3,475 research outputs found
Contrasting SYK-like Models
We contrast some aspects of various SYK-like models with large- melonic
behavior. First, we note that ungauged tensor models can exhibit symmetry
breaking, even though these are 0+1 dimensional theories. Related to this, we
show that when gauged, some of them admit no singlets, and are anomalous. The
uncolored Majorana tensor model with even is a simple case where gauge
singlets can exist in the spectrum. We outline a strategy for solving for the
singlet spectrum, taking advantage of the results in arXiv:1706.05364, and
reproduce the singlet states expected in . In the second part of the
paper, we contrast the random matrix aspects of some ungauged tensor models,
the original SYK model, and a model due to Gross and Rosenhaus. The latter,
even though disorder averaged, shows parallels with the Gurau-Witten model. In
particular, the two models fall into identical Andreev ensembles as a function
of . In an appendix, we contrast the (expected) spectra of AdS quantum
gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta
function.Comment: 45 pages, 17 figures; v2: minor improvements and rearrangements, refs
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Enhancement of field renormalization in scalar theories via functional renormalization group
The flow equations of the Functional Renormalization Group are applied to the
O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions,
d=4, to determine the effective potential and the renormalization function of
the field in the broken phase. In our numerical analysis, the infrared limit,
corresponding to the vanishing of the running momentum scale in the equations,
is approached to obtain the physical values of the parameters by extrapolation.
In the N=4 theory a non-perturbatively large value of the physical
renormalization of the longitudinal component of the field is observed. The
dependence of the field renormalization on the UV cut-off and on the bare
coupling is also investigated.Comment: 20 pages, 7 figures. To appear in Physical Review
Exact renormalization group equation in presence of rescaling anomaly II - The local potential approximation
Exact renormalization group techniques are applied to mass deformed N=4
supersymmetric Yang-Mills theory, viewed as a regularised N=2 model. The
solution of the flow equation, in the local potential approximation, reproduces
the one-loop (perturbatively exact) expression for the effective action of N=2
supersymmetric Yang-Mills theory, when the regularising mass, M, reaches the
value of the dynamical cutoff. One speculates about the way in which further
non-perturbative contributions (instanton effects) may be accounted for.Comment: 13 pages, no figures, uses JHEP3.cl
Identification and correction of systematic error in high-throughput sequence data
A feature common to all DNA sequencing technologies is the presence of base-call errors in the sequenced reads. The implications of such errors are application specific, ranging from minor informatics nuisances to major problems affecting biological inferences. Recently developed “next-gen” sequencing technologies have greatly reduced the cost of sequencing, but have been shown to be more error prone than previous technologies. Both position specific (depending on the location in the read) and sequence specific (depending on the sequence in the read) errors have been identified in Illumina and Life Technology sequencing platforms. We describe a new type of _systematic_ error that manifests as statistically unlikely accumulations of errors at specific genome (or transcriptome) locations. We characterize and describe systematic errors using overlapping paired reads form high-coverage data. We show that such errors occur in approximately 1 in 1000 base pairs, and that quality scores at systematic error sites do not account for the extent of errors. We identify motifs that are frequent at systematic error sites, and describe a classifier that distinguishes heterozygous sites from systematic error. Our classifier is designed to accommodate data from experiments in which the allele frequencies at heterozygous sites are not necessarily 0.5 (such as in the case of RNA-Seq). Systematic errors can easily be mistaken for heterozygous sites in individuals, or for SNPs in population analyses. Systematic errors are particularly problematic in low coverage experiments, or in estimates of allele-specific expression from RNA-Seq data. Our characterization of systematic error has allowed us to develop a program, called SysCall, for identifying and correcting such errors. We conclude that correction of systematic errors is important to consider in the design and interpretation of high-throughput sequencing experiments
Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method
According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87,
061107 (2005)], the triangular lattice of triangular air holes may allow to
achieve a complete photonic band gap in two-dimensional photonic crystal slabs.
In this work we present a systematic theoretical study of this photonic lattice
in a high-index membrane, and a comparison with the conventional triangular
lattice of circular holes, by means of the guided-mode expansion method whose
detailed formulation is described here. Photonic mode dispersion below and
above the light line, gap maps, and intrinsic diffraction losses of
quasi-guided modes are calculated for the periodic lattice as well as for line-
and point-defects defined therein. The main results are summarized as follows:
(i) the triangular lattice of triangular holes does indeed have a complete
photonic band gap for the fundamental guided mode, but the useful region is
generally limited by the presence of second-order waveguide modes; (ii) the
lattice may support the usual photonic band gap for even modes (quasi-TE
polarization) and several band gaps for odd modes (quasi-TM polarization),
which could be tuned in order to achieve doubly-resonant frequency conversion
between an even mode at the fundamental frequency and an odd mode at the
second-harmonic frequency; (iii) diffraction losses of quasi-guided modes in
the triangular lattices with circular and triangular holes, and in line-defect
waveguides or point-defect cavities based on these geometries, are comparable.
The results point to the interest of the triangular lattice of triangular holes
for nonlinear optics, and show the usefulness of the guided-mode expansion
method for calculating photonic band dispersion and diffraction losses,
especially for higher-lying photonic modes.Comment: 16 pages, 11 figure
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