Towards matrix model representation of HOMFLY polynomials

We investigate possibilities of generalizing the TBEM eigenvalue matrix model, which represents the non-normalized colored HOMFLY polynomials for torus knots as averages of the corresponding characters. We look for a model of the same type, which is a usual Chern-Simons mixture of the Gaussian potential, typical for Hermitean models, and the sine Vandermonde factors, typical for the unitary ones. We mostly concentrate on the family of twist knots, which contains a single torus knot, the trefoil. It turns out that for the trefoil the TBEM measure is provided by an action of Laplace exponential on the Jones polynomial. This procedure can be applied to arbitrary knots and provides a TBEM-like integral representation for the N=2 case. However, beyond the torus family, both the measure and its lifting to larger N contain non-trivial corrections in \hbar=\log q. A possibility could be to absorb these corrections into a deformation of the Laplace evolution by higher Casimir and/or cut-and-join operators, in the spirit of Hurwitz tau-function approach to knot theory, but this remains a subject for future investigation.Comment: 10 page

Emergent order in the spin-frustrated system DyxTb2-xTi2O7 studied by ac susceptibility measurements

We report the a.c. susceptibility study of Dy_xTb_{2-x}Ti_2O_7 with x in [0, 2]. In addition to the single-ion effect at Ts (single-ion effect peak temperature) corresponding to the Dy3+ spins as that in spin ice Dy_2Ti_2O_7 and a possible spin freezing peak at Tf (Tf < 3 K), a new peak associated with Tb^{3+} is observed in $\chi_{ac}(T)$ at nonzero magnetic field with a characteristic temperature T^* (Tf < T^* < Ts). T^* increases linearly with x in a wide composition range (0 < x < 1.5 at 5 kOe). Both application of a magnetic field and increasing doping with Dy3+ enhance T^*. The T^* peak is found to be thermally driven with an unusually large energy barrier as indicated from its frequency dependence. These effects are closely related to the crystal field levels, and the underlying mechanism remains to be understood.Comment: 7 pages, 5 figure

Small Fermi energy and phonon anharmonicity in MgB_2 and related compounds

The remarkable anharmonicity of the E_{2g} phonon in MgB_2 has been suggested in literature to play a primary role in its superconducting pairing. We investigate, by means of LDA calculations, the microscopic origin of such an anharmonicity in MgB_2, AlB_2, and in hole-doped graphite. We find that the anharmonic character of the E_{2g} phonon is essentially driven by the small Fermi energy of the sigma holes. We present a simple analytic model which allows us to understand in microscopic terms the role of the small Fermi energy and of the electronic structure. The relation between anharmonicity and nonadiabaticity is pointed out and discussed in relation to various materials.Comment: 5 pages, 2 figures replaced with final version, accepted on Physical Review

Optical Magnetometry

Some of the most sensitive methods of measuring magnetic fields utilize interactions of resonant light with atomic vapor. Recent developments in this vibrant field are improving magnetometers in many traditional areas such as measurement of geomagnetic anomalies and magnetic fields in space, and are opening the door to new ones, including, dynamical measurements of bio-magnetic fields, detection of nuclear magnetic resonance (NMR), magnetic-resonance imaging (MRI), inertial-rotation sensing, magnetic microscopy with cold atoms, and tests of fundamental symmetries of Nature.Comment: 11 pages; 4 figures; submitted to Nature Physic

Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure

The genomic landscape of cutaneous SCC reveals drivers and a novel azathioprine associated mutational signature

Cutaneous squamous cell carcinoma (cSCC) has a high tumour mutational burden (50 mutations per megabase DNA pair). Here, we combine whole-exome analyses from 40 primary cSCC tumours, comprising 20 well-differentiated and 20 moderately/poorly differentiated tumours, with accompanying clinical data from a longitudinal study of immunosuppressed and immunocompetent patients and integrate this analysis with independent gene expression studies. We identify commonly mutated genes, copy number changes and altered pathways and processes. Comparisons with tumour differentiation status suggest events which may drive disease progression. Mutational signature analysis reveals the presence of a novel signature (signature 32), whose incidence correlates with chronic exposure to the immunosuppressive drug azathioprine. Characterisation of a panel of 15 cSCC tumour-derived cell lines reveals that they accurately reflect the mutational signatures and genomic alterations of primary tumours and provide a valuable resource for the validation of tumour drivers and therapeutic targets

T-DNA insertion mutants reveal complex expression patterns of the aldehyde dehydrogenase 3H1 locus in Arabidopsis thaliana

The Arabidopsis thaliana aldehyde dehydrogenase 3H1 gene (ALDH3H1; AT1G44170) belongs to family 3 of the plant aldehyde dehydrogenase superfamily. The full-length transcript of the corresponding gene comprises an open reading frame of 1583 bp and encodes a protein of 484 amino acid residues. Gene expression studies have shown that this transcript accumulates mainly in the roots of 4-week-old plants following abscisic acid, dehydration, and NaCl treatments. The current study provided experimental data that the ALDH3H1 locus generates at least five alternative transcript variants in addition to the previously described ALDH3H1 mRNA. The alternative transcripts accumulated in wild-type plants at a low level but were upregulated in a mutant that carried a T-DNA insertion in the first exon of the gene. Expression of the transcript isoforms involved alternative gene splicing combined with an alternative promoter. The transcript isoforms were differentially expressed in the roots and shoots and showed developmental stage- and tissue-specific expression patterns. These data support the hypothesis that alternative isoforms produced by gene splicing or alternative promoters regulate the abundance of the constitutively spliced and functional variants

Observation of a J^PC = 1-+ exotic resonance in diffractive dissociation of 190 GeV/c pi- into pi- pi- pi+

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the pi- pi- pi+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV^2/c^2. The well-known resonances a1(1260), a2(1320), and pi2(1670) are clearly observed. In addition, the data show a significant natural parity exchange production of a resonance with spin-exotic quantum numbers J^PC = 1-+ at 1.66 GeV/c^2 decaying to rho pi. The resonant nature of this wave is evident from the mass-dependent phase differences to the J^PC = 2-+ and 1++ waves. From a mass-dependent fit a resonance mass of 1660 +- 10+0-64 MeV/c^2 and a width of 269+-21+42-64 MeV/c^2 is deduced.Comment: 7 page, 3 figures; version 2 gives some more details, data unchanged; version 3 updated authors, text shortened, data unchange

Carbon storage of headwater riparian zones in an agricultural landscape

<p>Abstract</p> <p>Background</p> <p>In agricultural regions, streamside forests have been reduced in age and extent, or removed entirely to maximize arable cropland. Restoring and reforesting such riparian zones to mature forest, particularly along headwater streams (which constitute 90% of stream network length) would both increase carbon storage and improve water quality. Age and management-related cover/condition classes of headwater stream networks can be used to rapidly inventory carbon storage and sequestration potential if carbon storage capacity of conditions classes and their relative distribution on the landscape are known.</p> <p>Results</p> <p>Based on the distribution of riparian zone cover/condition classes in sampled headwater reaches, current and potential carbon storage was extrapolated to the remainder of the North Carolina Coastal Plain stream network. Carbon stored in headwater riparian reaches is only about 40% of its potential capacity, based on 242 MgC/ha stored in sampled mature riparian forest (forest > 50 y old). The carbon deficit along 57,700 km headwater Coastal Plain streams is equivalent to about 25TgC in 30-m-wide riparian buffer zones and 50 TgC in 60-m-wide buffer zones.</p> <p>Conclusions</p> <p>Estimating carbon storage in recognizable age-and cover-related condition classes provides a rapid way to better inventory current carbon storage, estimate storage capacity, and calculate the potential for additional storage. In light of the particular importance of buffer zones in headwater reaches in agricultural landscapes in ameliorating nutrient and sediment input to streams, encouraging the restoration of riparian zones to mature forest along headwater reaches worldwide has the potential to not only improve water quality, but also simultaneously reduce atmospheric CO₂.</p