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

Timing of retinal neuronal and axonal loss in MS: a longitudinal OCT study

The objective of the study was to investigate the timing of central nervous system tissue atrophy in MS by evaluating longitudinal retinal volume changes in a broadly representative cohort with disease duration across the entire arc of disease. In this longitudinal study, 135 patients with MS and 16 healthy reference subjects underwent spectral-domain optical coherence tomography (OCT) at baseline and 2 years later. Following OCT quality control, automated segmentation of the peripapillary retinal nerve fiber layer (pRNFL), macular ganglion cell–inner plexiform layer (mGCIPL) and macular inner nuclear layer (mINL) was performed. Generalized estimation equations were used to analyze longitudinal changes and associations with disease duration and clinical measures. Participants had a median disease duration at baseline of 16.4 years (range 0.1–45.4). Nearly half (44 %) of the MS patients had previously experienced MS-related optic neuritis (MSON) more than 6 months prior. The MS patients demonstrated a significant decrease over 2 years of the pRNFL (−1.1 µm, 95 % CI 1.4–0.7, p < 0.001) and mGCIPL (−1.1 µm, 95 % CI −1.4 to −0.8, p < 0.001). This thinning was most pronounced early in the course of disease. These findings were irrespective of previous episodes of MSON. No consistent pattern of change was observed for the mINL (−0.03 µm, 95 % CI −0.2 to 0.2, p = 0.795). This longitudinal study demonstrated that injury of the innermost retinal layers is found in MS and that this damage occurs most rapidly during the early stages of disease. The attenuation of atrophy with longer disease duration is suggestive of a plateau effect. These findings emphasize the importance of early intervention to prevent such injury

On the exponential transform of lemniscates

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.Comment: 19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Birkhauser Verla

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

Factor XII mutations, estrogen-dependent inherited angioedema, and related conditions

The clinical, biochemical and genetic features of the conditions known as estrogen-dependent inherited angioedema, estrogen-associated angioedema, hereditary angioedema with normal C-1 inhibitor, type III angioedema, or factor XII angioedema are reviewed. Discussion emphasizes pathogenesis, diagnosis, and management