constrained to be symmetric under a global U(4) x U(4)' symmetry due to a discrete Z_2 "twin" parity, while the quartic part does not possess this symmetry. As a consequence, when the global symmetry is broken the Higgs fields emerge as light pseudo-Goldstone bosons, but with sizable quartic self-interactions. This structure allows the cutoff scale, \Lambda, to be raised to the multi-TeV region without significant fine-tuning. In the minimal version of the theory, the amount of fine-tuning is about 15% for \Lambda = 5 TeV, while it is about 30% in an extended model. This provides a solution to the little hierarchy problem. In the minimal model, the "visible" particle content is exactly that of the two Higgs doublet standard model, while the extended model also contains extra vector-like fermions with masses ~(1-2)TeV. At the LHC, our minimal model may appear exactly as the two Higgs doublet standard model, and new physics responsible for cutting off the divergences of the Higgs mass-squared parameter may not be discovered. Several possible processes that may be used to discriminate our model from the simple two Higgs doublet model are discussed for the LHC and for a linear collider.Comment: 22 page

Flux Stabilization in 6 Dimensions: D-terms and Loop Corrections

We analyse D-terms induced by gauge theory fluxes in the context of 6-dimensional supergravity models. On the one hand, this is arguably the simplest concrete setting in which the controversial idea of `D-term uplifts' can be investigated. On the other hand, it is a very plausible intermediate step on the way from a 10d string theory model to 4d phenomenology. Our specific results include the flux-induced one-loop correction to the scalar potential coming from charged hypermultiplets. Furthermore, we comment on the interplay of gauge theory fluxes and gaugino condensation in the present context, demonstrate explicitly how the D-term arises from the gauging of one of the compactification moduli, and briefly discuss further ingredients that may be required for the construction of a phenomenologically viable model. In particular, we show how the 6d dilaton and volume moduli can be simultaneously stabilized, in the spirit of KKLT, by the combination of an R symmetry twist, a gaugino condensate, and a flux-induced D-term.Comment: 24 pages, 1 figure v2:minor correction

The Complexity of the Empire Colouring Problem

We investigate the computational complexity of the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly $r > 1$ countries each. We prove that the problem can be solved in polynomial time using $s$ colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than $s/r$. However, if $s \geq 3$, the problem is NP-hard even if the graph is a forest of paths of arbitrary lengths (for any $r \geq 2$, provided $s < 2r - \sqrt(2r + 1/4+ 3/2)$. Furthermore we obtain a complete characterization of the problem's complexity for the case when the input graph is a tree, whereas our result for arbitrary planar graphs fall just short of a similar dichotomy. Specifically, we prove that the empire colouring problem is NP-hard for trees, for any $r \geq 2$, if $3 \leq s \leq 2r-1$ (and polynomial time solvable otherwise). For arbitrary planar graphs we prove NP-hardness if $s<7$ for $r=2$, and $s < 6r-3$, for $r \geq 3$. The result for planar graphs also proves the NP-hardness of colouring with less than 7 colours graphs of thickness two and less than $6r-3$ colours graphs of thickness $r \geq 3$.Comment: 23 pages, 12 figure

RNA sequencing reveals MMP2 and TGFB1 downregulation in LRRK2 G2019S Parkinson's iPSC-derived astrocytes

Non-neuronal cell types such as astrocytes can contribute to Parkinson's disease (PD) pathology. The G2019S mutation in leucine-rich repeat kinase 2 (LRRK2) is one of the most common known causes of familial PD. To characterize its effect on astrocytes, we developed a protocol to produce midbrain-patterned astrocytes from human induced pluripotent stem cells (iPSCs) derived from PD LRRK2 G2019S patients and healthy controls. RNA sequencing analysis revealed the downregulation of genes involved in the extracellular matrix in PD cases. In particular, transforming growth factor beta 1 (TGFB1), which has been shown to inhibit microglial inflammatory response in a rat model of PD, and matrix metallopeptidase 2 (MMP2), which has been shown to degrade α-synuclein aggregates, were found to be down-regulated in LRRK2 G2019S astrocytes. Our findings suggest that midbrain astrocytes carrying the LRRK2 G2019S mutation may have reduced neuroprotective capacity and may contribute to the development of PD pathology

Silicon and Germanium Nanostructures for Photovoltaic Applications: Ab-Initio Results

Actually, most of the electric energy is being produced by fossil fuels and great is the search for viable alternatives. The most appealing and promising technology is photovoltaics. It will become truly mainstream when its cost will be comparable to other energy sources. One way is to significantly enhance device efficiencies, for example by increasing the number of band gaps in multijunction solar cells or by favoring charge separation in the devices. This can be done by using cells based on nanostructured semiconductors. In this paper, we will present ab-initio results of the structural, electronic and optical properties of (1) silicon and germanium nanoparticles embedded in wide band gap materials and (2) mixed silicon-germanium nanowires. We show that theory can help in understanding the microscopic processes important for devices performances. In particular, we calculated for embedded Si and Ge nanoparticles the dependence of the absorption threshold on size and oxidation, the role of crystallinity and, in some cases, the recombination rates, and we demonstrated that in the case of mixed nanowires, those with a clear interface between Si and Ge show not only a reduced quantum confinement effect but display also a natural geometrical separation between electron and hole

GWAS analysis of handgrip and lower body strength in older adults in the CHARGE consortium

Decline in muscle strength with aging is an important predictor of health trajectory in the elderly. Several factors, including genetics, are proposed contributors to variability in muscle strength. To identify genetic contributors to muscle strength, a meta-analysis of genomewide association studies of handgrip was conducted. Grip strength was measured using a handheld dynamometer in 27 581 individuals of European descent over 65 years of age from 14 cohort studies. Genomewide association analysis was conducted on ~2.7 million imputed and genotyped variants (SNPs). Replication of the most significant findings was conducted using data from 6393 individuals from three cohorts. GWAS of lower body strength was also characterized in a subset of cohorts. Two genomewide significant (P-value< 5 × 10−8) and 39 suggestive (P-value< 5 × 10−5) associations were observed from meta-analysis of the discovery cohorts. After meta-analysis with replication cohorts, genomewide significant association was observed for rs752045 on chromosome 8 (β = 0.47, SE = 0.08, P-value = 5.20 × 10−10). This SNP is mapped to an intergenic region and is located within an accessible chromatin region (DNase hypersensitivity site) in skeletal muscle myotubes differentiated from the human skeletal muscle myoblasts cell line. This locus alters a binding motif of the CCAAT/enhancer-binding protein-β (CEBPB) that is implicated in muscle repair mechanisms. GWAS of lower body strength did not yield significant results. A common genetic variant in a chromosomal region that regulates myotube differentiation and muscle repair may contribute to variability in grip strength in the elderly. Further studies are needed to uncover the mechanisms that link this genetic variant with muscle strength