Towards the Amplituhedron Volume

21 pages; v2: version published in JHEPIt has been recently conjectured that scattering amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. In particular we demonstrate how the amplituhedron volume for NMHV amplitudes is determined by these differential equations. The new formulation allows for a straightforward geometric description, without any reference to triangulations. Finally we discuss possible implications for volumes related to generic N^kMHV amplitudes.Peer reviewe

Toric Construction of Global F-Theory GUTs

We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient space. We first construct three-dimensional base manifolds that are hypersurfaces in a toric ambient space. We search for divisors which can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations over these base manifolds. We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models. The complete database of models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out several examples in more detail.Comment: 35 pages, references adde

Critical Trapped Surfaces Formation in the Collision of Ultrarelativistic Charges in (A)dS

We study the formation of marginally trapped surfaces in the head-on collision of two ultrarelativistic charges in $(A)dS$ space-time. The metric of ultrarelativistic charged particles in $(A)dS$ is obtained by boosting Reissner-Nordstr\"om $(A)dS$ space-time to the speed of light. We show that formation of trapped surfaces on the past light cone is only possible when charge is below certain critical - situation similar to the collision of two ultrarelativistic charges in Minkowski space-time. This critical value depends on the energy of colliding particles and the value of a cosmological constant. There is richer structure of critical domains in $dS$ case. In this case already for chargeless particles there is a critical value of the cosmological constant only below which trapped surfaces formation is possible. Appearance of arbitrary small nonzero charge significantly changes the physical picture. Critical effect which has been observed in the neutral case does not take place more. If the value of the charge is not very large solution to the equation on trapped surface exists for any values of cosmological radius and energy density of shock waves. Increasing of the charge leads to decrease of the trapped surface area, and at some critical point the formation of trapped surfaces of the type mentioned above becomes impossible.Comment: 30 pages, Latex, 7 figures, Refs. added and typos correcte

Heterogeneous patterns of tissue injury in NARP syndrome

Point mutations at m.8993T>C and m.8993T>G of the mtDNA ATPase 6 gene cause the neurogenic weakness, ataxia and retinitis pigmentosa (NARP) syndrome, a mitochondrial disorder characterized by retinal, central and peripheral neurodegeneration. We performed detailed neurological, neuropsychological and ophthalmological phenotyping of a mother and four daughters with NARP syndrome from the mtDNA m.8993T>C ATPase 6 mutation, including 3-T brain MRI, spectral domain optical coherence tomography (SD-OCT), adaptive optics scanning laser ophthalmoscopy (AOSLO), electromyography and nerve conduction studies (EMG-NCS) and formal neuropsychological testing. The degree of mutant heteroplasmy for the m.8993T>C mutation was evaluated by real-time allele refractory mutation system quantitative PCR of mtDNA from hair bulbs (ectoderm) and blood leukocytes (mesoderm). There were marked phenotypic differences between family members, even between individuals with the greatest degrees of ectodermal and mesodermal heteroplasmy. 3-T MRI revealed cerebellar atrophy and cystic and cavitary T2 hyperintensities in the basal ganglia. SD-OCT demonstrated similarly heterogeneous areas of neuronal and axonal loss in inner and outer retinal layers. AOSLO showed increased cone spacing due to photoreceptor loss. EMG-NCS revealed varying degrees of length-dependent sensorimotor axonal polyneuropathy. On formal neuropsychological testing, there were varying deficits in processing speed, visual–spatial functioning and verbal fluency and high rates of severe depression. Many of these cognitive deficits likely localize to cerebellar and/or basal ganglia dysfunction. High-resolution retinal and brain imaging in NARP syndrome revealed analogous patterns of tissue injury characterized by heterogeneous areas of neuronal loss

Physics of Neutron Star Crusts

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.Comment: 182 pages, published version available at <http://www.livingreviews.org/lrr-2008-10

Function-Based Discovery of Significant Transcriptional Temporal Patterns in Insulin Stimulated Muscle Cells

Background: Insulin action on protein synthesis (translation of transcripts) and post-translational modifications, especially of those involving the reversible modifications such as phosphorylation of various signaling proteins, are extensively studied but insulin effect on transcription of genes, especially of transcriptional temporal patterns remains to be fully defined. Methodology/Principal Findings: To identify significant transcriptional temporal patterns we utilized primary differentiated rat skeletal muscle myotubes which were treated with insulin and samples were collected every 20 min for 8 hours. Pooled samples at every hour were analyzed by gene array approach to measure transcript levels. The patterns of transcript levels were analyzed based on a novel method that integrates selection, clustering, and functional annotation to find the main temporal patterns associated to functional groups of differentially expressed genes. 326 genes were found to be differentially expressed in response to in vitro insulin administration in skeletal muscle myotubes. Approximately 20 % of the genes that were differentially expressed were identified as belonging to the insulin signaling pathway. Characteristic transcriptional temporal patterns include: (a) a slow and gradual decrease in gene expression, (b) a gradual increase in gene expression reaching a peak at about 5 hours and then reaching a plateau or an initial decrease and other different variable pattern of increase in gene expression over time. Conclusion/Significance: The new method allows identifying characteristic dynamic responses to insulin stimulus, commo

A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List

Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions [1]. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://​nuweb1.​neu.​edu/​cydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the Kähler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list

Potential antiproteolytic effects of L-leucine: observations of in vitro and in vivo studies

The purpose of present review is to describe the effect of leucine supplementation on skeletal muscle proteolysis suppression in both in vivo and in vitro studies. Most studies, using in vitro methodology, incubated skeletal muscles with leucine with different doses and the results suggests that there is a dose-dependent effect. The same responses can be observed in in vivo studies. Importantly, the leucine effects on skeletal muscle protein synthesis are not always connected to the inhibition of skeletal muscle proteolysis. As a matter of fact, high doses of leucine incubation can promote suppression of muscle proteolysis without additional effects on protein synthesis, and low leucine doses improve skeletal muscle protein ynthesis but have no effect on skeletal muscle proteolysis. These research findings may have an important clinical relevancy, because muscle loss in atrophic states would be reversed by specific leucine supplementation doses. Additionally, it has been clearly demonstrated that leucine administration suppresses skeletal muscle proteolysis in various catabolic states. Thus, if protein metabolism changes during different atrophic conditions, it is not surprising that the leucine dose-effect relationship must also change, according to atrophy or pathological state and catabolism magnitude. In conclusion, leucine has a potential role on attenuate skeletal muscle proteolysis. Future studies will help to sharpen the leucine efficacy on skeletal muscle protein degradation during several atrophic states

Increased brain expression of GPNMB is associated with genome wide significant risk for Parkinson's disease on chromosome 7p15.3

Genome wide association studies (GWAS) for Parkinson's disease (PD) have previously revealed a significant association with a locus on chromosome 7p15.3, initially designated as the glycoprotein non-metastatic melanoma protein B (GPNMB) locus. In this study, the functional consequences of this association on expression were explored in depth by integrating different expression quantitative trait locus (eQTL) datasets (Braineac, CAGEseq, GTEx, and Phenotype-Genotype Integrator (PheGenI)). Top risk SNP rs199347 eQTLs demonstrated increased expressions of GPNMB, KLHL7, and NUPL2 with the major allele (AA) in brain, with most significant eQTLs in cortical regions, followed by putamen. In addition, decreased expression of the antisense RNA KLHL7-AS1 was observed in GTEx. Furthermore, rs199347 is an eQTL with long non-coding RNA (AC005082.12) in human tissues other than brain. Interestingly, transcript-specific eQTLs in immune-related tissues (spleen and lymphoblastoid cells) for NUPL2 and KLHL7-AS1 were observed, which suggests a complex functional role of this eQTL in specific tissues, cell types at specific time points. Significantly increased expression of GPNMB linked to rs199347 was consistent across all datasets, and taken in combination with the risk SNP being located within the GPNMB gene, these results suggest that increased expression of GPNMB is the causative link explaining the association of this locus with PD. However, other transcript eQTLs and subsequent functional roles cannot be excluded. This highlights the importance of further investigations to understand the functional interactions between the coding genes, antisense, and non-coding RNA species considering the tissue and cell-type specificity to understand the underlying biological mechanisms in PD